UNIVERSIDAD DE VIGO TESIS DOCTORAL

UNIVERSIDAD DE VIGO

TESIS DOCTORAL

Realizada en el Departamento de Química

Física Grupo de Química Cuántica

ESTUDIO QTAIM DE NITRILOS

Y

COMPUESTOS RELACIONADOS

José Luis López Fernández

Memoria para optar al grado de

Doctor por la Universidad de Vigo

Septiembre 2015

“Science may set limits to knowledge, but should not set limits to imagination”

Bertrand Russell

AGRADECIMIENTOS

Mi más sincero y profundo agradecimiento al Prof. Dr. Ricardo A.

Mosquera Castro, gracias a esfuerzo y dedicación fue posible terminar el

trabajo de esta tesis.

El Dr. Ricardo A. Mosquera me ha enseñado, corregido, orientado,

apoyado de manera que ha sobrepasado con mucho las expectativas que

uno desearía tener en un director de tesis.

Sin lugar a dudas una de las mejoras cosas que me ha deparado la vida

es haber conocido a Ricardo, mi primer contacto con él hace años tuvo

lugar cuando dirigió mi tesina de grado, con el tiempo lo más valioso que

he conseguido, no es el terminar este trabajo, sino tener un amigo de un

valor tanto profesional como personal inestimable. Mi agradecimiento

eterno para Ricardo.

Mi agradecimiento también al Departamento de Química-Física de la

Universidad de Vigo por poner a mi disposición los equipos informáticos

y programas de computación usados en la elaboración de la tesis.

DEDICATORIA

Quisiera dedicar esta tesis a todos aquellos que han dedicado parte del

tiempo de su vida a está fascinante parte del conocimiento humano

como es La Química Teórica, tanto profesional como si lo han hecho por

simple curiosidad o afición, creo que el tiempo es uno de los bienes más

preciados que tiene un ser humano, mi recuerdo para todos ellos.

Por supuesto también aquí quiero mencionar expresamente a mis

directores de tesis: Prof. Dr. Ricardo A. Mosquera y Prof. Dra. Aña María

Graña.

Y finalmente también va dedicada a aquellos que han “padecido” un

poco mi afición por la Química, mis hijos Elena y Luis Alberto.

TABLA DE CONTENIDOS

RESUMEN .............................................................................................. 1

1. INTRODUCCIÓN ............................................................................. 17

2. OBJETIVOS ..................................................................................... 25

3. DISCUSIÓN GENERAL ................................................................... 27

3.1 Methodology ............................................................................. 29

3.1.1 Density Functional Theory (DFT) ................................................... 29

3.1.2 An Overview on the Quantum Theory of Atoms in Molecules (QTAIM)... 39

3.1.3 Approximate Transferability........................................................... 43

3.1.4 On the limitations of the Resonance Model…………………………………52

3.2 Discusión general de resultados ....................................................... 59

4. TRABAJOS DE INVESTIGACION ................................................... 62

4.1 Aproximate Transferability in Alkanenitriles ......................................... 64

4.2 A Charge Denstiy Analysis on the Proximity Effect in Dicyanoalkanes ...... 74

4.3 Electron Density Analysis on the Protonation of Nitriles ......................... 82

4.4 Electron Density Analysis on the Alpha Acidity of Nitriles ....................... 88

4.5 QTAIM Study of Rearregement Reactions in Nitrogenated Compounds .. 100

5. CONCLUSIONES ........................................................................... 120

6. BIBLIOGRAFIA............................................................................... 126

Estudio QTAIM de nitrilos y compuestos relacionados

1

RESUMEN

Esta Tesis se origina dentro de una investigación más general sobre la

transferibilidad de grupos funcionales que en aquellos momentos

desarrollaba el Grupo de Química Cuántica de la Universidad de Vigo [1-

4]. A lo largo de su desarrollo los objetivos iniciales fueron modificados

para considerar también problemas de reactividad. En concreto se

examinaron las propiedades ácido-base de los nitrilos, considerando su

N-protonación y la abstracción de hidrógenos enlazados a la posición al

grupo nitrilo. Ambos estudios, que analizaban únicamente los estados

inicial y final de dichos procesos, se relacionaban con un nuevo objetivo

más general del grupo, el estudio de las limitaciones del modelo de

resonancia para describir la evolución electrónica en procesos químicos

simples [5-11]. Por último, recientemente se añadió un estudio sobre la

evolución de la densidad electrónica en algunas transposiciones que

tienen lugar con compuestos que guardan alguna relación con el grupo

nitrilo. De manera general, puede decirse que el presente trabajo se

centra en el estudio de las propiedades y comportamiento de nitrilos y

compuestos afines mediante el uso de la teoría cuántica de átomos en

moléculas (QTAIM) [12,13]. Sus objetivos concretos son: i) Definir grupos

atómicos aproximadamente transferibles en los alcanonitrilos; ii) Analizar

como la proximidad entre dos grupos CN afecta a la transferibilidad

atómica; iii) Obtener afinidades protónicas y acideces de diversos nitrilos,


2

relacionando sus valores con la estructura electrónica de los compuestos;

iv) Describir los efectos electrónicos que acompañan a los principales

procesos ácido-base que los nitrilos pueden experimentar; y v) Detallar

como evoluciona la densidad electrónica en etapas de procesos químicos

(transposiciones de Curtius, Beckmann y Hofmann) en que intervienen

compuestos nitrogenados estructuralmente semejantes a los nitrilos.

Formalmente, el trabajo se ha divido en seis secciones: Introducción,

Objetivos, Discusión General, Resultados y discusión (que contienen los

trabajos de investigación publicados o en proceso de publicación),

Conclusiones y Bibliografía.

En el primer capítulo se hace una breve descripción y encuadre del

trabajo dentro del marco de la teoría QTAIM, justificando el tipo de

estudio llevado a cabo y reseñando brevemente trabajos análogos que

fueron realizados en otras series de compuestos tales como aldehídos,

cetonas, éteres, etc. Dichos trabajos se utilizan como punto de

comparación con el de esta Tesis.

En el segundo capítulo se definen de manera explicita los objetivos

perseguidos. De manera genérica se alcanzarán a partir de analizar

propiedades atómicas y de enlace, definidas en el contexto de la QTAIM,

calculadas para nitrilos y compuestos afines.

El tercer capítulo combina la metodología empleada y una discusión

general de resultados, obligada por la normativa vigente en la

Universidad de Vigo en el caso de las Tesis presentadas como compendio


3

de trabajos de investigación. Para realizar este trabajo se han utilizado

varios tratamientos basados en la Mecánica Cuántica, tales como

cálculos Hartree-Fock (HF) y DFT/B3LYP (Density Functional Theory,

funcional B3LYP) y, principalmente, la teoría QTAIM (Quantum Theory of

atoms in molecules).

Aunque las funciones de onda contienen toda la información extraíble de

un sistema, su forma, en el caso molecular, suele ser demasiado

complicada para proporcionar de manera directa una imagen sencilla de

la molécula. Basta pensar que, incluso al nivel HF restringido (RHF) (sin

tener en cuenta la correlación electrónica), la parte electrónica de la

función de onda molecular obtenida con un método de combinación

lineal de orbitales atómicos (CLOA) o con su variante habitual, la

combinación de funciones base, es normalmente un determinante de

tantas funciones espín orbital como electrones. La función

polielectrónica resultante depende de las coordenadas de posición y

espín de todos los electrones y presenta numerosos parámetros. Resulta,

por tanto, fundamental, disponer de alguna magnitud o cantidad que

permita obtener información fácilmente visualizable de la función de

onda y refleje sus características fundamentales. Las funciones de

densidad son una vía tradicional para conseguir este objetivo. En este

trabajo, se utilizará la función densidad electrónica monodimensional e

independiente del espín, ρ(r). Esto es, la misma función del espacio

tridimensional que puede obtenerse por vía experimental a través de un


4

estudio de difracción de rayos X. En nuestro caso, sin embargo, dicha

función se obtiene por vía computacional integrando una función de

onda HF o a partir de los orbitales Kohn-Sham de un cálculo DFT.

Las diversas herramientas desarrolladas en el contexto de la QTAIM son

las que se usarán para analizar la función ρ(r) suministrada por los

cálculos HF o DFT. Por todo ello, en esta parte debe hacerse una

referencia a los métodos de obtención de la densidad electrónica y al

utilizado para su interpretación. Considerando que el método HF se

estudia suficientemente en los actuales programas de grado y postgrado,

sólo se presenta aquí una descripción general de la DFT (sección 3.1).

Respecto a la teoría QTAIM se ha optado por presentar únicamente una

breve introducción (sección 3.2), ya que existen excelentes monografías

[12-16] que recogen con detalle los extremos de esta teoría desarrollada

por Richard F. W. Bader [12-14] para analizar la densidad electrónica de

sistemas moleculares. Es importante, no obstante, recordar aquí que

esta teoría particiona el espacio físico real, a diferencia de otras

metodologías basadas en el espacio de configuración (espacio orbital) y

que trabaja sobre un observable físico, ρ(r), y no sobre entidades

matemáticas (orbitales moleculares) [17,18].

Otras dos secciones del tercer capítulo recogen aspectos generales de

dos temas fundamentales para esta Tesis y que son aplicaciones

habituales de la teoría QTAIM: transferibilidad aproximada (sección 3.3) y

revisión crítica de las predicciones del modelo de resonancia (sección


5

3.4). Debe señalarse que se ha demostrado que la transferibilidad

completa es un límite inalcanzable (como consecuencia de los teoremas

de Hohenberg y Kohn) [19,20], por lo que sólo es posible hablar de

transferibilidad aproximada. Por otro lado, las predicciones del modelo

de resonancia no son compatibles en numerosos casos con la evolución

de la densidad electrónica que muestran los análisis QTAIM.

En la cuarta sección se recopilan los artículos de investigación publicados

(los tres primeros [21-23]) o en fase de publicación (los dos últimos

[24,25]) que se han elaborado como consecuencia de este trabajo.

En un primer estudio se analizaron las propiedades atómicas y de enlace

de una serie de doce alcanonitrilos lineales en conformación

antiperiplanar [21]. El objetivo es analizar la transferabilidad de los

grupos CN, CH2 y CH3. La geometría de todos ellos fue optimizada con el

nivel de cálculo RHF/6-31G(d,p), obteniéndose posteriormente una

función de onda con una base que adicionaba funciones difusas sobre

todos los átomos: RHF/6-31++G(d,p). Se establece una clasificación para

los grupos anteriores en virtud de su transferabilidad aproximada. Debe

destacarse que el trabajo indica que no se observa transferabilidad de la

energía atómica, E(Ω). Por el contrario esta propiedad exhibe una

dependencia con el tamaño molecular. En el momento de la publicación

de este trabajo, este comportamiento había sido observado también en

otras series homólogas y se conocía como efecto Z [1-4,26,27]. No

obstante, en un estudio realizado paralelamente a esta Tesis [28],


6

nuestro grupo demostró que este problema tenía su origen en la forma

en que el programa AIMPAC calcula la energía atómica, aplicando la

relación virial, γ, sobre la integración atómica de la densidad de energía

cinética electrónica, K(r) [28,29]. Cuando se analiza la energía cinética

electrónica atómica, K(Ω), se observa, en cambio, una transferibilidad

semejante a la observada a partir de poblaciones electrónicas atómicas.

Como cabría esperar por los resultados ya conocidos de otras series de

compuestos el grupo metilo presenta un comportamiento específico

para moléculas pequeñas. Los grupos metileno se han clasificado de

acuerdo con su distancia al grupo CN. En este primer artículo también se

muestra que, tanto energías electrónicas moleculares calculadas, como

calores de formación experimentales, muestran un excelente ajuste a un

modelo de contribuciones de grupo en el que sólo se consideran los

grupos ciano (CN), CH3 y el número de grupos metileno. Este intrigante

comportamiento, que fue denominado “transferibilidad compensatoria”

por Bader [30], tiene un origen que puede remontarse a los estudios

sobre alcanos llevados a cabo por el propio Bader [31,32] y fue ya

también observado en otras series de moléculas funcionalizadas por

nuestro grupo [2,4,26].

En un segundo artículo se estudia el resultado de introducir en las

moléculas grupos funcionales adicionales al grupo CN original [22]. El

objetivo es estudiar las influencias mutuas entre grupos funcionales

(denominadas efecto de proximidad por Kehiaian [33]). Se realiza así un


7

estudio QTAIM de una serie de dicianoalcanos. En este caso se estudian

las propiedades atómicas y de enlace de 21 dicianoalcanos. En este

artículo se ha calculado también la entropía normalizada de Shannon

para la distribución electrónica, Sh(Ω) [34-36]. Las densidades

electrónicas analizadas fueron obtenidas con el nivel RHF/6-31++G(d,p)

aplicado sobre geometrías totalmente optimizadas con el nivel RHF/6-

31G(d,p). De nuevo se establece una clasificación de los grupos CN y CH2

al tiempo que se hace una comparativa con los resultados de trabajos

análogos. Se encuentra que los grupos ciano son estadísticamente

equivalentes cuando entre ellos hay una separación de al menos 14

grupos metileno. Los efectos del grupo CN sobre los grupos metileno son

casi independientes de la posición, en este aspecto se ha visto que los

hidrógenos son más sensibles que los átomos de carbono. También se ha

encontrado un comportamiento específico en un grupo metileno cuando

su número en la molécula es menor de 19. Debe señalarse, que a

diferencia de lo indicado en el trabajo anterior, en este artículo ya se

utiliza la propiedad K(Ω), en lugar de E(Ω), a la hora de estudiar

transferibilidades aproximadas. Asimismo, en el estudio se tuvieron en

cuenta dos tipos de confórmeros: aquellos con conformación

completamente antiperiplanar, t, y los que presentan un ángulo diedro

central de aproximadamente 60:, g.

Un tercer estudio se centra en la reactividad de los nitrilos frente a la

protonación [23]. A través de un análisis QTAIM se testearon las


8

predicciones del modelo de resonancia (RM) para una serie de 15 nitrilos.

En este caso se incluyeron también compuestos con conjugación π. Las

densidades electrónicas fueron obtenidas con dos niveles de cálculo

distintos: B3LYP/6-31++G** y HF/6-31**G**, sin que ello diese lugar a

encontrar diferencias significativas. Se observa que las afinidades

protónicas (PA) calculadas concuerdan en todos los casos con buena

precisión con las experimentales (salvo un caso la diferencia es siempre

inferior a 10 kJ mol-1). Como conclusión principal debe destacarse que

tras la protonación del cianocompuesto, el protón mantiene una elevada

carga positiva. De hecho, se concluye que las estructuras de Lewis del

tipo +H-N≡C-R son más adecuadas que las del tipo H-N≡C+-R y H-N+≡C-R

para describir la distribución electrónica de las especies protonadas.

Además, el estudio de las propiedades de enlace pone de manifiesto que

en el enlace N≡C aumenta la densidad electrónica π y se reduce la

densidad electrónica ς como consecuencia de la protonación. Asimismo,

durante la protonación de un cianocompuesto la densidad electrónica

molecular evoluciona de forma análoga a la observada en las O-

protonaciones y N-protonaciones de otros compuestos [6,37-40],

observándose transferencias de densidad electrónica entre átomos

vecinos. Así, comparando la evolución de la densidad electrónica en las

protonaciones de HCN y de sus derivados alquílicos, se observa que la

población electrónica del átomo de carbono del grupo ciano, N(C), es

siginificativamente mayor en los segundos, debido a la transferencia


9

desde otros átomos, particularmente desde los hidrógenos del grupo

alquilo que, una vez más, actúan como fuentes (en este caso) o

sumideros de densidad electrónica en el proceso químico tal como había

sido propuesto inicialmente por Stutchbury y Cooper [41]. También

resulta significativo que cuando el cianocompuesto contiene un sistema

con conjugación π, la protonación da lugar a una importante reducción

de la densidad electrónica π de dicho sistema, mientras que la densidad

electrónica ς se mantiene prácticamente inalterada. Por último, se

destaca que los procesos de protonación dan lugar a variaciones de

poblaciones electrónicas atómicas y energías atómicas que guardan una

buena correlación.

En el cuarto artículo se analiza la acidez de la posición al grupo ciano

[24], propiedad frecuentemente utilizada en síntesis orgánica [42]. Para

ello se considera una serie de 24 nitrilos sustituidos CNCHR1R2 con

diferentes grupos dadores y receptores de densidad electrónica. Se

comparan las densidades para cada compuesto neutro con la del

obtenido por su desprotonación en la posición que da lugar al anión

[CNCR1R2]-. Todas las densidades electrónicas se obtienen con

optimizaciones geométricas completas al nivel B3LYP/6-311++G(2d,2p)

6d. Se analiza: i) la estabilización del anión -desprotonado frente a la

desprotonación en otras posiciones; ii) El efecto de la sustitución sobre la

distribución electrónica y su relación con la diferencia de energía entre

las especies neutra y protonada y iii) la fiabilidad de las predicciones del


10

modelo de resonancia, tanto desde un punto de vista energético como

en términos de cargas atómicas.

En primer lugar es notoria la prioridad energética de la desprotonación

sobre las restantes. Esto se demuestra estudiando las diversas

desprotonaciones de dos cianuros de alquilo de cadena larga

(CN(CH2)9CH3 y CN(CH2)10CH3). La diferencia observada supera en todos

los casos los 100 kJ mol-1.

En principio, la presencia de sustituyentes que retiran densidad

electrónica reduce notablemente la energía de desprotonación. Así en la

serie CNCH3, (CN)2CH2, (CN)3CH, dichas energías presentan,

respectivamente, valores de 1549, 1376 y 1229 kJ mol-1. Asimismo, la

combinación del grupo ciano con otros aceptores de densidad

electrónica por efecto mesómero (-NO2, -COOCH3) da lugar a notables

reducciones de la energía implicada en el proceso (1402 y 1334 kJ mol-1,

respectivamente). Sin embargo, el efecto contrario no es tan claro

cuando se incluye un dador de densidad electrónica por resonancia (-OH,

-NH2), que no incrementan desprotE más allá de 3 kJ mol-1 con respecto al

caso del CNCH3. la longitud y topología de la cadena alquílica unida al

grupo -CH2 tampoco dan lugar a cambios significativos. Así, los valores

de desprotE no difieren en más de 10 kJ mol-1 de los hallados para CNCH3

cuando el grupo CH3 se reemplaza por etilo, isopropilo, alquilos de

cadena lineal larga o, incluso, un grupo CH2=CH-. Un poco más intenso es

el efecto observado con derivados fluorados (1527 y 1503 kJ mol-1 para


11

FCH2CN y F2CHCN, respectivamente). En cambio, la incorporación de

grupos hidrocarbonados que dan lugar a conjugación π con el grupo CN

(CH2=CH-CH2- y C6H5-CH2-) vuelve a provocar notables descensos de

desprotE (1458 y 1444 kJ mol-1, respectivamente). También, debe

destacarse que los grupos bencilo que incluyen sustituyentes receptores

por resonancia (NO2) reducen más desprotE. Por el contrario, si el

sustituyente incluído en el grupo bencilo es dador por resonancia (NH2),

la reducción observada para desprotE es menor. Incluso, se observan los

efectos debidos a la posición del sustituyente en el grupo bencilo que

predice el modelo de resonancia.

Por último, y en contraste con lo encontrado en los estudios de

protonación [23], se observa que, en general el modelo de resonancia

proporciona predicciones compatibles con las variaciones de población

electrónica atómica observadas en nuestro estudio QTAIM, desprotN(Ω).

Así, los incrementos de población electrónica observados en la especie

aniónica se reparten con mayor intensidad entre aquellos átomos sobre

los que el modelo de resonancia deslocaliza la carga negativa.

En el quinto artículo de esta Tesis se estudia la evolución de la densidad

electrónica en varios procesos de transposición que tienen lugar en

compuestos nitrogenados [25]. En primer lugar se considera la migración

de un átomo de hidrógeno para formar un isocianato con liberación de

N2 a partir de una acilazida (transposición de Curtius [43]). Además se

analizan dos migraciones de un grupo metilo: i) la formación de un catión


12

nitrilio (R-C+=N-R ↔ R-CN+-R’) a partir de la protonación de una oxima

en la etapa inicial de la transposición de Beckmann [44]; y ii) la evolución

de un anión haloamida hasta el correspondiente isocianato (etapa de la

transposición de Hofmann [45]). El estudio utiliza densidades

electrónicas B3LYP/6-311++G(d,p). En los tres casos se llevaron a cabo

cálculos IRC (intrinsic reaction coordinate), así como optimizaciones de

reactivos y productos con el mismo nivel de cálculo.

El estudio de la transposición de Curtius confirma el carácter concertado

establecido en trabajos recientes para el mecanismo de este proceso [46-

49]. En el estado de transición el átomo de hidrógeno (átomo migrante)

está simultáneamente unido a los átomos de C (enlace C-H en el

reactivo) y N (enlace N-H en el producto), según indica la existencia de

dos puntos críticos de enlace. Si bien, la distancia de enlace C-H es más

próxima en el estado de transición a la del reactivo que la del enlace C-N

a la que muestra en el producto. En el estado de transición la molécula

de N2 está prácticamente formada desde un punto de vista geométrico.

Respecto a las poblaciones electrónicas atómicas, llama la atención la

carga inicialmente negativa del átomo de nitrógeno central en la unidad

N-NN, que de acuerdo con la estructura de Lewis habitualmente

empleada para describir a la azida debería presentar carga positiva. A lo

largo de la reacción la carga del átomo de oxígeno se mantiene

prácticamente constante, mientras se observa una transmisión de


13

densidad electrónica desde H y C al átomo de N que terminará formando

parte del isocianato.

Nuestro estudio indica que la etapa seleccionada de la transposición de

Hofmann es un proceso elemental. El punto crítico del enlace C-N surge

al desaparecer el correspondiente al enlace C-C que se rompe en el

proceso. Esto no tiene lugar hasta después de la formación del estado de

transición y en todo ese intervalo de la reacción el enlace haloamida

continúa establecido. Se observa una reducción constante de la

población electrónica del C sp2 (coherente con la evolución desde un

enlace C-C a un C=N) y del C sp3 que, de manera semejante, reemplaza

un enlace C-C por un C-N. Es posible plantear que en el proceso

concertado tienen lugar dos transferencias electrónicas principales: de C

sp2 a Br y de C sp3 a N.

La etapa seleccionada de la reacción de Beckmann es también elemental.

El reactivo presenta una estructura compatible con un enlace C=N

mientras que la estructura del producto es compatible con la existencia

de un enlace C≡N. Sin embargo, el cálculo de las cargas atómicas sobre el

grupo C≡N del reactivo presenta valores que no coinciden con la forma

resonante que presenta este enlace triple y presentan mayor

coincidencia con una forma resonante similar a la encontrada para

cianocompuestos protonados : H+-N≡C-R. El enlace entre el grupo metilo

que migra y el nitrógeno aparece después del estado de transición

cuando se rompe su enlace al C sp2 y se rompe el enlace N-O. Al principio


14

de la reacción, antes del estado de transición, se produce transferencia

de carga del C sp2 al nitrógeno, ya que la carga del C que migra apenas

varía y después del estado de transición, la carga se transfieres desde

estos dos carbonos al nitrógeno.

Finalmente figuran las conclusiones extraídas del trabajo realizado, así

como las referencias bibliográficas. Como principales conclusiones

resaltamos las siguientes.

En los cianoalcanos lineales se han encontrado valores transferibles para

todas las propiedades atómicas y de enlace calculadas para el grupo CN.

Se exceptúa la energía atómica, que muestra una dependencia del

tamaño molecular, cuantificado por la suma de los números atómicos.

Este efecto, encontrado en otras series homólogas, es un artificio debido

a los diferentes valores del cociente virial. Por el contrario, la energía

cinética electrónica atómica si presenta valores transferibles. Los valores

de estas propiedades permiten considerar como cuasi-transferibles y

específicos de la serie de cianoalcanos a: i) Los átomos C y N del grupo

CN; ii) CH2 en α respecto al grupo CN; y iii) CH2 en β respecto al grupo CN.

El grupo CH3 terminal, el CH2 previo al grupo metilo terminal y el resto de

los grupos metileno de la cadena presentan un comportamiento similar

al de los n-alcanos. Además, los siguientes átomos presentan un

comportamiento específico: C en posición α en los nitrilos de metilo y

etilo; C en posición β en los nitrilos de etilo y propilo; así como C y N del

grupo CN en los cianuros de hidrógeno y metilo.


15

En los dicianoalcanos se observa una mayor sensibilidad a la

transferencia en las propiedades atómicas que en las propiedades de

enlace. Utilizando parámetros estadísticos se han caracterizado 12

grupos metilenos diferentes. La influencia mutua entre grupos CN (efecto

de proximidad) puede considerarse despreciable cuando estos grupos

están separados por más de 14 grupos metileno.

En los nitrilos protonados, el protón presenta una carga positiva grande

lo que indica que está más acorde con la estructura de Lewis H+N≡CR

que con las estructuras: HN+≡CR, HNC+R. La densidad

electrónica de los nitrilos se modifica con la protonación de manera

análoga a la observado para las protonaciones de O y N de otras series de

compuestos orgánicos.

La desprotonación de un metileno al grupo CN está significativamente

favorecida cuando el grupo CN se encuentra en conjugación π con grupos

de carácter atrayente de densidad electrónica por efecto mesómero. El

efecto de los grupos dadores de densidad electrónica, incluso por efecto

mesómero, no altera significativamente la energía del proceso. La

variación de las poblaciones atómicas en este proceso no presenta

contradicciones con el modelo de resonancia semejantes a las

observadas en proceceos de protonación o adición de hidruros.

La evolución de la densidad electrónica en etapas seleccionadas de las

transposiciones de Curtius, Beckmann y Hofmann indica un carácter

concertado para los tres procesos. Los nuevos enlaces formados durante


16

la reacción solo aparecen cuando los originales se rompen, después del

estado de transición. La transferencia de carga durante estas reacciones

tiene lugar implicando esencialmente al átomo que migra y a los átomos

unidos a él al principio y al final de la reacción.

.


17

1.- INTRODUCCIÓN

El grupo CN está considerado como uno de los principales grupos

funcionales. El uso de nitrilos en química orgánica preparativa comenzó a

adquirir importancia en la segunda mitad del siglo XIX. Sus características

propiedades reactivas lo convirtieron en un compuesto de uso común en

síntesis orgánica e inorgánica. En concordancia con su utilidad, su

estructura geométrica y electrónica ha sido objeto de una enorme

cantidad de estudios teóricos y experimentales [50]. Muchos de estos

estudios se centraron en la estructura del primer miembro de la serie de

los nitrilos, HCN, que se ha convertido en uno de los sistemas de

referencia más utilizados para testear métodos teóricos y niveles de

cálculo [51,52]. Los nitrilos, especialmente HCN, son también

importantes moléculas interestelares que han sido detectadas por

radioastronomía en varias fuentes [53].

En el estudio que se presenta en esta Tesis Doctoral juegan un papel

fundamental conceptos químicos como: similaridad, grupo funcional,

transferabilidad, efecto de proximidad, modelo de resonancia, etc. Los

conceptos de similaridad, grupo funcional y transferabilidad atómica han

jugado un papel muy importante en el desarrollo de la Química [54]. Sin

embargo, debe resaltarse que, normalmente, estos conceptos, han sido

empleados de manera intuitiva, sin tener en cuenta definiciones precisas

ni ningún tipo de cuantificación. Aceptando que las propiedades de la


18

materia son una manifestación de su estructura interna, la similaridad

entre substancias debe originarse en distribuciones de carga similares. En

1980 Carbó et al. [55] propusieron el primer índice de similaridad

mecano cuántico basado en las distribuciones de densidad electrónica de

las moléculas. Este índice marcó un punto de arranque para muchos

otros que han surgido posteriormente con objeto de abordar el

problema de evaluar la similaridad entre moléculas, entre otros

relacionados, cabe citar los índices de Cioslowski [56,57].

La densidad electrónica, ya sea obtenida a partir de cálculos

computacionales, como se hace en este trabajo, o bien

experimentalmente por métodos como la difracción de rayos X, puede

someterse a un análisis topológico. Aunque para esta tarea existen varios

métodos, entre ellos ha adquirido un notable grado de aceptación la

teoría cuántica de átomos en moléculas (QTAIM) desarrollada por Bader

[12,13]. Este será el método que utilizaremos fundamentalmente en

nuestro trabajo, aunque también se ha considerado el estudio topológico

de distintos campos escalares relacionados con ρ, como es el caso de su

laplaciana.

La introducción de la QTAIM hizo posible la partición de una molécula

de manera precisa y rigurosa (sin utilizar hipótesis ajenas a los principios

fundamentales) [58,59], en subsistemas discretos que verifican los

teoremas de la Mecánica Cuántica. Se puede demostrar de manera

precisa que esta división se realiza mediante superficies de flujo cero

para el gradiente de la densidad electrónica,ρ(r) [60-62]. Estas


19

superficies dividen el espacio en regiones, Ω, que se identifican con los

átomos de la molécula. Las propiedades atómicas se obtienen, entonces,

por integración de la correspondiente densidad de la propiedad sobre

esa región.

La teoría QTAIM ofrece la herramienta teórica para definir un grupo

funcional como un átomo (o grupo de átomos) que en una serie de

moléculas mantiene una similitud importante [61]. La similaridad de los

átomos a lo largo de una serie puede ser cuantificada por medio de un

índice de similaridad, como los introducidos por Cioslowski et al. [56,57]

o bien estimada comparando los valores de las propiedades atómicas en

varias moléculas [1-4]. Así, QTAIM proporciona una vía para establecer el

concepto de grupo funcional de manera cuantitativa. Se ha demostrado

que la transferabilidad perfecta de las propiedades es un límite

inalcanzable [19,20]. Por ello, se utiliza el término “transferabilidad

aproximada”. Este se aplica cuando las variaciones observadas en una

serie de moléculas son menores que los errores experimentales o se

aproximan a la precisión atribuida a los métodos numéricos.

La transferabilidad de átomos y grupos de átomos presenta una

aplicación práctica ampliamente utilizada en Química: predecir las

propiedades de una molécula a partir de las propiedades de sus

fragmentos constituyentes, esto es debido a la ligera variación que

presentan muchas propiedades atómicas a lo largo de series homólogas

de moléculas.


20

Nosotros estamos interesados en el estudio de las propiedades de

grupos funcionales obtenidos por combinación de los átomos de la teoría

QTAIM. Especialmente en comparar sus propiedades con objeto de

establecer límites para entornos moleculares en los que una propiedad o

grupo funcional pueda ser considerado aproximadamente transferible.

Estudios realizados en este departamento, de aplicación de la teoría

QTAIM, han permitido hacer una clasificación de los átomos de aldehídos

y cetonas [1,2], éteres [3,4] y otros compuestos [26,27] en grupos casi

transferibles. Para lograr estos resultados, se hizo uso de relaciones

empíricas encontradas y que no habían sido publicadas hasta ese

momento, tales como la relación entre varias propiedades atómicas y el

nivel de precisión con el que se determinan las superficies de flujo cero

[1]. Cabe añadir, que, pese a la presencia de diferentes grupos metileno

cuasi-transferibles, aldehídos, cetonas [2] y éteres [4] presentan un buen

ajuste lineal para la energía total HF y para el calor de formación

experimental con el número de grupos metileno presentes en la

molécula, de manera que para estas magnitudes la reproducción de

resultados para las moléculas de la serie nunca presentan discrepancias

en E mayores que 2.5 kJ mol-1 en éteres y 1.5 kJ mol-1 en aldehídos y

cetonas.

El término “efecto proximidad” fue acuñado hace más de 30 años [33] y

está relacionado con el desarrollo de modelos moleculares para

disoluciones de no electrolitos [63-64]. Estos modelos particionan una

molécula en bloques (“building blocks”) que se supone que son


21

independientes, transferibles y que están caracterizados por un conjunto

de parámetros empleados para calcular diversas propiedades de mezclas

de no electrolitos. El efecto de proximidad hace referencia a una de las

principales deficiencias de los modelos de contribuciones de grupos: la

interacción intramolecular entre dos o más grupos funcionales. Esta

afecta a sus propiedades así como a las de los grupos situados en su

entorno invalidando así la tranferabilidad [33]. Estas variaciones que

sufren las propiedades de los átomos debido a la presencia de otro grupo

funcional han sido usadas repetidamente en discusiones cualitativas

sobre el comportamiento de mezclas de compuestos polifuncionales

[65,66]. Se han propuesto varias soluciones para tratar este problema

desde variaciones empíricas de los parámetros de grupo dependiendo

de primeros y segundos vecinos [33] hasta correcciones cuantitativas

basadas en los análisis de población de Mulliken con la finalidad de

adaptar grupos definidos para compuestos monofuncionales a moléculas

polifuncionales [63]. La adecuación de todos estos tratamientos está

relacionada con la siguiente pregunta: ¿Son equivalentes (en una buena

aproximación) los cambios sufridos por la distribución electrónica de un

átomo en una molécula a la suma de los efectos producidos por estos

grupos funcionales en compuestos monofuncionales? o, por el contrario:

¿el efecto de proximidad involucra efectos cooperativos importantes

entre grupos funcionales?

La aplicación de QTAIM a las densidades electrónicas HF/6-31++G**

muestra que los átomos de oxígeno de las moléculas RO-(CH2)-OR’ son


22

significativamente diferentes de los correspondientes a los monoéteres

cuando n<4 [67]. Esto es, se confirma la existencia de un efecto de

proximidad cuando los oxígenos están separados por menos de cinco

enlaces. En esta tesis se estudia el efecto proximidad en α,ω-

dicianoalcanos usando un particionamiento QTAIM. Estos compuestos

han sido empleados para formar complejos con enlaces de hidrógeno y

compuestos de inclusión con urea [68], de interés en Química

Supramolecular [69]. Concretamente se estudia el efecto proximidad en

los grupos –CN y –CH2- usando criterios estadísticos para establecer los

límites de transferabilidad. Estos criterios se basan en las máximas

desviaciones presentadas por las propiedades de grupos que son

claramente transferibles en moléculas grandes para las que las

propiedades atómicas y de enlace son equivalentes sin lugar a duda. Este

procedimiento da lugar a un mayor número de grupos específicos que los

obtenidos en el trabajo sobre cianoalcanos lineales. También se estudia

en esta tesis si el efecto proximidad está compuesto por contribuciones

aditivas de los grupos funcionales aislados.

Generalmente se ha aceptado la aplicación del modelo de resonancia

(RM) para explicar la estructura y reactividad de compuestos orgánicos

[70,71] siendo una herramienta muy útil en Química. No obstante, el

análisis topológico de las densidades electrónicas realizados con la teoría

QTAIM para diversos procesos ha mostrado una evolución de la densidad

electrónica que no concuerda con las predicciones del modelo RM. Estos

desacuerdos aparecen incluso para procesos tan simples como


23

rotaciones internas [72,73], protonaciones [6,8,37-40] o adiciones de

hidruro [10]. Asimismo los resultados QTAIM son inconsistentes con las

estructuras de Lewis tradicionalmente aceptadas para algunos

compuestos cargados, tales como sales de diazonio [74] o éteres

protonados [37,38]. La publicación del primer estudio sobre los

desacuerdos entre RM y QTAIM fue seguida por una controversia acerca

de la adecuadabilidad de QTAIM para este tipo de estudios [75-77].

Actualmente la controversia parece que se ha inclinado en favor de la

aplicabilidad de QTAIM. Además, muchas de las conclusiones cualitativas

obtenidas a partir de estudios QTAIM sobre protonación y adiciones de

hidruro han sido confirmadas por estudios que emplean otros métodos

de analísis de las densidades electrónicas [8,10] tales como el

particionamiento de Hirshfeld [78,79].

Las estructuras de Lewis H-N=C+-R se han usado tradicionalmente para

describir los nitrilos protonados en varios mecanismos de reacción. Estas

estructuras son, en el marco del modelo RM, el resultado de tranformar

un par electrónico π del triple enlace N≡C en un enlace N-H.

Alternativamente, el proceso de protonación puede ser entendido como

la formación de un enlace dativo entre N y el protón usando un par

solitario (par no enlazante) del N, proceso representado por la fórmula

H+-X, que esta acompañado por una redistribución electrónica que afecta

a toda la molécula. Los hidrógenos actúan como una fuente muy efectiva

de densidad electrónica en está redistribución, tal y como confirman los

estudios sobre la basicidad de NH3 y una serie de metilaminas realizados


24

por Stuchbury y Cooper [41]. En esta Tesis se ha llevado a cabo un

estudio QTAIM sobre la protonación de varios ciano compuestos en fase

gas que permite analizar esta cuestión. También permite estudiar si el

triple enlace modifica las tendencias que se han observado hasta este

momento en otros compuestos. Las moléculas estudiadas en este trabajo

incluyen ciano alcanos lineales y ramificados así como compuestos en los

que la función ciano está conjugada con sistemas π deslocalizados, por lo

tanto ha sido posibles establecer tendencias según el tamaño de las

cadenas alquílicas lineales, el cambio conformacional, cadenas alquílicas

ramificadas, electronegatividad de sustituyentes y deslocalización π.

Además, la reacción de protonación se puede tomar como modelo de

estudio para analizar las tendencias que muestran ciertos compuestos en

su reactividad con sistemas electrofílicos. También la protonación a

menudo resulta ser un primer paso en muchos mecanismos de reacción,

por estos motivos se han calculado las afinidades protónicas de 15

nitrilos con objeto de estudiar la evolución de la densidad electrónica

durante la misma. La evolución de la densidad electrónica también ha

servido para testear el modelo de resonancia (RM), como ha sucedido en

otros estudios anteriores [5-11,37-40]. Las tendencias mostradas por el

proceso de protonación no son compatibles con las predichas por el

modelo de resonancia para procesos de protonación en fase gas.


25

2.- OBJETIVOS

De manera general esta tesis aborda analizar las propiedades

electrónicas de los nitrilos y de compuestos directamente

relacionados con ellos, sea por motivos de reactividad o de semejanza

estructural. En concreto se persiguen los siguientes objetivos:

1. Determinar en qué condiciones y de qué manera se pueden

considerar grupos aproximadamente transferibles en la serie de

nitrilos de alquilo. En este análisis se considera tanto el grupo

nitrilo (-CN) como los grupos metilo y metileno del resto alquílico.

2. Analizar como el efecto de proximidad entre grupos nitrilos puede

modificar las reglas de transferibilidad aproximada que se

obtengan como respuesta al objetivo anterior. Es decir, estudiar la

influencia mutua entre dos grupos nitrilo separados por un resto

alquílico, así como el efecto sufrido por los grupos metileno

intermedios, considerando la serie homóloga de los

dicianoalcanos, CN(CH2)nCN.

3. Obtener computacionalmente afinidades protónicas y acideces de

diversos nitrilos que presenten diferencias estructurales

significativas.


26

4. Describir los efectos electrónicos que acompañan a los principales

procesos ácido-base que experimentan los nitrilos: a) protonación

y b) abstracción de hidrógenos en posiciones α. La descripción

obtenida se comparará con la prevista según el modelo de

resonancia. Esta comparación permitirá evaluar la viabilidad del

modelo de resonancia para describir estos procesos.

5. Describir como evoluciona la densidad electrónica en ciertos

procesos que involucran a compuestos nitrogenados que guardan

cierta semejanza estructural con los nitrilos. Concretamente: a) la

formación de un isocianato y liberación de nitrógeno a partir de

una acilazida en la transposición de Curtius; b) la etapa inicial de la

transposición de Beckmann, que proporciona un catión nitrilio (al

que se asignan formas resonante R-C+=N-R y R-CN+-R’) a partir de

la protonación de una oxima; y c) la etapa de la transposición de

Hofmann que considera la evolución desde un anión haloamida

hasta el correspondiente isocianato.


27

3. DISCUSIÓN GENERAL


28


29

"Las teorías son redes: solo quién lance cogerá". Novalis (citado por Kart R. Popper en

la Lógica de la investigación científica)

3.1. METHODOLOGY

This chapter overviews the two methods which were most extensively

used throughout this Thesis: Density Functional Theory (DFT) and the

Quantum Theory of Atoms in Molecules (QTAIM). The first one has been

our usual tool to obtain electron densities, which were subsequentely

analyzed by means of the second one in order to get insight about the

chemical problems here addressed (presented in chapter 2 and discussed

in section 3.2). We have also included two sections devoted to a couple

of important issues we are directly involved in this Thesis: approximate

transferability and the limitations of the resonance model. As a lot of

work has been done previously on both we believe it is worth to make a

short review and introduce some general considerations on them before

presenting the results here obtained.

3.1.1. DENSITY FUNCTIONAL THEORY (DFT)

In computational chemistry, density functional theory (DFT) usually

stands for the Kohn–Sham implementation. Certainly, the initial

approaches to DFT can be traced back to the statistical method,

independently proposed by Thomas [80] and Fermi [81]. In this method,

the electron density of polyelectronic atoms is treated locally as a Fermi


30

gas in which the free-electron relations apply. Nevertheless, it is the

Kohn–Sham implementation which has gained ground, mainly due to its

similarity with the self-consistentfield Hartree–Fock method.

The Kohn–Sham formulation of DFT relies on the fact that the electron

density of the ground state of a system, can be computed as the density

of a system of independent particles, moving in an effective one-particle

potential, whose precise formal construction forms part of the method.

Once this effective potential has been determined, the Kohn–Sham

method solves self consistently the nonlinear Kohn–Sham equations

which contain an unknown exchange-correlation functional [82-84]. The

exchange-correlation functional contains the description of the electron–

electron interactions within the system. The theoretical foundation for

the Kohn–Sham method is the Hohenberg–Kohn theorems [85].

The first Hohenberg-Kohn theorem, as published in 1964, states that

there is a unique relation of the external potential Vext(r) (arising from the

positive charges of the nuclei) within an N electron system and its

(ground state) electron density ρ(r). Since the complete ground state

energy E0 is a unique functional of the electron density distribution ρ(r),

so must be its individual parts 1.

rVrVrTrE ext

int 1

In this expression we find a system-dependent part, Vext[ρ(r)], which

changes from one system to another. In contrast, two parts are universal,

in the sense that the form of the functional is independent of the actual

system determined by N, RA and ZA.


31

The system independent parts define the Hohenberg-Kohn functional 2.

rVrTrFHK

int 2

The second Hohenberg-Kohn theorem is nothing else than the variational

principle formulated for densities. Given any electron density distribution

ρ*(r) associated to an N electron system with external potential Vext, one

can state 3, with the equal sign only valid if ρ*(r) = ρ(r).

rVrVrTrEE ext

**** int0 3

Up till now, both the exact ground state density, ρ*(r), as well as the

Hohenberg-Kohn functional, FHK, are still unknown, so one cannot make

use of the Hohenberg theorems to calculate the molecular properties.

In the FHK both known and unknown parts can be identified 4 with

potential energy term, Vee, giving by 5, where J(ρ) is the classical

interaction of two charge densities and ENCL(ρ) contains all non-classical

parts. Thus, the complete energy functional can be written 6, where the

two first terms are known and the latter are unkonwn.

rVrTrF eeHK

4

rErdrdrr

rrrErJrV NCLNCLee

21

21

21

2

1

5

rErTrVrJrE NCLext

6

The basic problem is the unknown functional for the kinetic energy. A

solution to this problem was given by Kohn and Sham in the paper


32

published in 1965 [82], where they suggested to formaly split this

functional into two parts 7.

rTrTrT cS

7

where the first part Ts[ρ], the kinetic energy of the non interacting

electrons, will be expressed in a one particle approach similar to Hartree-

Fock, thus being well known, and the second, the correction to the

kinetic energy deriving from the interacting nature of the electrons (still

unknown part) contains the difference between the real functional T[ρ]

and the one particle term Ts[ρ], as well as the other remaining parts of

the total energy functional, which are still unknown, in a approximative

way. Thus one can write 9.

rErTrTrVrJrE NCLCSext

8

rErTrVrJrE XCSext

9

The so-called exchange-correlation functional EXC[ρ] (summation of

TS[ρ(r)] and ENCL[ρ(r)]) remains unknown and the rest are well defined

terms.

No reference is made in the proof to the Hartree–Fock level of

approximation. That is, the approximations made in DFT enter at the

level of the Hamiltonian, when an approximate form for the functional is

chosen. Such a Halmitonian can be expressed as a sum of one-electron

operators, has eigenfunctions that are Slater determinants of the

individual one-electron eigenfunctions, and has eigenvalues that are

simply the sum of the one-electron eigenvalues. Due to the similarity,


33

one can solve the Kohn-Sham equations using the same algorithms as in

the Hartree-Fock theory, including the usage of basis functions and the

self consistent field (SCF) approach.

Within an orbital expression the energy functional 9 may then rewritten

as 10.

rErdr

r

Rr

ZrE XC

N

i

ii

N

i

i

A Ai

Aii

ii

1

1

12

1

1

2

2

1

2

10

where N is the number of electrons and the density for a Slater

monodeterminantal wave function 11.

N

i

i rr1

2

11

If we undertake in the usual fashion to find the orbitals φ that minimize E

in 10 we find that they satisfy the pseudoeigenvalue equations 12.

rrf iii

KS ˆ

12

where the Kohn-Sham (KS) one-electron operator is defined as 13

where the exchange-correlation potential, defined by 14, is a so-called

functional derivative, and it is best described as the one-electron

operator for which the expectation value of the KS Slater determinant is

Exc.

A A

AXC

iKS

Rr

ZrVrd

r

rf

1

12

12

2

2

2ˆ

13

r

rErV xc

XC

1

14


34

Because the E of 10 that we are minimizing is exact, the orbitals φ must

provide the exact density. KS orbitals are determined expressing them

within a basis set of functions and the individual orbital coefficients are

determined by solution of a secular equation entirely analogous to that

employed for HF theory. Noneless, the KS orbitals are not the same as

the HF orbitals, and they lack of the physical interpretation of the HF one

electron molecular orbitals, but in some cases [86,87].

Therefore, the accuracy of a DFT calculation depends upon the quality of

the exchange–correlation (XC) functional. Exc is an unknown object that

includes all non-trivial many–body effects required to make KS theory

exact. The past two decades have seen remarkable progress in the

development and validation of XC density functionals [88-91]. There are

two main strategies for developing new functional, namely the

nonempirical and the semiempirical approach. The nonempirical

approach, favored in physics, is to construct functional subject to several

exact constraints. The typical nonempirical is the “Jacobs ladder” scheme

[92-95] advanced by Perdew and co-workers. This strategy can be viewed

as a ladder with five rungs, from the local density approximation (LDA) up

to the “divine” exact exchange and exact correlation functional. In this

approximation Exc[ρ(r)] is taken to be the exchange and correlation

energy of a homogeneous electron gas with density ρ=ρ(r). Although

there exists an exact expression for the exchange energy in this model,

the exact value of the correlation energy is known only in the limit of

very high densities. The semiempirical way to construct Exc[ρ(r)], which


35

has been very successful in chemistry, is to choose a flexible

mathematical functional form depending on one or more parameters

and then to fit these parameters to molecular thermochemical data. This

approach is only empirical in part because the functional form is guided

by theory.

The fisrt generation of functionals were the local spin density

approximation (LSDA), in which density functionals depend only on the

up- and down-spin (ς = α, β) local spin densities ρς. Although LSDA gives

accurate predictions for solid-state physics, it is not a useful model for

chemistry due to its severe overbinding of chemical bonds and

underestimation of barrier heights. The second generation of density

functionals is called the generalized gradient approximation (GGA), in

which functionals depend on the ρς and their gradients ρς. GGA

functionals have been shown to give more accurate predictions for

thermochemistry than LSDA ones, but they still underestimate barrier

heights. In third-generation functionals, two additional variables, the spin

kinetic energy densities, τς(r), are included in the functional form; such

functionals are called meta-GGAs. LSDAs, GGAs, and meta-GGAs are

“local” functionals because the electronic energy density at a single

spatial point depends only on the behavior of the electronic density and

kinetic energy at and near that point [96-98]; local functionals can be

mixed with nonlocal Hartree–Fock (HF) exchange as justified by the

adiabatic connection theory [99]. Functionals containing HF exchange are

usually called hybrid functionals, and they are often more accurate than


36

local functionals for maingroup thermochemistry. HF exchange would be

exact if the Kohn–Sham orbitals were the accurate ones determined by

the exact XC functional, which is unknown. We do, however, know some

properties of the exact XC functional, for example, it is nonlocal [100],

and these properties can serve as constraints during functional

development. In the last six years, the development of new functional

forms for meta-GGAs and hybrid meta-GGAs and their validation against

diverse databases have yielded powerful new density functionals with

broad applicability to many areas of chemistry. There has also been

much interest in including noncovalent interactions in DFT [93,101-107].

The B3LYP [99,108,109] functional, which is a hybrid GGA, is largely

responsible for DFT becoming one of the most popular tools in

computational chemistry. However, B3LYP is unable to describe van der

Waals complexes bound by medium-range interactions, such as the

interactions in methane dimers and benzene dimers. Kohn et al. [110]

point out that “the commonly used LDA and GGA, designed for

nonuniform electron gases, fail to capture the essence of vdW energies”.

Mourik and Gdanitz [111] confirmed this point by showing that the local

density approximation and some well-established GGA functional are

incapable of accounting for dispersion effects in a quantitative way. This

inability of B3LYP (and most of other popular functionals) to describe

accurately medium-range XC energy limits their applicability for

biological systems where medium-range dispersion-like interactions play

vital roles. For biological systems it is essential to describe London


37

dispersion forces (van der Waals attraction) accurately along with

electrostatic and hydrogen bond interaction. For those studies, those in

which we study stacking interaction, we use new improved functionals

like the MPW1B95 [112]. This functional belongs to the generation of

functionals called meta-GGAs, because it incorporates electron spin

density, density gradient, kinetic energy density, and Hartree-Fock (HF)

exchange. Spin density, density gradient, and kinetic energy density are

local properties of the density, although the latter two are sometimes

called semilocal whereas HF exchange is nonlocal. The inclusion of HF

exchange is a permanent feature of accurate exchange-correlation

functional. The one-parameter hybrid Fock-Kohn-Sham operator can be

written as 15, [113,114]

CorGCESEHFEH FFFX

FX

FF ˆˆˆ100

1ˆ100

ˆˆ

15

where FH is the Hartree operator (i.e., the nonexchange part of the HF

exchange operator), FHFE is the HF exchange operator, X is the percentage

of HF exchange, FSE is the Dirac-Slater local density functional for

exchange [115,116], FGCE is the gradient correction for the exchange

functional, and FCor is the total correlation functional including both local

and gradient-corrected parts and (where applicable) a dependence on

kinetic energy density. In this functional, Adamo and Barone´s mPW

exchange functional [117] is used for FGCE and Becke95 [109] functional

for FCor (meta-GGA). For the MPW1B95 model, X is optimized to minimize

the root-mean-square error for the AE6[118] representative atomization

energy database. This functional is suitable for general applications in


38

thermochemistry and gives good performance for hydrogen bonding and

weak interaction calculations [112].


39

“Es gibt nichts mehr praktisches al seine gute Theorie” (No hay nada más práctico que

una bunea teoría). Clausius

3.1.2. AN OVERVIEW ON THE QUANTUM THEORY OF ATOMS IN

MOLECULES (QTAIM)

QTAIM can be viewed as a topological analysis of the electron density

function, ρ(r),.As in any topological analysis, the localization of singular

points plays a basic role. In this case we have singular points in the real

space spanned by the 3 coordinates representing the position of any

electron, r. Looking at the relief map of ρ(r) in the plane of pyrrole (figure

1) that contains all its nuclei, we can observe ten local maxima, also

called electron density attractors, whose coordinates correspond very

approximately to those of the ten nuclei in the molecule. Along every

bond there is a saddle point with two negative eigenvalues of the

Hessian matrix of ρ(r). These points are also called bond critical points or

BCPs. Finally, inside the ring, we observe another saddle point, whose

Hessian matrix presents two positive eigenvalues. It is called a ring critical

point (or RCP) and it is characteristic of cyclic structures. Finally in

molecules like cubane, where there is a cage structure, we observe the

presence of a relative minimum, one per cage, which is named cage

critical point (CCP) and is surrounded by ring critical points, six in this

case. It this context, a recent paper by Castillo et al. has proved that in a


40

highly twisted system (1,12-difluorobenzo[c]phenanthrene) a cage

structure can be delimited by only two ring surfaces [119].

Figure 1. Relief plot of the electron density of pyrrole.

N 1 H 2

C 3

C 4

C 5

C 6

H 7

H 8

H 9

H 10

Figure 2. ρ(r) plot in the main plane of pyrrole.


41

The topological analysis also looks at the gradient paths of the electron

density, which are shown for the main plane of pyrrole in figure 2. We

observe they form a vector field where every group of field lines ends at

a different nucleus. These groups of lines are delimited by surfaces given

by what is known as the zero flux condition 16, which is a mathematical

condition rigorously derived [58] from Schwinger’s principle of stationary

action [59]. These surfaces are represented in the pyrrole plane as lines

that intersect a certain vanishing limit of the molecular electron density

defining the atomic basins, that are disjoints regions of the space (figure

3). In this context, an atom can be defined as the joint of a nucleus and

its electron basin. The integration of the proper density function within

the atomic basin provides the atomic properties, like the atomic electron

population 17, the atomic electron kinetic energy 18 or the atomic

volume 19.

0 rnr

16;

rdrN

17;

rdrrrK rr

2

,24

1

18;

rdv

19

Turning back to critical points, it has to be said that the conduction of the

eigenvector associated to the positive eigenvalue of every BCP gives rise

to the atomic interaction lines or bondpaths (figure 4). According to

Bader's original formulation of QTAIM, bondpaths are the physical


42

representation of chemical bonds [12], being a necessary and sufficient

condition for the existence of bondpaths. Nevertheless, the

interpretation of bondpaths in several systems (biphenyl, inclusion

complexes of He in adamantane, etc.) has risen significant controversies

[120-126].

N1 H2

C3

C4

C5

C6

H7

H8

H9

H10

N1 H2

C3

C4

C5

C6

H7

H8

H9

H10

N1 H2

C3

C4

C5

C6

H7

H8

H9

H10

Figure 3. Intersection of the zero flux surfaces (solid lines) and vanishing limit of (r)

(dots) with the main plane of pyrrole. ρ(r) lines in grey.

Figure 4. AIM2000 [127] plot showing the BCPs (between every pair of nuclei), the

RCP (inside the ring) and bondpaths of pyrrole.


43

3.1.3.- APPROXIMATE TRANSFERABILITY

9.747

9.748

9.749

9.750

9.751

9.752

9.753

1 4 7 10n

N(F

) [a

u]

9.335

9.336

9.337

9.338

9.339

9.340

9.341

1 4 7 10n

N(O

) [a

u]

F

C

(CH2) n

CH3

H H

H

C

O

(CH2) n

CH3

N(O) = 9.3387(2) au N(F) = 9.7503(2) au

|L(O)| < 6·10-4 au |L(F)| < 5·10-4 au

9.747

9.748

9.749

9.750

9.751

9.752

9.753

1 4 7 10n

N(F

) [a

u]

9.747

9.748

9.749

9.750

9.751

9.752

9.753

1 4 7 10n

N(F

) [a

u]

9.335

9.336

9.337

9.338

9.339

9.340

9.341

1 4 7 10n

N(O

) [a

u]

9.335

9.336

9.337

9.338

9.339

9.340

9.341

1 4 7 10n

N(O

) [a

u]

F

C

(CH2) n

CH3

H H

F

C

(CH2) n

CH3

H H

H

C

O

(CH2) n

CH3

N(O) = 9.3387(2) au N(F) = 9.7503(2) au

|L(O)| < 6·10-4 au |L(F)| < 5·10-4 au

Figure 5. Electron atomic populations of oxygen in a series of HCO(CH2)nCH3

aldehydes and fluorine in a series of FCH2(CH2)nCH3 1-fluoroalkanes. All the values are

computed for completely antiperiplanar conformers.

One of the first ideas that should be known about transferability is that,

as a consequence of the Hohenberg and Kohn's theorem [85] we can

only speak of approximate transferability [19,20]. This leads to define

transferability limits for comparing geometries and atomic and bond

properties of similar compounds. On first thoughts these limits should be

close to typical experimental errors or computational accuracy. This is

quite easy to establish for geometries, but not so for atomic properties.

In principle, 0.001 au could be a reasonable transferability limit for the

atomic electron population. In fact, this limit is achieved perfectly in

many cases, like comparison of oxygens of aldehydes [1] or fluorines of

fluroalkanes [128]. As we can see, looking at the corresponding averaged

electron populations and maximum deviation shown in parenthesis for


44

the least significant digit (figure 5). Nevertheless, the situation is different

for other series like carbonyl carbon of aldehydes or oxygen of

methylethers (figure 6).

-4·10-3 au <|L()| < 4·10-3 au

4.731

4.732

4.733

4.734

4.735

4.736

4.737

2 5 8 11n

N(C

) [a

u]

H

C

O

(CH2) n

CH3

8.344

8.345

8.346

8.347

8.348

8.349

8.350

1 4 7 10n

N(O

) [a

u]

H3C

O

(CH2) n

CH3

-4·10-3 au <|L()| < 4·10-3 au

4.731

4.732

4.733

4.734

4.735

4.736

4.737

2 5 8 11n

N(C

) [a

u]

H

C

O

(CH2) n

CH3

4.731

4.732

4.733

4.734

4.735

4.736

4.737

2 5 8 11n

N(C

) [a

u]

4.731

4.732

4.733

4.734

4.735

4.736

4.737

2 5 8 11n

N(C

) [a

u]

H

C

O

(CH2) n

CH3

H

C

O

(CH2) n

CH3

8.344

8.345

8.346

8.347

8.348

8.349

8.350

1 4 7 10n

N(O

) [a

u]

H3C

O

(CH2) n

CH3

8.344

8.345

8.346

8.347

8.348

8.349

8.350

1 4 7 10n

N(O

) [a

u]

8.344

8.345

8.346

8.347

8.348

8.349

8.350

1 4 7 10n

N(O

) [a

u]

H3C

O

(CH2) n

CH3

H3C

O

(CH2) n

CH3

Figure 6. Electron atomic populations of carbonyl carbon in a series of HCO(CH2)nCH3

aldehydes and oxygen in a series of CH3O(CH2)nCH3 methylethers. All the values are


To explain these cases we looked at L(), which is the integrated value of

the Laplacian of ρ(r), and which should be zero for an atom that is

perfectly delimited. We observe the absolute values of this property are

much larger when the transferability limit is not achieved. This allows

introducing a condition for L() values to study transferability.

Moreover, if we plot the atomic populations versus L() for every series

of compounds we observe that, within a certain interval of L() values,

there is a linear relation (figure 7). This allows us to represent a set of

atoms obtained with not so low L() values by the fitted intercept of the


45

electron population, written as N0(), which is the electron population

obtained with no integration error.

4.731

4.732

4.733

4.734

4.735

4.736

4.737

-3.0 -1.0 1.0 3.0 5.0L(C) [au]

N(C

) [

au

]

8.344

8.345

8.346

8.347

8.348

8.349

8.350

-4.0 -2.0 0.0 2.0 4.0L(C) [au]

N(O

) [

au

]

Nº(C) = 4.734 au Nº(O) = 8.346 au

4.731

4.732

4.733

4.734

4.735

4.736

4.737

-3.0 -1.0 1.0 3.0 5.0L(C) [au]

N(C

) [

au

]

8.344

8.345

8.346

8.347

8.348

8.349

8.350

-4.0 -2.0 0.0 2.0 4.0L(C) [au]

N(O

) [

au

]

Nº(C) = 4.734 au Nº(O) = 8.346 au

Figure 7. N() vs. L() plot for the carbonyl carbon in a series of HCO(CH2)nCH3

aldehydes and oxygen in a series of CH3O(CH2)nCH3 methylethers. All the values are


Atomic energy was a more problematic quantity for establishing

transferability limits. Looking again at the atomic energy of the oxygen

atom, E(O), of a homologous series of aldehydes [1], we observe that so

similar atoms like the oxygen of dodecanal and nonanal differed by

almost 30 kJ mol-1. The situation was completely similar for all the

ketones studied, with the oxygen atom becoming more destabilized

when the size of the molecule increases, and giving rise to unexpected

differences of the oxygen energy in position isomers, like 5-undecanone

and 6-undecanone (figure 8).


46

H

O

R

H3C

O

R

O

R

O

R

n(CH2)

-75.57

-75.56

-75.55

-75.54

-75.53

-75.52

-75.51

-75.50

0 3 6 9 12

E(O)[au]

O

R

O

R

E= 29 kJ mol-1H

O

R

H3C

O

R

O

R

O

R

n(CH2)

-75.57

-75.56

-75.55

-75.54

-75.53

-75.52

-75.51

-75.50

0 3 6 9 12

E(O)[au]

n(CH2)

-75.57

-75.56

-75.55

-75.54

-75.53

-75.52

-75.51

-75.50

0 3 6 9 12

E(O)[au]

-75.57

-75.56

-75.55

-75.54

-75.53

-75.52

-75.51

-75.50

0 3 6 9 12

E(O)[au]

O

R

O

R

O

R

O

R

E= 29 kJ mol-1

Figure 8. E(O) values for the series of aldehydes (open face circles) and several groups

of linear ketones including molecules with 1 to 12 carbon atoms. All values computed

with HF/6-31++G(d,p) electron densities.

This trend also holds for alkanols [26], methylethers and other kinds of

monoethers [3] and diethers [129] (figure 9a). It is not only a

characteristic of oxygens, but we also find it in the carbonyl carbons of

aldehydes and ketones [2] and in the carbons of linear alkanes [27], with

HF or DFT levels (figure 9b). The same situation was also observed in

every series of homologous compounds we have studied, like

cyanoalkanes [21] or fluoroalkanes [128]. Therefore, we inferred this

trend is common to any atom in any series and computational level and

could prevent atomic energy transferability.


47

R-OH

R-O-R’

R’O-R-OR’’-75.47

-75.45

-75.43

-75.41

-75.39

-75.37

-75.35

-75.33

-75.31

0 3 6 9 12n

E(O)[au]

R-OH

R-O-R’

R’O-R-OR’’-75.47

-75.45

-75.43

-75.41

-75.39

-75.37

-75.35

-75.33

-75.31

0 3 6 9 12n0 3 6 9 12n

E(O)[au]

-38.02

-38.01

-38.00

-37.99

0 3 6 9 12n(CH2)

E(C)[au]

R

HH

H

C

-37.03

-37.03

-37.02

-37.02

-37.01

-37.01

-37.00

0 3 6 9 12n(CH2)

E(C)[au]

H

O

RC

-38.02

-38.01

-38.00

-37.99

0 3 6 9 12n(CH2)

E(C)[au]

R

HH

H

C

-38.02

-38.01

-38.00

-37.99

0 3 6 9 12n(CH2)

E(C)[au]

R

HH

H

R

HH

H

C

-37.03

-37.03

-37.02

-37.02

-37.01

-37.01

-37.00

0 3 6 9 12n(CH2)

E(C)[au]

H

O

RC

-37.03

-37.03

-37.02

-37.02

-37.01

-37.01

-37.00

0 3 6 9 12n(CH2)

E(C)[au]

H

O

RC

Figure 9. E(O) values for series of n-alkanols, alkylmonoethers and alkyldiethers

calculated with HF/6-31++G(d,p)//HF/6-31G(d) electron densities (a). E(C) values of

the carbonyl carbon in a series of aldehydes and of methyl carbon of a series of

alkanes (b). n indicates the number of CH2 groups in the molecule.

Nevertheless, when the atomic energies of every series are plotted

versus the inverse of the total number of electrons in the molecule, Z, we

get an empirical linear relation (figure 10). It allows representing each

series of nearly transferable atoms by the intercept of this plot, which

would represent the energy for an infinity number of electrons, E().

This relationship also provides a method for classifying atoms into

different types as shown for aldehydes, methylketones and


48

dialkylketones (figure 10). We have observed this relation holds for the

rest of homologous series we have studied: alkanes [27], alkanols [26],

cyanoalkanes [21], fluoralkanes [128], ethers [3,4] and, diethers [67,129].

-75.58

-75.56

-75.54

-75.52

-75.50

-75.48

0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035

1/Z

E(O)[au]

E(O) = limZ E()

-75.58

-75.56

-75.54

-75.52

-75.50

-75.48

0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035

1/Z

E(O)[au]

-75.58

-75.56

-75.54

-75.52

-75.50

-75.48

0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035

1/Z

E(O)[au]

E(O) = limZ E()

Figure 10. E(O) vs. Z-1 plots for aldehydes (propanal to dodecanal),methylketones (2-

butanone to 2-dodecanone) and dialkylketones (CH3(CH2)nCO(CH2)mCH3) (n,m > 0,

n+m < 10).

Overall, the atomic energy was not found as a transferable property in

any homologous series. This problem comes from the fact QTAIM atomic

energies are usually computed correcting the atomic electron kinetic

energy, K(), with the molecular virial ratio (equation 20). This

method has computational advantages, because it avoids computing

two-electron interactions. It can be observed that, probably because of

the convergence criteria employed to obtain the molecular electron


49

density, the molecular virial ratio is linearly correlated with the inverse of

the number of electrons. In contrast, K() is nearly transferable for each

homologous series (figure 11) [28]. Therefore, E() linear dependence on

Z-1 is just a shortcoming due to virial ratio correction of K() values. In

fact, Cortés-Guzmán and Bader have demonstrated that nearly

transferable atomic energies can be obtained for a certain homologous

series when approaches its ideal value with high accuracy [29]. This

situation can be achieved using self consistent virial scaling (SCVS)

optimizations [130].

KE 1 20

-75.65

-75.55

-75.45

-75.35

-75.25

0.00 0.03 0.06 0.091/Z

E(O)/au

HRMeR R'RROH ROMeROEt ROR'

75.25

75.30

75.35

75.40

75.45

75.50

0.00 0.01 0.02 0.03 0.041/Z

K(O)/au

HR

MeR

MeOR

2.0004

2.0006

2.0008

2.0010

2.0012

2.0014

2.0016

2.0018

2.0020

0.00 0.01 0.02 0.03 0.041/Z

- HR

MeR

ROH

MeOR

-75.65

-75.55

-75.45

-75.35

-75.25

0.00 0.03 0.06 0.091/Z

E(O)/au


-75.65

-75.55

-75.45

-75.35

-75.25

0.00 0.03 0.06 0.091/Z

E(O)/au


75.25

75.30

75.35

75.40

75.45

75.50

0.00 0.01 0.02 0.03 0.041/Z

K(O)/au

HR

MeR

MeOR

75.25

75.30

75.35

75.40

75.45

75.50

0.00 0.01 0.02 0.03 0.041/Z

K(O)/au

HR

MeR

MeOR

2.0004

2.0006

2.0008

2.0010

2.0012

2.0014

2.0016

2.0018

2.0020

0.00 0.01 0.02 0.03 0.041/Z

- HR

MeR

ROH

MeOR

2.0004

2.0006

2.0008

2.0010

2.0012

2.0014

2.0016

2.0018

2.0020

0.00 0.01 0.02 0.03 0.041/Z

- HR

MeR

ROH

MeOR

Figure 11. Plots of E(), K() and vs. the inverse of the total number of electrons in

the molecule.


50

No significant problems were found for obtaining accurate transferability

limits for other atomic properties like the first moment of the electron

density, dipole moment, volume, or Shannon entropy, as well as for bond

properties.

F

CH3-CH2-CH2-(CH2)n-CH2-CH2-CH3

C

C

C

C C

5.240

5.245

5.250

-0.004 -0.002 0.000 0.002 0.004

L(C) [au]

N(C

) [a

u]

5.790

5.795

5.800

5.805

5.810

5.815

5.820

-0.004 -0.002 0.000 0.002 0.004

L(C) [au]

N(C

) [a

u]

C

C

C

C

C

FF

CH3-CH2-CH2-(CH2)n-CH2-CH2-CH3CH3-CH2-CH2-(CH2)n-CH2-CH2-CH3CH3-CH2-CH2-(CH2)n-CH2-CH2-CH3

CC

CC

CC

CC CC

5.240

5.245

5.250

-0.004 -0.002 0.000 0.002 0.004

L(C) [au]

N(C

) [a

u]

5.790

5.795

5.800

5.805

5.810

5.815

5.820

-0.004 -0.002 0.000 0.002 0.004

L(C) [au]

N(C

) [a

u]

5.240

5.245

5.250

-0.004 -0.002 0.000 0.002 0.004

L(C) [au]

N(C

) [a

u]

5.240

5.245

5.250

-0.004 -0.002 0.000 0.002 0.004

L(C) [au]

N(C

) [a

u]

5.790

5.795

5.800

5.805

5.810

5.815

5.820

-0.004 -0.002 0.000 0.002 0.004

L(C) [au]

N(C

) [a

u]

5.790

5.795

5.800

5.805

5.810

5.815

5.820

-0.004 -0.002 0.000 0.002 0.004

L(C) [au]

N(C

) [a

u]

C

C

C

C

C

Figure 11. N(C) vs. L(C) plots for nearly transferable carbons in 1-fluoroalkanes in

completely antiperiplanar conformer.

Once the transferability limits were established we investigated how

transferability is affected by diverse factors. One of the simplest is the

conformational change. If we take a series of functionalized linear

alkanes, like 1-fluoralkanes, in completely antiperiplanar arrangement,

we observe (using the above commented N() vs. L() plots shown in


51

figure 11), that carbons form a nearly transferable group, the same is

true for , , and atoms, whereas all the rest of the carbons (excluding

the terminal groups) belong to a common nearly transferable group

[128]. They are called by us normal or C carbons, and present the same

properties obtained for the inner methylenes of unfuctionalized n-

alkanes.

C

5.235

5.240

5.245

-0.004 -0.002 0.000 0.002 0.004

L(C) [au]

N(C

) [a

u]

5.790

5.795

5.800

5.805

5.810

5.815

5.820

-0.004 -0.002 0.000 0.002 0.004

L(C) [au]

N(C

) [a

u]

C

C

C

C

F

C

C

C

CH3-CH2-CH2-(CH2)n-CH2-CH2-CH3

C

5.235

5.240

5.245

-0.004 -0.002 0.000 0.002 0.004

L(C) [au]

N(C

) [a

u]

5.790

5.795

5.800

5.805

5.810

5.815

5.820

-0.004 -0.002 0.000 0.002 0.004

L(C) [au]

N(C

) [a

u]

C

C

C

C

F

C

C

C

C

5.235

5.240

5.245

-0.004 -0.002 0.000 0.002 0.004

L(C) [au]

N(C

) [a

u]

5.790

5.795

5.800

5.805

5.810

5.815

5.820

-0.004 -0.002 0.000 0.002 0.004

L(C) [au]

N(C

) [a

u]

C

C

C

C

F

C

C

C

C

5.235

5.240

5.245

-0.004 -0.002 0.000 0.002 0.004

L(C) [au]

N(C

) [a

u]

5.790

5.795

5.800

5.805

5.810

5.815

5.820

-0.004 -0.002 0.000 0.002 0.004

L(C) [au]

N(C

) [a

u]

C

C

C

C

F

C

C

C

5.235

5.240

5.245

-0.004 -0.002 0.000 0.002 0.004

L(C) [au]

N(C

) [a

u]

5.235

5.240

5.245

-0.004 -0.002 0.000 0.002 0.004

L(C) [au]

N(C

) [a

u]

5.790

5.795

5.800

5.805

5.810

5.815

5.820

-0.004 -0.002 0.000 0.002 0.004

L(C) [au]

N(C

) [a

u]

5.790

5.795

5.800

5.805

5.810

5.815

5.820

-0.004 -0.002 0.000 0.002 0.004

L(C) [au]

N(C

) [a

u]

C

C

C

C

F

C

C

C

C

C

C

CH3-CH2-CH2-(CH2)n-CH2-CH2-CH3CH3-CH2-CH2-(CH2)n-CH2-CH2-CH3CH3-CH2-CH2-(CH2)n-CH2-CH2-CH3

Figure 12. N(C) vs. L(C) plots for nearly transferable carbons in 1-fluoroalkanes in

gauche conformers.

Rotating from anti to gauche conformer, we observe that the population

of and carbons is different, but they continue as different types. In

contrast, C cannot be distinguished from and carbons, which are not

specific groups in gauche conformers (figure 12) [128]. In summary, , ,


52

and carbons of an alkyl chain are significantly influenced by a

functional group in antiperiplanar arrangement, but this influence

reduces to and in gauche. This trend also holds for other series and

computational levels [131].

3.1.4. ON THE LIMITATIONS OF THE RESONANCE MODEL

The resonance model (RM) is still one of the most often employed tools

for explaining the mechanism of chemical processes or predicting their

products. The study and application of this model consumes a significant

amount of time to chemistry students. Nevertheless diverse evidences

found by several research groups point to its inadequacy to describe the

evolution of the electron density in various simple chemical processes.

Even, RM cannot explain some experimental facts like the evolution of

pKas along certain series of organic compounds. Conformational

equilibria, protonations or hydride additions are examples of simple

processes where the resonance model leads to explanations that

contradict those obtained using modern quantum chemical methods for

the electron density analysis. Among them, the quantum theory of atoms

in molecules (QTAIM) [12,13] can be considered as a very reliable one, as

it is based exclusively on the basic principles of Physics without

introducing any other hypothesis.


53

Several QTAIM studies have contradicted well known and

generally accepted conclusions of the RM. To the best of our knowledge,

Wiberg and Laidig’s work on the origin of ester and amide resonance

[72], can be reported as the first serious difference between QTAIM

results and RM explanations. This work shows that in diverse R-CO-XR’

compounds, comprising formamide(XR’=NH2), formic acid (XR’=OH),

methyl formate (XR’=OCH3), etc., the atomic electron population of

nitrogen/oxygen, N(X), is smaller in the transition states for the C-X

rotation than in the corresponding planar conformers. In contrast, N(O)

remains nearly constant along this process. According to the RM, the

non-planar geometry of transition states for C-X rotation breaks the

electron delocalization along the O=C-X unit (usually represented by

resonant forms: O=C-X ↔ O--C=X+) present in the planar conformer.

Clearly, RM predicts that, at transition states and with regard to

conformers, N(X) should be larger, as the O--C-X+ form should have a

negligible weight, and N(O) should be smaller. These results, obtained

initially at the HF level, were confirmed later at the MP2 level [73].

Slightly later, Slee and MacDougall observed that the comparison of

QTAIM atomic electron populations, N(Ω), of allyl ions and the

corresponding neutral compounds is not in line with the evolution of

electron density expected with the resonance model [132]. In this

context, it should be mentioned that the publication of the first of

Wiberg’s papers on “ester/amide resonance” led to a long argument

about the reliability of QTAIM atomic populations [75], ended by clear


54

demonstrations of unreliability of the basic postulates against QTAIM

charges [76,77]. Moreover, the same kind of contradiction between RM

predictions and QTAIM relative charges observed for simple amides and

esters was also obtained for thioformamide [133].

In the same vein, Glaser and Chao obtained that the electron

density distribution of diazonium ions are inconsistent with the

commonly used Lewis structure R-N+≡N and would be better

represented by a combination of two unconnected structures: R+···N≡N

and R+···N-≡N+ [74,134]. Also, the acidity sequence followed by dimethyl

sulfide, sulfoxide and sulfone, cannot be explained by the RM, which

reverses the order. In contrast, QTAIM atomic populations explain the

real sequence and provide no evidence for the delocalization of the

charge from the anionic carbon in the rest of the anion [135].

In the second half of the 90’s our group started a systematic study

on protonation processes of oxygenated compounds employing QTAIM

as basic tool for analyzing the evolution of the molecular electron density

(computed at diverse computational levels: HF, B3LYP, MP2 and

sometimes QCISD) along the protonation. This study comprised

carbonylic compounds [1,2]. linear [3,4] and cyclic ethers [38,136]. The

general conclusion obtained was that the positive charge was mainly

concentrated on the proton while the oxygen formally attached to it

does not reduce its electron population, as postulated by classic

protonation scheme shown in figure 13. On the contrary, N(O) increases

upon protonation, gaining electron density from the remaining hydrogen


55

atoms in the molecule, as had been previously proposed by Stutchbury

and Cooper [41].

R1

O

R2 R1

O

R2

H+

+ H+

Figure 13. Classic mechanism of protonation for carbonyl compounds

+ H+

+406

-25

+310

-105 -105

-83 -39

-112

-112

-47 -76 a

b

Figure 14. Evolution of atomic electron population, ΔN(Ω), upon protonation of

propanone. All values in au multiplied by 103.

Later on, our work was extended to other systems of practical

interest, as uracil and cytosine [5,6,39], and to compounds without

oxygen, like nitriles [23] or indole [40]. RM was only able to predict the

stability sequence of protonated forms and explain the changes exhibited

by most of the bond properties upon protonation. Even, both the O- and

N-protonated forms of uracil and cytosine are found to be better

described by RO-H+ and RN-H+ forms than by the classical RO+-H and RN+-


56

H structures. Again, according to the QTAIM analysis the electron charge

gained by the proton is mainly provided by the other hydrogens of the

molecule. The study of several model systems, like vinylketone, methyl

formiate and N-methyl formamide [6] led us to explain the previously

reported stability sequence of uracil [5] and cytosine protonated forms,

as well as the evolution of atomic electron populations. Thus, we

developed an alternative model, not based on the resonance concept but

mainly on electrostatic interactions [6,39], which we think can be applied

to any protonation. This model is based upon the following points: i) the

donation of electron population is easier when the atomic number is

smaller; ii) the closer the distance to the proton is, the easier the electron

donation will be; iii) the donation of electron population between

bonded atoms follows the direction of the bond. The orientation of the

bond with regard to the proton can make the electron transference

easier (if the electron density approaches the proton), or more difficult (if

the electron density moves away from the proton) (see, respectively,

hydrogens labeled “a” and “b” in figure 14); and iv) π-transferences are

generally easier than ς ones, when both are possible.

At this point, we should highlight that other modern methods for

electron density analysis, like the Hirshfeld scheme [78], implemented

for several computational levels [79], which was employed to analyze

several simple oxygenated compounds [8], provide different absolute

values for the evolution of atomic electron populations, ΔN(Ω), but the

same qualitative description, contradicting RM expectations.


57

As protonation can be considered as a model for electrophilic

attacks, our group also studied how activant and deactivant substituents

modify the evolution of electron density in this process. QTAIM analysis

carried out the protonation of a set of aniline derivatives, indicates that

most of the electron density gained by the proton is provided neither by

the nitrogen atom nor by activant substituens like OH [7]. In a similar

way, the acidity of phenol derivatives can be rationalized on the basis of

atomic QTAIM properties, but not on the RM predictions [9].

On the other hand, the evolution of molecular electron density upon

hydride addition, (simple model for nucleophilic attacks), computed both

with QTAIM or Hirshfeld methods, has been shown to display general

trends that are also not in line with RM predictions summarized in the

scheme shown in figure 15 [10]. Thus, we observe that most of the

electron density provided by the hydride is not taken by the oxygen. In

fact ΔN(O) never reaches 0.2 au, whereas for the carbon attached to

hydride ΔN(C) always exceeds 0.4 au and ΣΔN(H) goes from 0.44 au to

0.53 au in the compounds hitherto studied. When the study is repeated

using other anionic nucleophiles (CN-, OH-) the results do not change

substantially.

R1

O

R2 R1 R2

H- +

O H-

Figure 15. Classic mechanism for hydride addition to carbonyl compounds.


58

Among the discrepancies observed between RM predictions and

relative atomic charges, we highlight the specific behavior of

heteroatoms, X, reducing the extent of electron reorganization with

regard to that displayed when they are replaced by carbons [6]. In fact C-

X bonds were found to act as barriers to ς-electron reorganization,

precluding (or reducing substantially) the transference of ς electron

density throughout them [6]. We thought of interest to show if the

discrepancies previously described for pyrimidinic and puric bases

[5,6,39], affect in general to all heterocycles. In particular, it was shown

that RM predictions are not in line with conclusions derived from the

QTAIM analysis carried out for the protonation (in some cases, also other

processes) of diverse heterocycles: indoles [40], 1,3-azoles [137], and

anthocyanidins [138].


59

3.2. DISCUSIÓN GENERAL DE RESULTADOS

De acuerdo con la normativa vigente, se presenta en esta sección una

discusión que unifica los resultados presentados en los artículos

contenidos en la sección 4. En esta Tesis se ha abordado el estudio de la

estructura y reactividad de nitrilos y compuestos relacionados utilizando

la Teoría Cuántica de Átomos en Moléculas (QTAIM).

Hemos considerado de interés, comenzar caracterizando la estructura

electrónica de los nitrilos más simples: los cianoalcanos. Para ello, se

analizaron las propiedades atómicas y de enlace de una serie de doce

alcanonitrilos lineales en conformación antiperiplanar [21]. Se estudió en

que condiciones se podía considerar como cuasi-transferibles a los

grupos CN, CH2 y CH3.

Nuestro siguiente reto consistía en averiguar como se distorsiona está

imagen de la estructura electrónica considerando dos posibles

alteraciones:

i) La presencia de un sustituyente en la molécula. De entre todos

los posibles hemos considerado únicamente la introducción de

otro grupo ciano en la molécula.

ii) Que tenga lugar un proceso reactivo. Hemos considerado los

dos principales procesos ácido-base que pueden experimentar

los cianocompuestos: protonación y liberación de un protón

desde un carbono al grupo funcional.


60

El primer estudio nos ha permitido establecer que el efecto de

proximidad en los dicianoalcanos es importante y se mantiene como

estadísticamente significativo sobre la distribución electrónica hasta que

ambos grupos se separan por más de 14 grupos CH2 [22].

Con el segundo grupo de estudios hemos podido comprobar que: a) las

distorsiones introducidas por la protonación afectan al total de la

molécula, de manera particular a los átomos de hidrógeno [23]; b) los

protones mantienen una elevada carga positiva en el nitrilo, de manera

que la especie protonada está mejor descrita por una estructura de Lewis

del tipo +H-N≡C-R que por las tipo H-N≡C+-R o H-N+≡C-R [23]; c) la

desprotonación está significativamente favorecida sobre las restantes

en todos los cianocompuestos estudiados; d) Sólo los sustituyentes que

retiran densidad electrónica por efecto resonante reducen notablemente

la energía de desprotonación; y e) en general el modelo de resonancia

proporciona predicciones compatibles con las variaciones de población

electrónica atómica en la desprotonación de un nitrilo [24].

Por último, se estudia la evolución dinámica de la densidad electrónica

en tres procesos de transposición que tienen lugar en compuestos

nitrogenados, concluyéndose que en todos ellos la reacción tiene lugar

en una sola etapa y de forma concertada [25]. La reacción transcurre de

forma similar en los tres casos: el enlace se forma después del estado de

transición cuando ya se ha roto el enlace original. La transferencia de

carga se produce esencialmente entre los átomos implicados en la

transposición: el átomo que migra y los enlazados a él en el reactivo y el


61

producto.


62

4. TRABAJOS DE INVESTIGACIÓN

4.1. Approximate Transferability in Alkanenitriles, J. L. López, M. Mandado, A. M. Graña, R. A. Mosquera, Int. J. Quantum Chem. 86 (2002) 190. 4.2. A Charge Density Analysis on the Proximity Effect in Dicyanoalkanes, J. L. López, M. Mandado, M. J. González Moa, R. A. Mosquera Chem. Phys. Lett. 422 (2006) 558. 4.3. Electron Density Analysis on the Protonation of Nitriles, J. L. López, A. M. Graña, R. A. Mosquera J. Phys. Chem. A 113 (2009) 2652. 4.4. Electron Density Analysis on the Alpha Acidity of Nitriles, J. L. López, A. M. Graña, R. A. Mosquera Chem. Soc. Adv. Para ser sometido (2015). 4.5. Electron Density Evolution in Rearregements on Nitrogenated Compounds, J. L. López, R. A. Mosquera, A. M. Graña Eur. J. Org. Chem. Para ser sometido (2015).


63

Approximate Transferabilityin Alkanenitriles

JOS LUIS LÓPEZ, MARCOS MANDADO, ANA M. GRAÑA,RICARDO A. MOSQUERADepartamento de Química Física, Universidade de Vigo, Lagoas-Marcosende, E-36200 Vigo,Galicia, Spain

Received 4 October 2000; revised 19 March 2001; accepted 15 May 2001

ABSTRACT: The atomic and bond properties of a series of alkanenitriles werecalculated in order to analyze the transferability of the CN, methyl, and methylene groups.The calculations were carried out using the atoms in molecules (AIM) theory onRHF/6-31++G∗∗//RHF/6-31G∗∗ wave functions obtained for compounds CN–R(R ranging from H to C11H23). Linear correlations between L() and N() were used toestablish N(CH2) and N(CH3) nearly transferable values. Average values and maximumdifferences to the mean value of several properties were used for classifying the CN group.It shows a transferable behavior along the CN–R series for R > Et. The methyl grouppresents specific properties when R < Pr. The methylene groups can be classifiedconsidering both their position with respect to the end of the chain and the position withrespect to the CN group. The atomic energy displays a dependence on the molecular size.Although this behavior does not allow to consider this property as transferable, both theab initio total electronic molecular energies and the experimental heats of formation can befitted, by linear regression analysis, as a function of the number of methylene groups.© 2002 John Wiley & Sons, Inc. Int J Quantum Chem 86: 190–198, 2002

Key words: AIM; transferability; energy additivity; functional group; nitriles

Correspondence to: R. A. Mosquera; e-mail: [email protected].

Contract grant sponsor: Government of Galicia.Contract grant number: PGIDT-99X130102B.Contract grant sponsor: CICyT.Contract grant number: PD98-1085.

International Journal of Quantum Chemistry, Vol. 86, 190–198 (2002)© 2002 John Wiley & Sons, Inc.


64

APPROXIMATE TRANSFERABILITY IN ALKANENITRILES

Introduction

T he cyano group, CN, is known as one of thefundamental functional groups in chemistry.

The use of nitriles in preparative organic chemistrybegan to acquire importance in the second half ofthe nineteenth century. Their useful characteristicreactions converted them in very common reagentsboth in organic and inorganic synthesis. In accor-dance with their utility, its electron structure hasbeen the subject of a tremendous amount of exper-imental and theoretical studies [1]. Many of themconcentrated on the structure of the first member ofthe nitrile series, HCN, which became part of themost usual benchmark systems to test theoreticalmethods and calculation levels [2, 3]. Nitriles, es-pecially HCN, are also important interstellar mole-cules that had been detected by radioastronomy invarious sources [4].

The concepts of similarity, functional group, andatomic transferability have played a very importantrole in the historical development of chemistry [5].However, these concepts were usually employed inan intuitive way, without including accurate defi-nitions and quantifications. Accepting that proper-ties of matter are caused by the internal structure,the similarity between substances must originate insimilar charge distributions. In 1980 Carbó et al. [6]proposed the first quantum mechanical similarityindex based on the electron density distributions ofmolecules. This index was a starting point for manyothers that also faced the problem of measuring thesimilarity between complete molecules. The devel-opment of Bader’s atoms in molecules (AIM) theory[7, 8] made possible to split a molecule, in a uniqueand accurate way [9], into discrete subsystems thatverify the theorems of quantum mechanics. It can beaccurately deduced that this division is performedby the zero-flux surfaces for the gradient of thecharge density, ∇ρ(r) [10 – 12]. These surfaces dividethe spaces into regions, , that are readily identi-fied with the constituent atoms of the molecule. Theproperties of the atom are obtained by the integra-tion of a corresponding property density over thatregion.

AIM provides the theoretical tool to define afunctional group as an atom (or groups of atoms)that present in a series of molecules keeps an impor-tant similarity along the series [13]. The similarityof the atoms along a molecule series can be quan-tified by a similarity index, as those introduced byCioslowski et al. [14, 15], or described by comparing

the values of the atomic properties for several mole-cules [16 – 23]. Although absolute transferability ofthe properties has proved to be an unattainable limit[24, 25], the concept of transferability for atoms andgroups of atoms is still widely invoked in chem-istry to predict the properties of a molecule fromthe properties of its constituent fragments. This is,at least, partially due to the very slight variationexperienced by many atomic properties along ho-mologous series of molecules. Variations that arebelow the limits of the experimental error or withinthe accuracy of numerical methods, allow us tospeak of approximately transferable groups.

We are interested in the study of the proper-ties of the functional groups obtained by combiningthe atoms of the AIM theory. Especially in com-paring their properties in order to establish limitsfor the molecular environments in which a certainproperty of a functional group can be consideredas approximately transferable. In our recent stud-ies the application of the AIM theory has allowedthe classification of the atoms of aldehydes, ketones[21, 22], other carbonyl compounds [26, 27], andethers [23, 28, 29] into nearly transferable groups.To achieve these results, we have found and madeuse of empirical relationships that had not beenreported previously, such as the relationship be-tween several atomic properties and the level ofaccuracy with which the zero-flux surfaces weredetermined, or the dependency of the energy prop-erties on the size of the molecule. Because of thisdependency, the energy properties cannot be con-sidered transferable. Nevertheles, for alkyl linearaldehydes, ketones [21], and ethers [23], we havefound that linear fittings for both the HF total en-ergy, E, and the experimental heat of formation, tothe number of methylene groups, n, in the molecule,provide excellent reproductions of those magni-tudes for every molecule in the series (maximumdiscrepancies for E do not overpass 2.5 kJ mol−1 inethers, and 1.5 kJ mol−1 in aldehydes and ketones).

Methodology

Atomic and bond properties were computed us-ing the AIMPAC [30] series of programs on RHF/6-31++G∗∗//RHF/6-31G∗∗ [31, 32] wave functionsobtained with the Gaussian 94 program [33]. Thecalculations were performed on 12 molecules of lin-ear alkanenitriles, R–CN, with R ranging from H toC11H23 (Table I). For all the compounds we havestudied the conformation corresponding to the an-

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY 191


65

LÓPEZ ET AL.

tiperiplanar disposition of all the C–C–C–C dihedralangles and alternate disposition for the terminalmethyl group in relation to the main skeleton.

To establish the transferability of the nitrile,methylene, and methyl groups several atomic andbond properties were calculated and analyzed. Theatomic properties here considered were electronpopulation, N(), total energy, E(), first momentof the charge density, r1(), and the volume en-closed by the interatomic zero-flux surfaces and the0.001 a.u. charge density contour surface, ν(). Theintegrated values of the Laplacian of the chargedensity (multiplied by −h2/16mπ2) were taken intoaccount as a check of the accuracy of the numeri-cal integration of the atomic properties. Other usualerror estimators for the accuracy obtained in thedetermination of the atomic properties [differencebetween the total electronic energy of the molecule,E, and the value obtained by summation of E(),Eq. (1), and the equivalent quantity for the elec-tron population] are shown for every molecule inTable I. The values presented by both quantities in-dicate that the atomic properties have been obtainedwith enough accuracy for our purposes.

δE = E −∑

E(). (1)

The following properties of the C–N and C–Cbonds were also taken into account: the internucleardistance, R; the ellipticity, ε = (λ1/λ2) − 1, where|λ1| > |λ2| are the two positive eigenvalues of the

Hessian of the charge density at the bond criticalpoint (BCP); the charge density at the BCP, ρ(rc),and the total energy density at the BCP H(rc) =G(rc) + V(rc), G(rc), and V(rc) being, respectively, thekinetic and potential energy densities.

The criterion here employed to establish transfer-able values for these properties were based uponthe maximum differences to the mean value of theproperty. When the maximum differences exceedthe admissible value, and transferable values couldnot be obtained in this way (this usually happenswith some atomic properties), we have looked forrelationships between the integrated values of theproperties and L(). When a linear dependencebetween the property and L() is obtained, the in-tercept of the line (i.e., the value it would havehad when the zero-flux surface had been deter-mined with absolute accuracy) is considered as thetransferable value [21]. Also, we have studied thedependences displayed by some integrated prop-erties on the molecular size (quantified by Z, thesummation of the atomic number of the atoms inthe molecule). Different behavior patterns for the Zdependence were also used to classify the propertieshere computed.

Atomic Populations

The N() values obtained for every carbon atomalong the series of molecules shown in Table I

TABLE ITotal electron energy, E, virial ratio, V/T, experimental heat of formation,a Hf, and error estimators (see text) incompounds 1–12.b

Molecule R E −V/T∑

N() − N c ∑E() − E Hf

∑L()

1 H −92.8807 2.0023 0.00021 −0.0002 135.14 −2.63×10−5

2 Me −131.9362 2.0017 0.00060 −0.0002 74.04 6.64×10−4

3 Et −170.9746 2.0014 0.00087 0.00009 51.6 −3.94×10−4

4 Pr −210.0131 2.0012 0.00247 0.00055 31.2 −2.55×10−3

5 Bu −249.0512 2.0011 −0.00083 −0.00075 11.1 2.80×10−3

6 Pn −288.0892 2.0010 −0.00026 −0.00073 — 2.39×10−3

7 Hx −327.1273 2.0009 0.01876 0.00461 −31 −2.80×10−2

8 Hp −366.1653 2.0009 0.00642 0.00103 −50.6 −5.19×10−3

9 Oc −405.2033 2.0008 0.00724 0.00121 — −5.90×10−3

10 No −444.2413 2.0008 0.03810 0.00834 −91.6 −4.80×10−2

11 De −483.2792 2.0008 0.00132 −0.0028 −113.4 5.37×10−3

12 Un −522.3173 2.0007 0.01509 0.00235 — −1.35×10−2

a Ref. [34].b All quantities are in a.u., but Hf in kJ mol−1.c Total number of electrons in the molecule.

192 VOL. 86, NO. 2


66


TABLE IITransferable and specific values of the atomicproperties for different atoms according to theirposition with respect to CN (α, β, or further away, n)and to their position with respect to CH3(terminal = T, α to the terminal = P, and furtheraway = n).a

N() r1() v()

CN 13.378 5.536 21.58Cα 5.700 5.511 4.94Cβ 5.790 5.643 4.82Cn 5.806 5.668 4.74CP 5.794 5.654 4.85CT 5.778 5.690 5.73

CαP 5.687 5.491 5.03CαT 5.657 5.489 5.90CβP 5.778 5.629 4.92CβT 5.755 5.649 5.81

a N() and r1() in a.u. and v() in cm3 mol−1.

have been classified considering maximum differ-ences of 5 × 10−3 a.u. as the limit for approximatetransferability in this quantity. Table II shows theN(C) transferable values obtained by averaging allthe atomic populations inside a group displayingsmaller differences than 5 × 10−3 a.u. Accordingto this criterion, 6 groups with different behaviorpatterns have been found: (i) The CN group forwhich the atomic population shows no dependencyon the value of L() nor on the value of Z, so thetransferable value can be directly obtained as the av-erage value when molecules 1 and 2 are excluded. Ifmolecule 3 is also considered as a specific case, themaximum differences are not reduced. (ii) C in α tothe CN group (henceforth, Cα) for which a transfer-able value of the population is also obtained as amean value excluding molecules 2 and 3. For mole-cule 2, Cα belongs to a terminal methyl group; andfor molecule 3, Cα belongs to a methylene previ-ous to the terminal methyl. Both terminal methyl(CT), and methylene bonded to a methyl (CP) areconsidered as different behavior patterns, as waspreviously found in n-alkanes [17, 20], aldehydes,and ketones [22]. Once again, maximum differencesdo not decrease if molecule 4 is excluded. (iii) Cin β to the CN group (henceforth, Cβ) for whichthe transferable value can be obtained as an aver-age of molecules 5–12. (iv) The remaining C (Cn),excluding CT and CP, for which N(C) is found todepend linearly on L(C) (Fig. 1). The r2 value ex-

FIGURE 1. Plot of the electron population of the Cn

atoms vs. L(Cn).

ceeds 0.90. The intercept of the straight line is takenas the transferable value of the property. (v) C in α tothe terminal methyl in the chain (CP) for which a lin-ear dependence on L(C) is also obtained (r2 = 0.92).(vi) C at the end of the chain, that is, those belong-ing to the terminal methyl group (CT) for which thetransferable value is obtained as a mean value whenmolecules 2 and 3 are excluded. Summing up, tak-ing into account the specific cases: those atoms that(at the same time) are α and T, β and T, α and P, andβ and P, a total of 10 different groups can be found.As a general rule, electron population increases asthe distances to the terminal methyl and to the CNgroup increase. Thus, the populations for Cα and Cβ

are larger as the distance to the methyl group in-creases, the populations for CT and CP increase withthe distance to the CN group, and the largest popu-lations are found for the “standard” carbons in themiddle of the chain, Cn. N() values obtained forCT, CP, and Cn (Table II) in this series do not differby more than 3 × 10−3 a.u. from the correspondingN() in hydrocarbons. The values obtained in thesame level of calculation for n-dodecane are 5.779,5.792, and 5.803 a.u. for CT, CP, and Cn, respectively.

Energies

The results obtained for the total electronic en-ergy, E, of the molecules here studied (Table III)indicate, as was previously found for several ho-mologous series (alkanes, aldehydes and ketones,and ethers), that E values can be very well fit-ted by expression 2 (Fig. 2), where n indicates thenumber of methylene groups in the molecule andE(CH2) and E0 represent, according to a group con-tribution scheme, respectively, the energy of themethylene and the addition of the energies of the



67

LÓPEZ ET AL.

TAB

LEII

IE

ner

gie

s(a

.u.)

for

the

ato

ms

of

the

CN

gro

up

,an

dfo

rth

ed

iffer

entm

eth

ylen

ean

dm

eth

ylg

rou

ps

inm

ole

cule

s1–

12.

ZN

CC

H2α

CH

2β

CH

2γ

CH

2δ

CH

2ε

CH

2ξ

CH

2η

CH

2θ

CH

2ι

CH

2P

CH

3

114

−55.

2782

−37.

0713

222

−55.

2691

−37.

1658

−39.

5015

330

−55.

2540

−37.

1781

−38.

9189

−39.

6236

438

−55.

2456

−37.

1720

−38.

9302

−39.

0156

−39.

6492

546

−55.

2392

−37.

1677

−38.

9258

−39.

0309

−39.

0414

−39.

6470

654

−55.

2355

−37.

1650

−38.

9219

−39.

0261

−39.

0563

−39.

0361

−39.

6490

762

−55.

2322

−37.

1629

−38.

9200

−39.

0225

−39.

0503

−39.

0506

−39.

0363

−39.

6479

870

−55.

2296

−37.

1609

−38.

9185

−39.

0212

−39.

0500

−39.

0483

−39.

0532

−39.

0352

−39.

6474

978

−55.

2275

−37.

1599

−38.

9158

−39.

0199

−39.

0487

−39.

0466

−39.

0507

−39.

0518

−39.

0349

−39.

6463

1086

−55.

2265

−37.

1593

−38.

9153

−39.

0179

−39.

0451

−39.

0446

−39.

0480

−39.

0486

−39.

0500

−39.

0316

−39.

6461

1194

−55.

2252

−37.

1583

−38.

9138

−39.

0173

−39.

0468

−39.

0459

−39.

0486

−39.

0484

−39.

0498

−39.

0504

−39.

0328

−39.

6448

1210

2−5

5.22

39−3

7.15

76−3

8.91

26−3

9.01

61−3

9.04

51−3

9.04

34−3

9.04

71−3

9.04

72−3

9.04

81−3

9.04

84−3

9.04

98−3

9.03

11−3

9.64

46

FIGURE 2. RHF/6-31++G∗∗//RHF/6-31G∗∗ energiesvs. number of CH2 groups, n, for molecules 4–12.

CN and CH3 groups.

E = nE∗(CH2) + E0. (2)

Table IV shows how this fitting is significantlyimproved when molecules 1–3 are excluded. Nev-ertheless, the exclusion of more molecules does notintroduce any meaningful improvement. Even stan-dard deviations, σE0 and σ [E∗(CH2)], for the fittingparameters are enlarged when molecule 4 is also ex-cluded. This confirms nitriles 4–12 can be treated asan homologous series suitable for any kind of groupcontribution treatment of their energies. Also, whena similar fitting to the number of methylene groupsis tested for the experimental standard heat of for-mation (Table I), the results also indicate a very goodadditivity for this magnitude (Table IV), though inthis case no significant improvement is obtained byexluding molecules 2 and 3.

In spite of this linear behavior, neither CH3, CN,nor CH2 groups present a common energy alongthe series. In fact, the CH2 group energies, obtainedby adding their atomic energies, can differ by morethan 329 kJ (CH2

α of molecule 12) from the E∗(CH2)value. It has to be pointed out that most of these dif-ferences overpass the limits of the total integrationerror for the energy, δE [Eq. (1)], which reachs a max-imum value of 21.8 kJ mol−1 (molecule 10). Thesedifferences between the AIM-calculated group ener-gies, E(CH2), and E∗(CH2) are shown in Figure 3. Itcan be said that they are the result of two combinedeffects: (a) The position of the CH2 group with refer-ence to the CN functional group and to the methylgroup, positions used above to define nearly trans-ferable methylenes for nonenergetic properties andclassify the methylenes (Table II). (b) The effect ofthe total size of the molecule, quantified by the sum-mation of its nuclear charges, Z, and displayed inFigure 3 for every group of Table III, and previously

194 VOL. 86, NO. 2


68


TABLE IVFitting parameters for the different fits to the number of methylene groups in the molecules tested in molecules1–12, for the electron energy and for the heat of formation (Table I).a

Series E0 (a.u.) E∗(CH2) (a.u.) σE0 × 105 (a.u.) 105σE∗(CH2) (a.u.) 1 − r2 E (kJ mol−1)

2-12 −131.93669 −39.03808 1.4 0.2 3.5 × 10−12 1.33-12 −131.93692 −39.03805 1.2 0.2 1.8 × 10−12 14-12 −131.93714 −39.03802 0.5 0.8 2.8 × 10−13 0.25-12 −131.93721 −39.03801 0.5 0.8 2.5 × 10−13 0.2

Hf H

f (CH2) σHf σH

f (CH2) (Hf )

(kJ mol−1) (kJ mol−1) (kJ mol−1) (kJ mol−1) r2 (kJ mol−1)

2-12 93.7 −20.7 0.5 0.1 0.99990 1.03-12 93.0 −20.6 0.5 0.1 0.99994 0.64-12 93.2 −20.6 0.7 0.1 0.99991 0.65-12 93.5 −20.6 1.0 0.1 0.99987 0.7

a Intercepts E0 and (Hf )0, slopes E∗(CH2) and H

f (CH2). E and (Hf ) refer, respectively, to the maximum differences between

the computed or experimental value and that obtained with the fitting equation.

found in aldehydes, ketones, and ethers, thoughnever found for n-alkanes for which a good trans-ferability of energies was previously obtained [20].

The effect due to the size of the molecule on thegroup energy is significantly smaller than the onederived from the group position. Thus, the largestdifference related with the size of the molecule(46.1 kJ mol−1) is found between the CH2

α groupsof n-butanenitrile, 4, and n-dodecanenitrile, 12. Itreduces to 38.8 kJ mol−1 for the CHβ groups andto 27.1 kJ mol−1 for the CH2

P. On the other hand,

FIGURE 3. Relative energy of the CH2 groups vs. thesize of the molecule expressed as Z, the summation ofthe atomic numbers of the atoms in the molecule.Energies are relative to the slope of the fitting of the totalelectron energies of molecules 4–12 shown in Figure 2.

the difference between the E(CH2α) and E(CH2

β)varies from 269.2 kJ mol−1 in n-hexanenitrile, 6,to 276.0 kJ mol−1 in n-butanenitrile, 4. ThoughE(CH2) for groups in γ and further away disposi-tions to the CN are separately plotted in Figure 3,the differences among them are very small (themaximum difference within the same molecule is16.8 kJ mol−1). In fact, these differences are evensmaller than the total integration error for the en-ergy, δE. This suggests that all of them can beincluded in a common CH2

n group, as was foundfrom their N(C) values.

Figure 3 also shows the CH2α, CH2

β , andCH2

P destabilizations in relation to the additivelyfitted E∗(CH2) value. These destabilizations are notcompensated by the negative relative energies ofthe remaining CH2 groups and can be relatedto the smaller electron populations presented bygroups connected or close to more electronegativegroups (CN or CH3). It has been found thatboth groups have a cooperative effect that en-large the relative destabilization of the two spe-cific methylenes (CH2

αP and CH2βP) of molecules 3

and 4. The final compensation of positive and neg-ative relative energies that supports the linear addi-tivity relationship (2) is obtained taking into accountthat the sum of the CN and CH3 group energiesis more negative than the E0 parameter for all themolecules (2 excluded, though it had not been in-cluded in the linear fitting). Nevertheless, it has tobe pointed out that the total energy of acetonitrile is



69

LÓPEZ ET AL.

in very good agreement with the intercept of Eq. (2),as was found between the intercept of this equationfor ketones and dimethylketone and for aldehydesand ethanal [21, 22].

The methyl group is destabilized as the molec-ular size increase along the series. Though this de-stabilization is really smaller (12.2 kJ mol−1 be-tween molecules 4 and 12) than that found formethylenes, it is still significantly larger thanany difference between CH3 in n-alkanes. In fact,our calculated values for E(CH3) in n-eicosane(−39.63347 a.u.), n-dodecane (−39.63394 a.u.), andn-pentane (−39.63429 a.u.) differ by less than2.2 kJ mol−1 and cannot be presented as an exam-ple of the Z dependence of the group energies. Onthe other hand, this destabilization was found as26.8 kJ mol−1 in the CH3

α of methoxyethers, whencomparing these group energies for methoxybutaneand methoxydecane. These facts seem to indicatethat the presence of an electronegative substituentin the molecule is crucial to observe this Z effect.When the values of E(CH3) of nitriles are comparedwith those of a n-alkane (n-dodecane), we concludethat this group is more stabilized in nitriles.

Finally, the CN group is stabilized by the elec-trons supplied by the alkyl chain with respect to theHCN molecule, but this stabilization is reduced asthe length of the chain increases. This results in thebehavior displayed in Figure 4. It can be observedthat the energy of the nitrogen atom is less and lessnegative as Z increases. On the other hand, the en-ergy of the C atom is first stabilized by increasingthe chain (methyl and ethyl groups) and then expe-riences a continuous destabilization.

FIGURE 4. Relative energies of the C and N atoms andthe CN group vs. the size of the molecule expressedas Z, the summation of the atomic numbers of the atomsin the molecule. Energies are relative to thecorresponding values in molecule 12.

First Moment of the Electron Charge

For this property no appreciable relationshipwith Z was found. Thus, we have establishedtransferable values by using mean values and de-pendences on L(). The patterns of behavior areexactly the same found for the electron populationand the procedure to obtain transferable values isalso the same. The highest values for methyl car-bons whose charge is, therefore, further (in average)from the nucleus (Table II). The calculated values forn-dodecane are 5.693, 5.647, and 5.661 for CT, CP,and Cn, respectively. The differences with the valuesin Table I are within 7 × 10−3 only slightly higherthan those admissible to define a group.

Atomic Volume

Patterns of behavior and transferable values forvolumes were obtained in the same way, that is, byusing dependences on L() for Cn and CP and byusing mean values in the other cases. For the atomicvolume the admissible maximum difference was es-tablished in 5 × 10−2 cm3 mol−1, which comparessatisfactorily with the usual limit of the experimen-tal accuracy for molecular volumes. Once more, wecan compare the results with those obtained for CT,CP, and Cn atoms in n-dodecane (5.74, 4.82, and4.71 cm3 mol−1, respectively). Once again, the dif-ferences allow us to establish that CT, CP, and Cn

atoms are similar to those in hydrocarbons.

Geometrical Features

The optimized geometries of the completely an-tiperiplanar conformer of compounds 1–12 are verysimilar. Table V shows transferable values for bonddistances and bond angles obtained as mean val-ues for the series. Mean values in every case arecalculated excluding the smallest molecule contain-ing the bond or the angle. It can be concluded thatmolecules in the series show common geometricalfeatures, with an angle N–C–C slightly smaller than180 as it has been shown previously [35]. Oncemore, the values observed for geometric parame-ters including atoms distant from the CN group arein good agreement with the same parameters in n-alkanes (maximum differences in bond distances are7 × 10−4 Å and less than 0.01 in bond angles). Thebond distances allow us to distinguish six different

196 VOL. 86, NO. 2


70


TABLE VTransferable values of the bond distances (R)according to the position of the atoms with respect tothe CN group (α, β, or further away, n) and to theterminal group (terminal = T, α to the terminal = P,and further away = n).a

R0 (Å) R (Å)

N≡C 1.1328 1.1352(4)C–Cα 1.4668 1.4723(4)Cα–Cβ 1.5317 1.5349(1)Cβ–Cn 1.5263 1.5286(1)Cn–Cn — 1.5277(2)CP–CT — 1.5294(2)

N≡C–Cα 179.88 179.50(6)C–Cα–Cβ 112.24 112.36(2)Cα–Cβ–Cγ 111.68 111.90(3)Cβ–Cγ –Cδ 112.61 112.87(3)Cγ –Cδ–Cε 112.91 113.17(2)Cn–Cn–Cn — 113.29(7)Cn–CP–CT — 113.05(7)

a Values in brackets represent maximum differences to themean value in the last digit. R0 represents the specific value(if any) for the first molecule in the series containing this typeof bond.

types of bonds: C–N, C–Cα, Cα–Cβ , Cβ–Cn, Cn–Cn,and CP–CT bonds, which agree with the differenttypes of atoms found in atomic properties. It shouldbe emphasized that bonds Cn–CP are included inthe group Cn–Cn and bonds Cβ–Cn are in a specificgroup. It could indicate that CP atoms are more sim-ilar to Cn than Cβ , which is in agreement with thevalues obtained for N() and r1().

Bond Properties

The values obtained for bond ellipticity (Table VI)can be classified by considering the same atomsused for the above described properties. Values forCn–Cn, Cn–CP, and CP–CT bonds are in very goodagreement with those corresponding to n-alkanes:13 × 10−3, 15 × 10−3, and 6.9 × 10−3, respectively,in n-dodecane. Ellipticity is exactly zero only formolecule 1, which means that it is the only moleculewhere the charge density of the CN group presentsa perfect cylindrical symmetry.

The ρ(rc) values shown in Table VI can also beclassified considering the same types of atoms forthese molecules. All the values are positive, which istypical of covalent bonds. The ρ(rc) values are veryhigh for CN bonds, indicating an important chargeaccumulation between these atoms. Once more, re-sults for bonds implying Cn, CP, and CT atoms arein very good agreement with those correspondingto n-dodecane (0.2556 a.u. for Cn–Cn and 0.2542 a.u.for CP–CT). In both cases, alkanes and alkanenitriles,it is impossible to distinguish Cn–CP bonds fromCn–Cn bonds. The charge density is smaller in C–Cα

bonds, that present a decreasing in the bond or-der.

Table VI also contains the H(rc) values. This quan-tity presents a negative sign in all the bonds, whichindicates the covalent nature of all these bonds [36].The values of this property are considered trans-ferable in the same groups as charge density doesand they also agree very well with those corre-sponding to n-dodecane (−0.2200 a.u. for Cn–Cn

and −0.2185 a.u. for CP–CT). The highest value ofH(rc) corresponds to the C–C bond, which accumu-

TABLE VITransferable values for bond properties according to the position of the atoms with respect to the CN group(α, β, or further away, n) and to the terminal group (terminal = T, α to the terminal = P, and further away = n).a

103ε ρ(rc) (a.u.) H(rc) (a.u.)

C≡N 0.0 0.0 1.3 0.4919 0.4912(1) −0.8740 −0.2912(2)C–Cα 0.0 11 8.1 0.2687 0.2666(1) −0.2890 −0.2902 −0.2159(1)Cα–Cβ 16 24 22.0 0.2504(2) −0.2152 −0.2213(2)Cβ–Cγ 9 17 16.0 0.2552 0.2561(3) −0.2201 −0.2203(1)Cn–Cn 14.0 0.2557(3) −0.2204(2)Cn–CP 15.0CP–CT 7.2 0.2545(1) −0.2189(1)

a Values in brackets represent maximum differences to the mean value in the last digit. Values in first and second columns representspecific values (if any) in the first molecules of the series containing this type of bond.



71

LÓPEZ ET AL.

lates the greatest charge density in the internuclearzone, that is, the bond that has the highest values forρ(rc) and ε.

Conclusions

We have found transferable values for all theatomic and bond properties calculated, but the en-ergy, which displays variation with molecular size,cannot be considered as a transferable property. Thecomparison of the different values for the proper-ties, and the different patterns of variation with Zin the case of the energy, allow us to consider dif-ferent types of transferable atoms in alkanenitriles:(i) C and N atoms of the CN group; (ii) C in α to theCN group; (iii) C in β to the CN group; (iv) carbonof the terminal methyl group; (v) C previous to theterminal methyl group; and (vi) remaining C in thechain, whose behavior is similar to the C in hydro-carbons. On the other hand, a total of eight specificheavy atoms are present in the smallest linear alka-nenitriles: (i) C α of molecules 2 and 3; (ii) C β inmolecule 3 and 4; and (iii) C and N of the CN groupin molecules 1 and 2.

ACKNOWLEDGMENTS

Financial support by the autonomous govern-ment of Galicia (Project PGIDT-99X130102B), andCICyT, Spain (PD98-1085) is gratefully acknowl-edged. We are also indebted to Prof. R. F. W. Baderfor providing us a copy of AIMPAC suite of pro-grams and to CESGA for computer time. One of us(M.M.) thanks Universidade de Vigo for a postgrad-uated fellowship.

References

1. Shorter, J. In Patai, S.; Rapport, Z., Eds. The Chemistry ofTriple-Bonded Functional Groups; Wiley: Chichester, 1994;Chapter 5.

2. Botschwina, P.; Horn, M.; Matuschewski, M.; Schick, E.;Sebals, P. J Mol Struct (Theochem) 1997, 400, 119.

3. Allen, F. H.; Garner, S. E. In Patai, S.; Rapport, Z., Eds.The Chemistry of Triple-Bonded Functional Groups; Wiley:Chichester, 1994; Chapter 2.

4. Irvine, W. M. Space Sci Rev 1999, 90, 203.5. Rouvray, D. H. Topics Curr Chem 1995, 173, 1.6. Carbó, R.; Leyda, L.; Arnau, M. Int J Quantum Chem 1980,

17, 1185.7. Bader, R. F. W. Atoms in Molecules—A Quantum Theory;

International Series of Monographs on Chemistry, No. 22;Oxford University Press: Oxford, 1990.

8. Bader, R. F. W. Chem Rev 1991, 91, 893.

9. Bader, R. F. W. Can J Chem 1998, 77, 86.

10. Srebenik, S.; Bader, R. F. W. J Chem Phys 1975, 63, 3945.

11. Bader, R. F. W. Pure Appl Chem 1988, 60, 145.

12. Schwinger, J. Phys Rev 1951, 82, 914.

13. Bader, R. F. W.; Popelier, P. L. A.; Keith, T. A. Angew ChemInt Ed Engl 1994, 33, 620.

14. Cioslowski, J.; Nanayakkara, A. J Am Chem Soc 1993, 115,11213.

15. Cioslowski, J.; Stefanov, B. B.; Constans, P. J Comput Chem1996, 17, 1352.

16. Wiberg, K. B.; Bader, R. F. W.; Lau, C. D. J Am Chem Soc1987, 109, 1001.

17. Bader, R. F. W.; Carroll, M. T.; Cheeseman, J. R.; Chang, C.J Am Chem Soc 1987, 109, 7968.

18. Bader, R. F. W.; Larouche, A.; Gatti, C.; Carroll, M. T.; Mac-Dougall, P. J.; Wiberg, K. B. J Chem Phys 1987, 87, 1142.

19. Bader, R. F. W.; Keith, T. A.; Gough, K. M.; Laidig, K. E. MolPhys 1992, 75, 1167.

20. Bader, R. F. W.; Bayles, D. J Phys Chem A 2000, 104, 5579.

21. Graña, A. M.; Mosquera, R. A. J Chem Phys 1999, 110, 6606.

22. Graña, A. M.; Mosquera, R. A. J Chem Phys 2000, 113, 1492.

23. Vila, A.; Carballo, E.; Mosquera, R. A. Can J Chem 2000, 78,1535.

24. Bader, R. F. W.; Becker, P. Chem Phys Lett 1988, 148, 452.

25. Riess, J.; Münch, W. Theoret Chim Acta 1981, 58, 295.

26. Graña, A. M.; Mosquera, R. A. Chem Phys 1999, 243, 17.

27. Graña, A. M.; Mosquera, R. A. J Comput Chem 1999, 20,1444.

28. Vila, A.; Mosquera, R. A. J Phys Chem 2001, 115, 1264.

29. Vila, A.; Mosquera, R. A.; Hermida-Ramón, J. M. J MolStruct (Theochem) 2001, 541, 149.

30. Bader, R. F. W.; co-workers, Eds. AIMPAC: A suite of pro-grams for the Theory of Atoms in Molecules; McMasterUniversity, Hamilton, Ontario, Canada, L8S 4M1. [email protected].

31. Clark, T.; Chandrasekar, J.; Spitznagel, G. W.; Schleyer, P. R.J Comput Chem 1983, 4, 294.

32. Hariharan, P. C.; Pople, J. A. Theor Chim Acta 1973, 28, 213.

33. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.;Johnson, B. G.; Robb, M. A.; Cheeseman, J. R.; Keith, T. A.;Petersson, G. A.; Montgomery, J. A.; Raghavachari, K.; Al-Laham, M. A.; Zakrzewski, V. G.; Ortiz, J. V.; Foresman,J. B.; Cioslowski, J.; Stefanov, B. B.; Nanayakkara, A.; Challa-combe, M.; Peng, C. Y.; Ayala, P. Y.; Chen, W.; Wong, M. W.;Andres, J. L.; Replogle, E. S.; Gomperts, R.; Martin, R. L.;Fox, D. J.; Binkley, J. S.; DeFrees, D. J.; Baker, J.; Stewart,J. J. P.; Head-Gordon, M.; Gonzalez, C.; Pople, J. A. Gaussian94; Gaussian: Pittsburgh, PA, 1995.

34. NIST Chemistry Webbook, NIST Standard Reference Data-base Number 69, February 2000 Release, National Insti-tute of Standards and Technology, Gaithersburg, MD 20899(http://webbook.nist.gov).

35. Ishii, K.; Nakayama, H.; Koyama, K. Yokoyama, Y.; Ohashi,Y. Bull Chem Soc Jpn 1997, 70, 2085.

36. Cremer, D.; Kraka, E. Croat Chem Acta 1984, 57, 1259.

198 VOL. 86, NO. 2


72


73

A charge density analysis on the proximity effect in dicyanoalkanes

Jose Luis Lopez, Marcos Mandado, Marıa J. Gonzalez Moa, Ricardo A. Mosquera *

Departamento de Quımica Fısica, Facultade de Quımica, Universidade de Vigo, Lagoas-Marcosende, ES36310-Vigo, Galicia, Spain

Received 10 January 2006; in final form 5 March 2006Available online 10 March 2006

Abstract

QTAIM atomic and bond properties of 21 linear alkyl dicyanoalkanes of formula NC(CH2)nCN (n = 0–20), and three larger mole-cules: C32H66, NC(CH2)30CH3, and NC(CH2)30CN, indicate that cyano groups can be considered statistically equivalent to those of alarge cyanoalkane when they are separated by at least 14 methylene groups. When n < 19 there is at least one methylene group in thedicyanoalkane that differs significantly from those of NC(CH2)30CH3 or NC(CH2)30CN. Every cyano group produces an effect onthe methylenes that is nearly independent of the position of the other one, hydrogens being more sensitive than carbons. 2006 Elsevier B.V. All rights reserved.

1. Introduction

The term ‘proximity effect’ [1] was coined more than 20years ago and it is related to the development of molecularmodels for non electrolytes solutions [2]. These models dis-sect a molecule into building blocks that are assumed to beindependent, transferable, and characterised by a set ofparameters employed to compute diverse properties ofnon electrolyte mixtures. The proximity effect makes refer-ence to one of the main shortcomings of group contribu-tions models: the intramolecular interaction between two(or more) functional groups that affects their propertiesand those of the groups placed in their surroundings, inval-idating group transferability [3]. Thus, variations under-gone by the properties of atoms because of the presenceof another functional group has been invoked in qualitativediscussions on the behaviour of several mixtures of poly-functional compounds [4–6]. Several treatments have beenproposed to deal with this effect, ranging from empiricalvariations of the group parameters depending on their firstand second neighbouring groups [1], to quantitative correc-tions based upon Mulliken population analysis to adaptgroups defined for monofunctional compounds to poly-

functional molecules [3]. The suitability of these diversetreatments can be related to one question: are the changesundergone by the electron distribution of a certain atom ina molecule with two functional groups equivalent (in agood approximation) to the summation of the effects pro-duced by these functional groups in monofunctionalisedcompounds? or, on the contrary, does the proximity effectinvolve important cooperative effects between both func-tional groups?

The application of the Quantum Theory of Atoms in Mol-ecules (QTAIM) [7,8] on HF/6-31++G** electron densitiesproved that the oxygen atoms of RAOA(CH2)nAOAR 0

molecules are significantly different from those of the corre-sponding monoethers when n < 4 [9], confirming the pres-ence of the proximity effect when the oxygens are separatedby less than five bonds. QTAIM was also employed to ana-lyse the specificity of methylene groups placed between thetwo oxygens of diethers [10].

This work revisits the proximity effect using the QTAIMpartitioning but focusing on a,x-dicyanoalkanes. Thesecompounds have been recently employed to form hydro-gen-bonded complexes and inclusion compounds with urea[11], that are of practical interest in supramolecular chem-istry [12]. Atomic and bond properties of cyanoalkaneswere analysed in a previous QTAIM study [13], concludingthe approximate transferability of the ACN and ACH3

0009-2614/$ - see front matter 2006 Elsevier B.V. All rights reserved.

doi:10.1016/j.cplett.2006.03.019

* Corresponding author. Fax: +34 968 812 321.E-mail address: [email protected] (R.A. Mosquera).

www.elsevier.com/locate/cplett

Chemical Physics Letters 422 (2006) 558–564


74

mailto:[email protected]

groups for CH3A(CH2)nACN molecules when n > 2, andthat of ACH2A groups separated by three bonds fromACN and by two bonds from ACH3. This conclusion dif-fers from those obtained for homologous series that con-tain oxygen atoms: aldehydes and ketones [14], ethers[15], and alkanols [16]. In fact, ACH2A groups in thesecompounds are significantly modified by the functionalgroup when they are separated up to four bonds. Neverthe-less, it is a consequence of extending the Hohenberg andKohn theorem [17] to open systems [18] that perfect trans-ferability is an unreachable limit [19]. Therefore, we onlycan speak about approximate transferability that is foundwithin a certain transferability limit. It fact, most of theapproximate transferability studies hitherto performedwith the QTAIM have employed diverse subjective limits oftransferability and some of them, even, present alternativeconclusions depending on the specific criteria considered.However, Lorenzo et al. [20] revisited the approximatetransferability in n-alkanes by using statistical criteria forestablishing the limits of transferability. They concludedthat the ACH2A groups separated by three or four bondsfrom the ACH3 are specific groups in n-alkanes.

This Letter investigates the proximity effect on the ACNand ACH2A groups in a,x-dicyanoalkanes using statisticalcriteria for establishing the limits of transferability. Thesecriteria are based on the maximum deviations displayedby the properties of clearly transferable groups in largemolecules (see Section 2 for details), for which the atomicand bond properties can be considered equivalentundoubtedly. This procedure provides a larger number ofspecific groups than those obtained in previous works[13–16]. We also aim to explore if the proximity effect ismade up by additive contributions of isolated functionalgroups.

2. Computational details

HF/6-31++G** charge densities for full optimisedgeometries at the HF/6-31G** level were obtained forthe completely antiperiplanar conformers of the 21CNA(CH2)nACN molecules verifying 0 6 n 6 20, hereaf-ter denoted by their n value. Three larger molecules werealso studied. They included one n-alkane, C32H66 (A), onecyanoalkane, NC(CH2)30CH3 (C), and one dicyanoal-kane, NC(CH2)30CN (D). These molecules were fully opti-mised from the completely antiperiplanar conformation, t,and from that obtained after rotating the central dihedralangle to 60, g. All of these calculations were carried outusing the GAUSSIAN-98 program [21] setting the criterionfor SCF convergence to 1012 au. Although DFT calcula-tions would not increase the computational cost substan-tially, HF calculations were used in order to compare ourresults with those previously obtained for cyanoalkanes[13] and diethers [9,10] at the same level. Moreover, theHF method was proved to provide similar results, forstudies of transferability, to those obtained with DFT cor-related methods [22]. The topological QTAIM charge

density analysis was performed with the AIMPAC pack-age of programs [23].

This work is mainly concerned with atomic propertiessuch as the atomic electron population, N(X), the atomickinetic energy, K(X), and the normalized Shannon entropyof the electron distribution, Sh(X), as well as with bondproperties such as the bond distance, R, and the electrondensity at the bond critical points (BCP), q(rc). The prop-erties above were previously proved to be the very usefulin QTAIM studies of group transferability [13–16,20,22,24]. Moreover, the use of K(X) instead of the totalatomic energy, E(X), is required for transferability studies[25], unless the charge densities used satisfy the virial theo-rem to a high approximation, like those obtained in selfconsistent virial scaling (SCVS) calculations in the calcula-tion of E(X) [26].

The summations of QTAIM N(X) and E(X) valuesobtained in this work reproduce the total electron popula-tion, N, and the HF molecular energy, E, with a maximumdifference of 0.004 au and 4.0 kcal mol1 respectively. NoQTAIM atom was integrated with absolute values of theL(X) function [7] larger than 3.0 · 103 au. This accuracylevel was obtained at a larger computational cost for theg conformers than for the t ones. Thus, PROMEGA algo-rithm with a large number of gaussian quadrature rays wasrequired for the former, whereas PROAIM with standardintegration conditions was enough for the latter.

N(X) and L(X) values obtained for nearly transferableatoms display very good linear relationships, as previouslyfound in several studies on approximate transferability fordiverse series of compounds [9,10,13–16,20,24,27–29] andby Aicken and Popelier looking for an improvement inthe accuracy of computed atomic properties [30]. Also here,as in all the reported cases, the slopes of these N(X) vs.L(X) fitting lines approach 1 which indicates that L(X)mimics approximately the error made in the calculationof N(X). Therefore, the values of N(X) shown in this workwere obtained by correcting those computed by numericalintegration, Ncomp(X), with the corresponding value of theL(X) function through Eq. (1).

NðXÞ ¼ N compðXÞ þ LðXÞ ð1ÞLimits of transferability for atomic and bond properties

used throughout this work (Table 1) were establishedaccording to a statistic criterion: the maximum deviationwith respect to the mean value of groups that could be con-sidered equivalent ‘a priori’ in t conformers. Here weassume this equivalence for the cyano groups of C andD, the methyl groups of n-alkane A and cyanoalkane C,and the methylenes of the central backbone of the threelarge molecules that are separated from the ACN andACH3 groups by at least 9 and 3 methylene groups respec-tively. To obtain the limits of transferability for N atomswe have also considered the ACN groups of dicyanoalk-anes 16–20.

The effect on a given atomic property, A, of atom, X, ofa methylene due to a group in k or l positions can be

J.L. Lopez et al. / Chemical Physics Letters 422 (2006) 558–564 559


75

computed using Eqs. (2) and (3) respectively, where CHm2

represents a nearly transferable methylene of a n-alkane.

DAkðXÞ ¼ ½AðXÞkCH2 ½AðXÞmCH2

ð2ÞDAlðXÞ ¼ ½AðXÞlCH2

½AðXÞmCH2ð3Þ

When a methylene is simultaneously k and l to the func-tional groups, CHkl

2 , the cooperative effects on the electrondensity can be measured calculating the correspondingatomic excess property, DAE, defined with Eq. (4).

DAEðXÞ ¼ ½AðXÞklCH2þ ½AðXÞmCH2

½AðXÞkCH2 ½AðXÞlCH2

ð4Þ

3. Results and discussion

3.1. Comparison between large alkanes, cyanoalkanes, and

dicyanoalkanes

The values presented by the atomic properties, N(X),Sh(X) and K(X), of the cyano groups of the large dic-yanoalkane D are equivalent to those of the long cyanoal-kane C within 104 au for t conformers (Table 2). The same

agreement is obtained when comparing properties obtainedfor the g conformers of these molecules. Maximum differ-ences between properties computed for g and t conformersof the same molecule reach 4 · 104 au. Therefore, theproximity effect due to functional groups placed at theextremes of a long alkyl chain like that (n = 30) is belowcomputational accuracy or experimental errors and canbe considered negligible, as assumed for determining thetransferability limits presented in Table 1. Atomic proper-ties of D and A also show the transferability of the terminalACH3 group, which is unmodified by the t/g conforma-tional change. Moreover, the ACHm

2A (m representing posi-tions further than h) are not only equivalent in cyano anddicyanoalkanes but also to those of n-alkanes (Table 2). Inthis case the transferability limit has to be set to 4 · 104 auwhen considering g conformers.

As previously found for n-alkanes [20] the effect of themethyl groups over the properties of the neighbouringACH2A groups reaches up to the c position both in A

and C. Moreover, the properties of these groups, includingthe ACH3, are equivalent in both molecules. It must benoticed that the specificity of the ACHct

2 A group is givenby the properties of the carbon, whereas those of hydro-gens can be considered equivalent to those of a ACHm

2Agroup (Table 2). This also agrees with previous resultsobtained for n-alkanes [20]. On the other hand, the effectof the ACN group over the ACH2A reaches up to h posi-tion (the first 8 ACH2A groups) both in the cyanoalkane C

and the dicyanoalkane D. However, now the specificity ofthe ACHg

2 A and ACHh2A groups is provided by the hydro-

gens. This indicates the electron density of H and its asso-ciated properties are more sensitive to the proximity ofhigh electronegative groups than those of C. The fact thathydrogens tend to exceed the electron population changes

Table 2Nearly transferable atomic properties for C32H66 (A), NC(CH2)30CH3 (C) and NC(CH2)30CN (D) in t conformers

N(X) C Ha

N(X) K(X) Sh(X) N(X) K(X) Sh(X)

CN 4.8525 37.1295(1) 2.0593(1) 8.5459 55.1822 3.1064CHa

2 5.6966 37.6061(1) 2.3703(1) 1.0158 0.6388(1) 2.9045

CHb2 5.7882(1) 37.6635(1) 2.4055(1) 1.0648 0.6618 2.9474

CHc2 5.8064 37.6743(1) 2.4110(1) 1.0907 0.6711 2.9770(1)

CHd2 5.8039(1) 37.6722 2.4101(1) 1.0906 0.6711 2.9768

CHe2 5.8056(1) 37.6729(1) 2.4108 1.0949 0.6727 2.9824(1)

CHf2 5.8056(1) 37.6730(1) 2.4108 1.0948 0.6726(1) 2.9824

CHg2 5.8059(1) 37.6730(1) 2.4110 1.0961(1) 0.6731 2.9842(1)

CHh2 5.8059(1) 37.6730(1) 2.4110 1.0960(1) 0.6731 2.9841

CHm2 5.8062(1) 37.6732(1) 2.4111(1) 1.0968(1) 0.6734(1) 2.9853(1)

CHct2 5.8067(1) 37.6737 2.4113 1.0967 0.6733 2.9855(1)

CHbt2 5.8067(1) 37.6745 2.4113(1) 1.0967 0.6731 2.9863

CHat2 5.7942(1) 37.6574(1) 2.4095(1) 1.0939 0.6726(1) 2.9879

CH3 5.7790 37.6359 2.4360(1) 1.0809b 0.6601(1)b 3.0001b

1.0776(1)c 0.6590(1)c 2.9997c

Maximum discrepancies in the least significant digit are shown in parenthesis. All values but Sh(X) in au.a Values in CN correspond to the nitrogen atom.b Hydrogen in antiperiplanar arrangement to the carbon backbone.c Hydrogens in gauche arrangement to the carbon backbone.

Table 1Limits of transferability employed throughout the work

C H N

N(X) 0.0002 0.0004 0.0003Sh(X) 0.0001 0.0003 0.0001K(X) 0.0001 0.0001 0.0001

C„N CAC CAH

q(rc) 0.0001 0.0001 0.0001R 0.0001 0.0001 0.0001

All values in au but those of Sh(X) and R (in A).

560 J.L. Lopez et al. / Chemical Physics Letters 422 (2006) 558–564


76

experienced by carbons is not a new finding. For instance,the hydrogens in oxygenated and nitrogenated compoundsundergo the largest changes of the electron populationunder protonation or hydride addition processes, accord-ing to QTAIM and Hirshfeld partitionings [31].

Table 3 gathers the bond properties of C„N, CAC, andCAH bonds in large molecules. Like the atomic properties,they display transferable values for A, D, and C. However,bond properties are less sensitive and the specificity of sev-eral ACH2A groups is not shown by them. Thus, the effectof the ACH3 group over the bond properties of CAC andCAH bonds reaches up to b and a positions respectively,q(r) being the most sensitive bond property. On the otherhand, the effect of the ACN group over the bond propertiesreaches up to CcACd and CfAH bonds.

The rotation around the central CAC bond of A, D, andC introduces important variations in the atomic propertiesof all the atoms attached to this bond (Fig. 1). These vari-ations reduce along the carbon chain quickly. Nevertheless,methylenes that are a to d to the central bond differ fromthose considered transferable in t conformers more thanthe transferability limits presented in Table 1. Anyway,they do not affect at all the properties of methyl groupsin A and C. The properties of cyano and its neighbouringmethylenes are slightly affected (below 4 · 104 au forN(X)) in C and D. These groups would be coincident withthose of t conformers increasing the transferability limitsfor N(C) and N(N) to 4 · 104 au.

3.2. Approximate transferability in dicyanoalkanes

As found in previous works for other alkyl chains [13–16,20], an excellent linear correlation is found between thetotal molecular energies, E, and the number of methylenegroups, n, for the series of linear alkyl dicyanoalkanes in t

conformation. The residues of the molecular energies arenever larger than 0.5 kJ mol1 when the regression line isobtained by fitting compounds 8–20 (E = 39.03804n 184.63472, all values in au). Table 4 collects the atomic properties of the ACN group

in dicyanoalkanes with 0 P n P 20, approximate transfer-able values are remarked in bold face. It is noticeable thatthe N atom is more affected by the proximity of the otherACN group than the C. N(X) and K(X) values are notinfluenced significantly when n P 11 for C and n P 14for N, whereas Sh(X) turns out to be slightly more sensitiveto the proximity effect and its values does not converge upto n P 14 for C and n P 16 for N. Nevertheless, Sh(C) andSh(N) in molecules 11–13 and 14–15 do not differ respec-tively by more than 0.0002 and 0.0003 with regard to thetransferable value and could be included in the set of trans-ferable values.

It has to be mentioned that, using the transferability rule(n > 3) previously obtained for CH3O(CH2)nOCH3 dimeth-oxyethers [9] in dicyanoalkanes, the cyano groups presentan average electron population of 13.3950 au (RMS =8 · 104) that differs significantly from the correspondingvalue in C and D (13.3984 au) and from that reported in

Table 3Nearly transferable bond properties for C32H66 (A), NC(CH2)30CH3 (C)and NC(CH2)30CN (D) in t conformers

R [A] q(r) [au] R [A] q(r) [au]

N„C 1.1353 0.4910 CaAH 1.0849 0.2916CACa 1.4722(1) 0.2667(1) CbAH 1.0862 0.2903CaACb 1.5349(1) 0.2504(1) CcAH 1.0890 0.2865CbACc 1.5286(1) 0.2561(1) CdAH 1.0888 0.2866CcACd 1.5294 0.2555 CeAH 1.0891 0.2861CmACm 1.5294(1) 0.2557(1) CfAH 1.0891 0.2861CbtACat 1.5294 0.2560 CmAH 1.0892 0.2859CatACt 1.5278(1) 0.2544 CatAH 1.0885 0.2867

CtAH 1.0866(1)a 0.2855(1)a

1.0858b 0.2861(1)b

Maximum discrepancies in the least significant digit are shown inparenthesis.

a Hydrogen in antiperiplanar arrangement to the carbon backbone.b Hydrogens in gauche arrangement to the carbon backbone.

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

0 3 6 9 12 15i

Ng

( Ω)-

Nt ( Ω

) [au

·103 ]

C(dicyano)

H(dicyano)

C(cyano)

H(cyano)

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

0 3 6 9 12 15i

Ng

( Ω)-

Nt ( Ω

) [au

·103

]

C(alkane)

H(alkane)

C(cyano)

H(cyano)

(a)

(b)

Fig. 1. Plot of the variations due to the g/t conformational changeexperienced by atomic electron populations (au multiplied by 103) of acertain group placed at i bonds from the ACN group (a) or from themethyl group (b). N(H) at i = 0 in plot (a) refers to the nitrogen atom.



77

the transferability study of cyanoalkanes (13.398 au) [13].In contrast, the atomic electron population of the oxygenatom extrapolated to L(O) = 0 through N vs. L linear rela-

tionships, N0(O), for the set of CH3O(CH2)nOCH3

(3 < n < 12) compounds (9.3163 au) [9] is in very goodagreement with the N0(O) value obtained for alkyl meth-oxyethers (9.3161 au) [28]. This points the proximity effecton functional groups is more intense in dicyanoalkanesthan in diethers.

The ACH2A groups in dicyanoalkanes 0–20 are consid-ered equivalent to those of D when the values of theiratomic and bond properties are within the range estab-lished by the maximum deviations shown in Table 1.Otherwise they are considered specific groups, which arenamed indicating their position with regard to both func-tional groups (Table 5). Since the influence of the ACNgroup in large cyanoalkanes and dicyanoalkanes reachesup to the h position for hydrogens, all the ‘a priori’expected ACH2A specific groups for the series of alkyldinitriles are presented in a matrix fashion in Table 5.The Table is completed with other groups to indicate thatnearly transferable values are achieved when the ACH2Agroups are placed further away from the cyano groups.

The properties of the carbon of a methylene group con-verge to those of the nearly transferable ACHm

2A groupwhen n > 16 (for these molecules the calculated main valuesof N(C), Sh(C) and K(C) are respectively 5.8061 au, 2.4110and 37.6731 au). On the other hand, the specificity of thecorresponding hydrogen is increased by the presence oftwo ACN groups. In this case the atomic properties ofmethylenic hydrogen converge to those of ACHm

2A whenn > 19, thus increasing the effect of the ACN groups up

Table 4Atomic properties of the ACN group for the dicyanoalkanes of formulaNC(CH2)nCN (0 < n < 20) in t conformer

n N(X) Sh(X) K(X)

C N C N C N

0 4.6566 8.3433 1.9497 3.0338 37.0015 55.10021 4.7991 8.4714 2.0322 3.0772 37.0938 55.15552 4.8442 8.5109 2.0548 3.0928 37.1257 55.17063 4.8442 8.5228 2.0546 3.0972 37.1249 55.17524 4.8491 8.5327 2.0576 3.1012 37.1276 55.17785 4.8501 8.5360 2.0583 3.1026 37.1274 55.17846 4.8509 8.5400 2.0585 3.1040 37.1288 55.18067 4.8514 8.5412 2.0587 3.1045 37.1291 55.18088 4.8519 8.5428 2.0587 3.1051 37.1295 55.18149 4.8519 8.5434 2.0589 3.1054 37.1293 55.1816

10 4.8521 8.5443 2.0592 3.1057 37.1293 55.181811 4.8523 8.5444 2.0592 3.1058 37.1294 55.181712 4.8525 8.5447 2.0592 3.1059 37.1297 55.181713 4.8523 8.5451 2.0592 3.1060 37.1294 55.182414 4.8523 8.5454 2.0593 3.1061 37.1295 55.182415 4.8524 8.5453 2.0595 3.1061 37.1295 55.1823

16 4.8525 8.5455 2.0593 3.1062 37.1296 55.1821

17 4.8526 8.5454 2.0595 3.1063 37.1295 55.1822

18 4.8526 8.5455 2.0593 3.1062 37.1297 55.1821

19 4.8526 8.5456 2.0593 3.1063 37.1297 55.1822

20 4.8526 8.5456 2.0595 3.1063 37.1295 55.1821

Transferable values are highlighted in italic-bold face. All values but Sh(X)in au.

Table 5Relative atomic electron population corrected with Eq. (1) for the specific ACH2A groups for the dicyanoalkanes of formula NC(CH2)nCN (0 < n < 20) int conformer

a b c d e f g h i j

a C 103.9H 82.6

b C 16.8 17.1H 33.2 32.8

c C 1.0 0.6 0.5H 6.9 6.6 6.2

d C 1.7 2.0 2.1 2.2H 6.7 6.6 6.4 6.4

e C 0.2 0.5 0.7 0.4 0.7H 2.2 2.2 2.1 2.1 2.1

f C 0.2 0.6 0.5 0.6 0.5 0.6H 2.3 2.2 2.2 2.1 2.2 2.1

g C 0.0 0.3 0.4 0.0 0.3 0.2 0.2H 0.9 0.8 0.8 0.8 0.8 0.8 0.7

h C 0.0 0.3 0.2 0.3 0.2 0.2 0.5 0.0H 1.0 1.0 0.9 0.9 0.9 0.9 0.9 0.9

i C 0.2 0.1 0.2 0.1 0.2 0.4 0.0 0.1 0.2H 0.4 0.3 0.3 0.3 0.4 0.3 0.3 0.3 0.5

j C 0.0 0.2 0.1 0.2 0.4 0.0 0.2 0.0 0.2 0.2H 0.4 0.3 0.4 0.3 0.4 0.3 0.3 0.3 0.5 0.5

The groups are named by their positions with respect to the ACN groups. All values are in au multiplied by 103 and relative to the transferable methylenes(ACHa

2A to ACHm2A) listed in Table 2.



78

to the i position (for molecules with n > 19 the main valuesof N(H), Sh(H) and K(H) are respectively 1.0966, 2.9851and 0.6732 au).

Since the bond properties are found to be less sensitiveto the effect of the ACN group, as found for dicyanoalkaneD, the specificity of the ACH2A groups along the alkylchain seems to be more reduced when these propertiesare employed.

Employing the rough transferability criterion used in theprevious study of cyanoalkanes [13] (5.103 au for N(C)),we obtain no modification in the number of specific meth-ylenes in the long molecules (Ca and Cb) and three specificmethylene groups in small dicyanoalkanes (Caa, Cab, andCbb). Nevertheless, if the same criterion is extended toN(H) we observe that the specificity of groups has to beextended up to d position, in accordance with the resultobtained for diverse series of oxigenated compounds. Theproximity of other ACN group gives rise to ten specificgroups (ACHaa

2 A,ACHab2 A, . . . ,ACHdd

2 A) .The variation of the atomic properties introduced in the

diverse methylenes by the second ACN group with regardto those of a long cyanoalkane, like C, (Fig. 2) indicatesthat hydrogens are more sensitive than carbons to theproximity effect. It can also be observed that the intensityof the proximity effect on a certain methylene is practicallyindependent (if Ccc is excluded) on the nature of the meth-ylene. In fact DN(X) is practically equal for every kind ofcarbon and hydrogen in Fig. 2 and its value only dependsupon the distance to the other ACN group, k.

Another question of practical importance is if the prox-imity effect could be considered additive or if it displays sig-nificant cooperativity. That is, if the modification of theatomic properties of a specific methylene group, likeACHac

2 A with respect to a transferable ACHm2A (common

to every functional group and n-alkanes) can be obtained

summing the corresponding differences between ACHa2A

and ACHm2A and ACHc

2A and ACHm2A, when ACHa

2Aand ACHc

2A are nearly transferable groups for a cyanoal-kane (in this case). Fig. 3 indicates this is a very goodapproximation for most of the specific groups here defined.The only significant discrepancies (exceeding 8 · 104 auand representing always less than 3% of the total variationof atomic electron population) are obtained for aa, ab, ac,and bb methylenes. It has to be mentioned this trend is notfollowed by other homologous series, like dimethoxyetherswhere significant cooperative effects can be observed inDNE(CH2) even for CHdc

2 (0.0164 au) or CHdd2 (8 · 104

au).

4. Conclusions

Atomic properties are more sensitive than the bondproperties in studies of group transferability. The use ofstatistical parameters such as the maximum deviation forestablishing the limits of transferability allows to distin-guish a larger number of specific groups than the oneobtained in previous works [9,10]. Thus, the following 12methylene groups can be distinguished for a large cyanoal-kane: CHa

2, CHb2, CHc

2, CHd2, CHe

2 , CHf2 , CHg

2 , CHh2, CHm

2,CHct

2 , CHbt2 and CHat

2 , where CHm2 is the methylene group

for which the influence of the functional group is negligible,and the properties are equivalent to those of an internalCH2 of a large n-alkane. ACH3 and ACH2A groups dis-play transferable properties for large alkanes, cyanoalk-anes, and dicyanoalkanes. The properties of the cyanogroups are also transferable from large cyanoalkanes tolarge dicyanoalkanes. H atoms are more sensitive to the

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

2

0 2 4 6 8 10k

ΔΔ ΔΔ(

NΩΩ ΩΩ

)

C H

C H

C H

C H

C H

α α

β β

γ γ

δ δ

ε ε

Fig. 2. Plot of the variations experienced by the electron population (aumultiplied by 103) of C and H of a certain methylene group when a secondACN group is attached at k bonds from it. DN(Ca) is computed as thedifference between N(Ca) in a certain dicyanoalkane where the corre-sponding CH2 group is separated k bonds from the other ACN group andthat in CNA(CH2)30ACH3. All data were computed for t conformers.

-1

0

1

2

3

4

5

6

0 2 4 6 8 10

k

ΔΔ ΔΔN

E01·

ua[ )C(

3 ]

αβγδε

-2

-1

0

0 2 4 6 8 10kΔΔ ΔΔ

NE

01·ua[ )

H(3 ]

Fig. 3. Plot of the excess electron population, DNE(X), of C and H atoms(in au multiplied by 103) of specific methylenes shown in Table 5. DNE(X)values computed with Eq. (4) for t conformers. k represents the number ofmethylenes between the specific group and the second functional group.



79

presence of ACN than C, however they are less sensitive tothe presence of a ACH3.

The mutual influence between two ACN groups (prox-imity effect) in alkyl dinitriles is negligible when n > 14.The specificity is mainly due to the N atom whose atomicproperties converge to a transferable value later than thoseof C. The presence of two ACN increases the specificity ofthe ACH2A groups, their atomic properties does not con-verge to those of a large dicyanoalkane or cyanoalkaneuntil the i position due to the hydrogens, whose atomicproperties converge to a transferable value later than thoseof C. The effects observed in a specific methylene of a dic-yanoalkane can be considered as the summation of thosedue to independent CN groups if we exclude the methyl-enes of molecules CN(CH2)nCN with n < 4, where cooper-ative effects for the atomic electron population are between5.7 · 103 and 8 · 104 au. This trend cannot be extendedto other homologous series.

The effect of the conformation change was studied con-sidering the rotation around the CAC central bond ofC32H66, NC(CH2)30CH3, and NC(CH2)30CN. We havefound significant differences for methylene groups thatare a to d to that bond. Nevertheless the conformationaleffect does not change the conclusions here presented ifthe transferability limits for N(C) and N(N) are increasedto 4 · 104 au.

Acknowledgements

We thank Luis Alberto Lopez for his encouraging sup-port and ‘Centro de Supercomputacion de Galicia’ (CES-GA) for access to their computational facilities.

References

[1] H.V. Kehiaian, Fluid Phase Equilibria 13 (1983) 243.[2] S.I. Sandler, Models for Thermodynamic and Phase Equilibria

Calculations, Marcel Dekker, New York, 1994.[3] S.-T. Lin, S.I. Sandler, J. Phys. Chem. A 104 (2000) 7099.

[4] D. Gonzalez-Salgado, C.A. Tovar, C.A. Cerdeirina, E. Carballo, L.Romanı, Fluid Phase Equilibria 199 (2002) 121.

[5] S. Delcros, J.R. Quint, J.P.E. Grolier, H.V. Kehiaian, Fluid PhaseEquilibria 113 (1995) 1.

[6] H.S. Wu, S.I. Sandler, AIChE Journal 35 (1989) 168.[7] R.F.W. Bader, Atoms in Molecules – A Quantum Theory Interna-

tional Series of Monographs on Chemistry, vol. 22, Oxford Univer-sity Press, Oxford, 1990.

[8] R.F.W. Bader, Chem. Rev. 91 (1991) 893.[9] A. Vila, R.A. Mosquera, Chem. Phys. Lett. 345 (2001) 445.

[10] A. Vila, E. Carballo, R.A. Mosquera, J. Mol. Struct. (THEOCHEM)617 (2002) 219.

[11] A.E. Aliev, K.D.M. Harris, P.H. Champkin, J. Phys. Chem. B 109(2005) 23342.

[12] K.D.M. Harris, in: J.L. Atwood, J.W. Steed (Eds.), Encyclopedia ofSupramolecular Chemistry, vol. 2, Marcel Dekker, New York, 2004,pp. 1538–1549.

[13] J.L. Lopez, M. Mandado, A.M. Grana, R.A. Mosquera, Int. J.Quantum Chem. 86 (2002) 190.

[14] A.M. Grana, R.A. Mosquera, J. Chem. Phys. 113 (2000) 1492.[15] A. Vila, R.A. Mosquera, J. Chem. Phys. 115 (2001) 1264.[16] M. Mandado, A.M. Grana, R.A. Mosquera, J. Mol. Struct.

(THEOCHEM) 584 (2002) 221.[17] L. Lorenzo, R.A. Mosquera, Chem. Phys. Lett. 356 (2002) 305.[18] P. Hohenberg, B. Kohn, Phys. Rev. B 136 (1964) 864.[19] J. Riess, W. Munch, Theor. Chim. Acta 58 (1981) 295.[20] R.F.W. Bader, P. Becker, Chem. Phys. Lett. 148 (1988) 452.[21] M.J. Frisch et al., GAUSSIAN 98, Revision A.7., Gaussian Inc.,

Pittsburgh, PA, 1998.[22] M. Mandado, R.A. Mosquera, A.M. Grana, Chem. Phys. Lett. 355

(2002) 529.[23] AIMPAC: A suite of programs for the Theory of Atoms in

Molecules; R.F.W. Bader and coworkers, Eds. McMaster University,Hamilton, Ontario, Canada, L8S 4M1. Available from:<[email protected]>.

[24] M. Mandado, A.M. Grana, R.A. Mosquera, J. Mol. Struct.(THEOCHEM) 572 (2001) 223.

[25] M. Mandado, A. Vila, A.M. Grana, R.A. Mosquera, J. Cioslowski,Chem. Phys. Lett. 371 (2003) 739.

[26] F. Cortes-Guzman, R.F.W. Bader, Chem. Phys. Lett. 379 (2003) 183.[27] A.M. Grana, R.A. Mosquera, J. Chem. Phys. 110 (1999) 6606.[28] A. Vila, E. Carballo, R.A. Mosquera, Can. J. Chem. 78 (2000) 1535.[29] P.B. Quinonez, A. Vila, A.M. Grana, R.A. Mosquera, Chem. Phys.

287 (2003) 227.[30] F.M. Aicken, P.L.A. Popelier, Can. J. Chem. 78 (2000) 415.[31] M. Mandado, C. Van Alsenoy, R.A. Mosquera, J. Phys. Chem. 108

(2004) 7050.



80


81

Electron Density Analysis on the Protonation of Nitriles

Jose Luis Lopez, Ana M. Grana, and Ricardo A. Mosquera*Departamento Quımica Fısica, UniVersidade de Vigo, Lagoas-Marcosende, 36310-Vigo, Galicia (Spain)

ReceiVed: December 14, 2008; ReVised Manuscript ReceiVed: January 9, 2009

The applicability of the resonance model to explain the evolution of electron density was tested for a set of15 nitriles whose protonation processes were studied by means of the quantum theory of atoms in molecules(QTAIM). The electron densities were obtained at the B3LYP/6-31++G**//B3LYP/6-31++G** and HF/6-31++G**//HF/6-31++G** levels. QTAIM atomic and bond properties do not follow the trends that shouldbe expected according to the resonance model and our results are more in line with a H+-NtC-R Lewisstructure than with the H-N+tC-R and H-NdC+-R ones. Also, reasonable agreement between experimentaland calculated PA values as well as good correlations between variations in atomic energies and populationsas a result of protonation were found.

Introduction

The applicability of the resonance model (RM) to explainthe structure and reactivity of organic compounds has beengenerally accepted1,2 and has proved to be a very useful tool inchemistry. Nevertheless, topological analysis of electron densi-ties carried out with the quantum theory atoms in molecules(QTAIM)3,4 for diverse processes have reported evolutions ofthe electron density that are not in line with the predictionsprovided by the RM. These disagreements appear even for sosimple processes as internal rotations,5,6 protonations,7-9 orhydride additions.10 Also, QTAIM results are inconsistent withthe Lewis structures traditionally accepted for some chargedcompounds, like diazonium salts11 or protonated ethers.12-14 Thepublication of the first study reporting on the disagreementsbetween RM and QTAIM was followed by a controversy aboutthe suitability of QTAIM for this kind of studies.15-17 Nowadays,this controversy seems to be solved clearly in favor of QTAIMapplicability.16,17 Moreover, most of the qualitative conclusionsobtained from QTAIM studies on protonation and hydrideaddition are confirmed by other electron density analysis,9,10 likeHirshfeld partitioning.18,19

H-NdC+-R Lewis structures have been traditionally em-ployed for describing protonated nitriles in diverse reactionmechanisms. These structures are, in the context of the RM,the result of transforming one π electron pair of the NtC triplebond into the N-H bond. Alternatively, the protonation processcould be understood as the formation of a dative bond betweenN and proton using the nitrogen lone pair, a process representedby the H-N+tC-R resonance form. These are basically thesame schemes used for explaining protonations at other elec-tronegative sites, which have been recently found in controversywith the QTAIM studies carried out for the N-protonation ofindole,20 O-protonation of simple carbonyl systems,9 and N/O-protonations on diverse pyrimidinic bases.7,8,21 All of thesestudies point to H+-X-R structures (XdO or N and the X-Rbond being single or double). QTAIM results for these systemsalso indicate that the formation of the H+-X bond is ac-companied by an electron density redistribution affecting thewhole molecule. Hydrogens act very effectively as a source ofelectron density for this redistribution, as reported by Stuchbury

and Cooper studying the basicity of NH3 and the series ofmethylamines.22

In this work, we have carried out a QTAIM study on theprotonation of several cyanocompounds. This allows to studyif the triple bonding modifies the trends hitherto observed forother compounds. The molecules here studied include both linearand branched cyanoalkanes as well as compounds where thecyano function is conjugated with π delocalized systems. Thus,we have been able to establish trends for the size of linear alkylchains (1-6), conformational change (4, 7), alkyl chainramification (2, 3, 8, 9), electronegativity of the substitutents(2, 10), and π-delocalization (11-15) (Table 1).

Computational Details

QTAIM allows the partitioning of a molecule into disjointsubsystems without resorting to hypothesis alien to quantummechanics.3,4 With a few exceptions,23 each of these subsystemsconsists of a nucleus, which acts as an attractor for thetrajectories of the gradient of the electron density vector field,3F(r), and its associated atomic basin, throughout thesetrajectories spread. An atom, Ω, is defined as the union of theattractor and its associated basin, and it is surrounded by zeroflux surfaces for 3F(r). The integration of the proper densityfunctions within these limits provides diverse atomic propertiessuch as the electron population, N(Ω), or the total atomicelectron energy, E(Ω). In this article, we have considered the σand π components of the atomic electron population, Nσ(Ω)and Nπ(Ω), respectively.

QTAIM also recovers main elements of molecular structurein terms of the critical points, rc, of the electron density, F(r).Prominent among them are the bond critical points (BCPs),which are located roughly in between every pair of bondedatoms. Although the relationship between the presence of a BCPand the existence of a chemical bonding has become acontroversial and it is still a debated point of the theory,24-29

the electron density at a certain BCP is regarded as an indicatorfor bond strength.

All the neutral (1 to 15) and protonated (1+ to 15+) specieshere considered (Table 1) were fully optimized at the HF/6-31++G(d,p) and B3LYP/6-31++G(d,p) levels using the pro-gram GAMESS.32 The optimization was performed using theself-consistent virial scaling (SCVS) method introduced by Lehd* To whom correspondence should be addressed.

J. Phys. Chem. A 2009, 113, 2652–26572652

10.1021/jp811023x CCC: $40.75 2009 American Chemical SocietyPublished on Web 02/23/2009


82

and Jensen31 until the molecular virial ratio, γ, obtained differsfrom its ideal value by less than 3 × 10-6. This procedure hasproved to solve32 shortcomings previously reported for QTAIMatomic energies.33 Nevertheless, as the atomic energies areobtained by correcting atomic electron kinetic energies, K(Ω),with γ, and part of the electron kinetic energy is considered inDFT within the exchange-correlation term, we will only madeuse of E(Ω) values obtained with HF electron densities. Incontrast, for the sake of simplicity, we will only refer to B3LYPN(Ω) electron populations. In this case, both computationallevels give rise to different absolute N(Ω) values, but the relativevalues obtained for the protonation process, ∆N(Ω), aresignificantly similar and correlated (Figure 1) if we exclude someexceptions like the decrease of electron population at the C ofthe cyano group, which is always more depleted according tothe B3LYP level (around 0.055 au more, but in delocalizedsystems 11-15 where the difference exceeds 0.09 au). Signifi-cant differences between ∆NHF(Ω) and ∆NB3LYP(Ω) values are

also observed for the C in R to the cyano group in delocalizedsystems. They range is from 0.049 au in 13 to 0.061 au in 11.

The electron densities obtained were analyzed with theQTAIM by means of the program AIMPAC.34,35 The accuracyof the integrated properties was tested using the differencesbetween molecular properties and those obtained by summationof the properties of the fragments [N - ΣN(Ω) or E - ΣE(Ω)](Table 1). These differences are always smaller (in absolutevalue) than 2 × 10-3 au and 1.2 kJ/mol respectively, which arefound to be accurate enough comparing with other works carriedout at similar theoretical levels. In the same vein, the integratedvalues of the laplacian of the electron density in all of the atomicfragments, L(Ω), are always smaller (in absolute value) than10-3 au.

Proton affinities at the N atom (Table 1) were calculatedtaking into account the thermal and zero point vibrationalcorrections (unscaled) obtained for protonated and neutralspecies. The correction term for transforming reaction internalenergies into reaction enthalpies was considered as well.

Results and Discussion

Atomic and bond properties of neutral nitriles, as well as the32F(r) topology, have been described thoroughly in a previousHF study by Aray et al.36 As our results for neutral moleculesare in perfect agreement with theirs, we focus our discussionon the effects of protonation.

Proton Affinities. There is a reasonable agreement betweencomputed and experimental37 proton affinities (PAs), which areslightly improved at the B3LYP/6-31++G(d,p) level withregard to the HF/6-31++G(d,p) one (Table 1) and previous HFvalues obtained with smaller basis sets.38 The only exceptionfor this general trend is benzonitrile, 13, where the HF/6-31++G(d,p) PA is closer to the experimental one. This moleculedisplays the largest discrepancy between B3LYP and experi-mental PA (18 kJ mol-1), whereas most of them are below 10kJ mol-1.

The largest PAs correspond to delocalized systems 12-15.In fact, according to Table 1, PAs of nitriles increase withmolecular size and π-delocalization. Also, cyanoalkanes 2-9display a good linear correlation (r2 ) 0.98) between PAs andN(H+) (Figure 2). PAs of delocalized 11-15 apart less than 7kJ mol-1 from this fitting line, whereas 1 and 10 are clearoutliers.

TABLE 1: Proton Affinities (kJ mol-1) and Accuracy Estimators for QTAIM Integrations for the R-CtN Molecules HereStudied

R PA (HF) PA (B3LYP) PAa N - ΣN(Ω)b E - ΣE(Ω)c |L(Ω)|d

1 H 721.1 710.3 712.9 -0.4 (0.0)f -0.4 (-0.2)f 0.52 CH3 791.7 786.4 779.2 0.1 (0.0) 0.1 (-0.2) 0.23 CH3CH2 804.7 800.2 794.1 -0.6 (0.2) -0.4 (0.0) 0.14 CH3(CH2)2 anti 810.7 807.3 798.4e 0.2 (0.4) 0.1 (0.1) 0.95 CH3(CH2)3 811.5 810.8 802.4 1.2 (1.9) 0.7 (1.2) 0.76 CH3(CH2)4 813.5 814.1 -0.3 (1.2) -0.2 (0.7) 0.87 CH3(CH2)2 gauche 810.2 807.0 -1.5 (-0.3) -0.9 (-0.4) 0.18 CH(CH3)2 815.1 810.6 803.6 -0.1 (0.4) -0.2 (0.0) 0.79 C(CH3)3 824.1 820.6 810.9 1.0 (0.2) 0.5 (-0.2) 0.910 CF3 678.8 671.8 688.4 0.3 (0.7) 0.0 (0.2) 0.511 CH2dCH 802.7 795.2 784.7 -0.6 (0.2) -0.8 (0.5) 1.012 CH2dCH-CHdCH 836.7 835.6 1.0 (-0.6) -1.0 (-0.6) 0.913 C6H5 826.6 829.4 811.5 2.0 (0.8) 1.0 (0.1) 0.914 C10H7 (R) 849.0 848.3 -0.6 (0.1) -0.5 (0.2) 0.415 C10H7 () 849.4 848.8 -0.1 (0.4) -0.6 (0.7) 1.3

a Experimental values taken from ref 37. b Values in au multiplied by 103. c In kJ mol-1. d Maximum absolute value of integrated L(Ω) in theneutral molecule and its protonated species, in au multiplied by 103. e Experimental value assigned to the most stable conformer in this table.f Values for protonated species in parenthesis.

Figure 1. Variations experienced by the atomic populations, ∆N(Ω),of 1-12 upon N-protonation as computed from HF and B3LYP electrondensities. All values in au multiplied to 103. The line shown in plotcorresponds to the ideal ∆NHF(Ω) ) ∆NB3LYP(Ω) equivalence.

Protonation of Nitriles J. Phys. Chem. A, Vol. 113, No. 11, 2009 2653


83

The PA values shown in Table 1 could be taken as anindication that electron delocalization raises the PA. Neverthe-less, we should also notice that the size of the substituents, andmore concretely the number of hydrogens in the molecule,increase PA values. Thus, when we compare PAs obtained forsaturated and unsaturated substituents with similar size or similarnumber of hydrogens (e.g., 3 and 11) we realize the PA for anitrile bearing an unsaturared substituent is lower than that forthe corresponding compound with a saturated group.

Protonation Effects on Atomic Electron Populations. Asa general trend, we observe (Figure 3) that the proton keeps avery positive charge when attached to the cyanocompound(always larger than +0.62 au), which is more in line with aH+-NtC-R Lewis structure than with the H-N+tC-R andH-NdC+-R ones. This charge is more positive than thatcomputed at the same level for the N-protonated forms ofpyrimidinic bases (+0.48 to +0.51 au).7 They are also largerthan those computed at the MP2/6-311++G(d,p) level forprotonated methylamine (+0.477 au) and protonated methyl-enimine (+0.511 au).9 As the computational level does not affectvery much QTAIM charges, we can say that the positive chargeat the proton grows with the s character of N hybridization.This trend was not found for O-protonations, where the atomiccharge of the proton remains around +0.66 au independentlyon the O hybridization as shown with MP2/6-31++G(d,p)studies on linear alkyl ethers13 and ketones39 and B3LYP/6-31++G(d,p) studies on cyclic ethers14 and pyrimidinic bases.7

The electron density of the molecule evolves upon protonationfollowing the mechanism previously reported for other O-pro-tonations7-9,21 and N-protonations.7,8,20,21 Thus, for 1 the electrondensity gained by the proton is provided by the N atom, whichloses 0.335 au of σ electron density and 0.010 au of π electrondensity. Nevertheless, the electron population of the N atom isnot reduced in the protonated form, but enlarged. This is dueto the deformation of the electron density in the whole moleculeproduced by the proton, which gives rise to electron densitytransferences between neighboring atoms.8 Thus, N receivesfrom C 0.360 and 0.112 au of σ and π density respectively in1. At the same time, the H atom transfers 0.171 and 0.019 of σand π electron density to the C. It can be observed that theproton enlarges more the polarization of the π density in NtCthan in the σ one. The reason may be that the σ electron pair isalready much more polarized than the π ones in the neutralmolecule (1.575 au of the σ pair belongs to the N basin, whereas

1.331 au of each of the π pairs are within that basin, all datataken from molecule 1).

When the H of HCN is replaced by an alkyl group, theelectron population lost by the C atom is significantly reduced.This is due to the σ electron density provided by the neighboringalkyl group, R, which increases with the size of the group,though approaching a convergence limit. Thus, the electrondensity provided by R represents approximately 2/3 parts of thetotal electron transference for a long chain cyanoalkane, like 6.Most of this electron population supplied by the alkyl groupcomes from the depletion of hydrogen electron populations. Infact, the electron populations of the carbons in the alkyl group(2-10) present little variations that are sometimes positive(Figure 3). ∆N(Ω) variations experienced by each of thehydrogen atoms can be rationalized using the scheme presentedin previous papers to explain the protonation trends of uracil8

and cytosine.21 Thus, (i) the closer the distance to the proton,the easier the electron density donation; and (ii) the donation

Figure 2. Plot of B3LYP/6-31++G(d,p) PAs (in kJ mol-1) vs N(H+)(in au) for 2-9 and 11-15. The fitting line corresponds to alkyl 2-9.Compounds 1 and 10 are clearly outside of this linear fitting and arenot shown in the figure.

Figure 3. Variations of atomic electron population, ∆N(Ω), experi-enced upon protonation by 1-10 (in au multiplied by 103) and electronpopulation gained by the proton (in italics). ∆N(Ω) is only shown forone of those atoms related by symmetry.

TABLE 2: Variations of Atomic π-Electron Population (inau Multiplied by 103) Experienced by 11-15 uponProtonation; ∆N(R) Indicates the Summation of π and σAtomic Electron Populations Experienced by the Whole RGroup.

∆Nπ(N) ∆Nπ(CCN) ∆Nπ(CR) ∆Nπ(CR) ∆N(R)

11 233 -75 32 -143 -13912 265 -30 50 -216 -19413 250 -47 53 -189 -20114 264 -23 53 -225 -24815 263 -28 54 -220 -233

2654 J. Phys. Chem. A, Vol. 113, No. 11, 2009 Lopez et al.


84

of electron population between bonded atoms follows thedirection of the bond. The orientation of the bond with regardto the proton makes the electron transference easier (when theelectron density approaches the proton) or more difficult (whenthe electron density moves away the proton). Thus, for instance,the hydrogens bonded to C3 in butanenitrile 4 lose less electronpopulation (-0.030 au) than the hydrogen in antiperiplanararrangement bonded to C4 (-0.045 au) (Figure 3).

When the alkyl chain experiences an internal rotation, as from4 to 7, the only ∆N(Ω) values significantly affected are thoseof the group rotated, where the electron transfers among thediverse atoms are reorganized taking into account the neworientation and distances to the proton, as can be seen in Figure3. We have also considered an eclipsed conformation of theterminal methyl for this compound, where the two out of planehydrogens are in favorable orientations to transfer electrondensity to C4 and the in plane hydrogen orientates its C-H bondmoves electron density away the proton. The result is the formerexperiences depletions of -0.040 au in the protonated form,whereas the later only reduces its population in -0.021 au.

The presence of branched substituents, like Pri (in 8) or But

(in 9) has qualitatively the same effect as the enlargement ofthe alkyl chain. Nevertheless branched substituents are quan-titatively more efficient to increase the electron donation, asthey arrange more hydrogens close to the proton, which act aselectron density sources. Thus, it can be observed that Pri

experiences larger transferences than Prn, Bun, and even Pen

(Figure 3). This is also true for But, but this substituent doesnot suppose any increase of electron transference with regardto Pri.

When the hydrogens of 2 are replaced by much moreelectronegative atoms, like in 10, the electron populationtransferred to the proton is reduced. In this case, the carbon ofthe CF3 group is the largest donor. It is also significant that

electron density gained by the nitrogen achieves its maximumin the series (Figure 3).

The protonation of nitriles that contain π-conjugated substit-uents shows a significant contrast with that of cyanoalkanes(Table 2). Thus, the carbon atoms of the substituent experiencean important reduction of π-electron density upon protonation,whereas the σ-electron density remains practically unchangedas in cyanoalkanes. This reduction of Nπ(C) is combined withsmaller donations from hydrogen atoms. Nevertheless, π-elec-tron transferences from the substituent in the molecules herestudied (11-15) are so large that the total transferences to theprotonated nitrile exceed always those observed for largecyanoalkanes (showing larger electron density increases at Nand the proton). It is also significant that the electron densitylost by the carbon of the nitrile group upon protonation is muchsmaller in molecules with conjugated substituents than incyanoalkanes. We also observe that the amount of π-electrondensity donated increases with the size of the substituent.

The protonations of R and isomers of cyanonaphtaleneinvolve very similar electron transfers, moving 0.476 and 0.471

Figure 4. Variations of atomic electron population, ∆N(Ω), experi-enced upon protonation by 11-15 (in au multiplied by 103) and electronpopulation gained by the proton (in italics). ∆N(Ω) is only shown forone of those atoms related by symmetry.

Figure 5. Relationship between the variations in atomic energies andpopulations as a result of protonation.

Figure 6. Variation of atomic energy, ∆E(Ω), (in kJ mol-1) experi-enced upon protonation by 3 and 11 and electronic energy gained bythe proton (in italics). ∆E(Ω) is only shown for one of those atomsrelated by symmetry.

Figure 7. Plot of variations experienced (all values are in au but R isin Å) upon protonation by the bond properties in molecule 6. Valuesrefer to differences between protonated and neutral molecules inabsolute values.



85

au from the bicyclic systems to the H+-NC region, respectively.The most significant ∆N(Ω) difference between both systemscorresponds to the R hydrogen of the unsubstituted cycle thatis in cis arrangement to the cyano group, HRc. We can observe(Figure 4) that ∆N(HRc) is positive (+0.015 au) for R-cyanon-apthalene and negative (-0.027 au) for -cyanonaphtalene,whereas the remainig ∆N(H) and ∆N(C) couples of values donot differ by more than 0.008 au (excluding the C-H groupnext to the nitrile group that is R in the former and in thelatter). ∆N(HRc) in R-cyanonapthalene is the only positive valueobserved in the R group of both molecules. It can be explainedbecause of the proximity between HRc and the proton attachedto the cyano group. This proximity provides an easy way forapproaching electron density in the unsubstituted ring to theproton. The different position and orientation of the CN groupin -cyanonaphtalene prevents this mechanism and HRc playsits usual role in protonations as electron source.

Protonation Effects on Atomic Energies. Figure 5 showsthe relationships between the variations in atomic energies andpopulations as a result of protonation. Good correlations arefound when 10 is excluded. For C atoms, R groups, and protons,atomic energies become more negative as populations increase,

whereas for N atoms the opposite effect is found. Also, N atomsexhibit the worst correlation factor (R2 ) 0.80). As it could beinferred from Figure 5, R atoms show the smallest variationsin both energies and populations because they are farther froma proton than atoms in the CN group. For R groups, differencesfor several atoms are summed up, but if separated atoms wereconsidered the same effect could be found, that is as the distancefrom the proton increases the differences decrease. It is alsonoticeable that these atoms are those where variations of N(Ω)provide the smallest effect on E(Ω). The only atom stabilizedby protonation is the N atom of the CN group, which is theonly one gaining electron density upon protonation in all ofthe molecules. Thus, the positive values of PAs came from thestabilization gained by N and proton, which exceeds thedestabilization experienced by the remaining atoms.

Comparing molecules with saturated and unsaturated sub-stituents of similar size (3 and 11), we notice (Figure 6) thatthe smallest reduction of electron density in the carbon of theCN group when R is unsaturated gives rise to a smaller atomicdestabilization in the protonated compound. In contrast, Runsaturated groups result much more destabilized upon proton-ation (563 kJ mol-1 in 11 vs 428 kJ mol-1 in 3, or 525 kJ mol-1

in 13 vs 440 kJ mol-1 in 6). Overall, the summation of atomicdestabilization in 11-15 exceeds that of comparable saturatedcompounds.

Protonation Effects on Bond Properties. The effects ofN-protonation on the bond properties could be exemplified bycyanohexane (6) (Figure 7). In this molecule, it can be observedthat, as a general rule, the effects on the bond properties (R,F(rc), H(rc), and ε) decrease as the distance to the protonincreases. Nevertheless, significant fluctuations are found as wemove further in the alkyl chain: so, H(rc) shows higherdifferences for the CR-C bond than for the C-CR one.Figures 8 and 9 show variations of F(rc), and H(rc) regardingto variations in CtN and C-C bond lengths, respectively. Bothfigures exhibit almost linear relationships. ∆ε values are notshown as they are always very small.

For all CtN bonds, the bond shortens upon protonation(∆R < 0), whereas F(rc) decreases (∆F(rc) < 0) and H(rc)becomes less negative (∆H(rc) > 0). The shortening of the CtNbond is apparently contradictory with changes found for F(rc)and H(rc), which could be associated to the decrease of charge

Figure 8. Plot of variation of F(rc) and H(rc) vs the variation of thedistance of the C-N bond. Values refer to differences betweenprotonated and neutral molecules. All values are in au but ∆R is in Å.

Figure 9. Plot of variation of F(rc) and H(rc) vs the variation of the distance of the C-C bonds. Values refer to differences between protonatedand neutral molecules. All values are in au but ∆R is in Å.

2656 J. Phys. Chem. A, Vol. 113, No. 11, 2009 Lopez et al.


86

density in the bond critical point and so to the weakening ofthe bond. However, it should be taken into account that theproperties in the bond critical point only reflect what happensto σ density as the π density is out of the plane of the bond.Then, the shortening of the bond length and the changes in bondproperties upon protonation are compatible with the increaseof the π density and the decrease of the σ density in the CtNbond, which confirms the important π character of the CtNbond in protonated compounds and so the predominance of theresonance form containing a triple bond (H+-NtC-R).

From Figure 9 it could be inferred that when the bond lengthremains constant all of the properties of the BCP remain alsounchanged. This happens for C-C bonds placed further awaywithin the R group. The most negative values of ∆R correspondto the most negative ones of ∆H(rc) and to the most positiveones of ∆F(rc). So, when the bond shortens, bond propertiesreflect a strengthening of the bond, whereas the opposite happenswhen the bond lengthens.

Conclusions

After the protonation of cyanocompounds, the proton keepsa very positive charge, which is more in line with aH+-NtC-R Lewis structure than with the H-N+tC-R andH-NdC+-R ones. This is also confirmed by the increase ofthe π density and the decrease of the σ density in the CtNbond obtained from results of its bond properties.

The electron density of HCN evolves upon protonationfollowing the mechanism previously reported for other O-pro-tonations7-9,21 and N-protonations7,8,20,21 due to the deformationof the electron density in the whole molecule produced by theproton, which gives rise to electron density transferencesbetween neighboring atoms. When the H of HCN is replacedby an alkyl group the electron population lost by the C atom issignificantly reduced, due to the σ-electron density providedby the neighboring alkyl group, R. When the alkyl chainexperiences an internal rotation, the only ∆N(Ω) valuessignificantly affected are those of the group rotated. For nitrileswith π-conjugated substituents, an important reduction ofπ-electron density appears upon protonation, whereas the σ-elec-tron density remains practically unchanged as in cyanoalkanes.

Also, we have found a reasonable agreement betweenexperimental and calculated PA values as well as goodcorrelations between variations in atomic energies and popula-tions as a result of protonation.

Acknowledgment. We are indebted to “Centro de Super-computacion de Galicia” (CESGA) for access to their compu-tational facilities and to “Xunta de Galicia” and Spanish MECfor financial support through, respectively, projects C217122P-64100 and CTQ2006-15500/BQU.

References and Notes(1) Carey, F. A.; Sundberg, R. J. AdVanced Organic Chemistry; Kluwer

Academic: New York, 2001.(2) Wheland, G. W. Resonance in Organic Chemistry; Wiley: New

York, 1955.(3) Bader, R. F. W. Atoms in Molecules: A Quantum Theory; Oxford

University Press: New York, 1990.(4) Bader, R. F. W. Chem. ReV. 1991, 91, 893.(5) Wiberg, K. B.; Laidig, K. E. J. Am. Chem. Soc. 1987, 109, 5935.(6) Wiberg, K. B.; Breneman, C. M. J. Am. Chem. Soc. 1992, 114,

831.(7) Gonzalez Moa, M. J.; Mosquera, R. A. J. Phys. Chem. A 2003,

107, 5361.(8) Gonzalez Moa, M. J.; Mosquera, R. A. J. Phys. Chem. A 2005,

109, 3682.(9) Mandado, M.; Van Alsenoy, C.; Mosquera, R. A. J. Phys. Chem.

A 2004, 108, 7050.(10) Mandado, M.; Van Alsenoy, C.; Mosquera, R. A. Chem. Phys. Lett.

2005, 405, 10.(11) Glaser, R.; Choy, G. S. K. J. Am. Chem. Soc. 1993, 115, 2340.(12) Vila, A.; Mosquera, R. A. J. Phys. Chem. A 2000, 104, 12006.(13) Vila, A.; Mosquera, R. A. Chem. Phys. Lett. 2000, 332, 474.(14) Vila, A.; Mosquera, R. A. Tetrahedron 2001, 57, 9415.(15) Perrin, C. J. Am. Chem. Soc. 1991, 113, 2865.(16) Laidig, K. E. J. Am. Chem. Soc. 1992, 114, 7912.(17) Gatti, C.; Fantucci, P. J. Phys. Chem. 1993, 97, 11677.(18) Hirshfeld, F. L. Theor. Chim. Acta 1977, 44, 129.(19) De Proft, F.; Van Alsenoy, C.; Peeters, A.; Langenaker, W.;

Geerlings, P. J. Comput. Chem. 2002, 23, 1198.(20) Otero, N.; Gonzalez.Moa, M. J.; Mandado, M.; Mosquera, R. A.

Chem. Phys. Lett. 2006, 428, 249.(21) Gonzalez Moa, M. J.; Mandado, M.; Mosquera, R. A. Chem. Phys.

Lett. 2006, 428, 255.(22) Stutchbury, N. C. J.; Cooper, D. L. J. Chem. Phys. 1983, 79, 4967.(23) Alcoba, D. R.; Lain, L.; Torre, A.; Bochicchio, R. C. Chem. Phys.

Lett. 2005, 407, 379.(24) Cioslowski, J.; Mixon, S. T. Can. J. Chem. 1992, 70, 443.(25) Bader, R. F. W. J. Phys. Chem. A 1998, 102, 7314.(26) Haaland, A.; Shorokhov, D. J.; Tverdova, N. V. Chem.sEur. J.

2004, 10, 4416.(27) Poater, J.; Sola, M.; Bickelhaupt, F. M. Chem.sEur. J. 2006, 12,

2889.(28) Bader, R. F. W. Chem.sEur. J. 2006, 12, 2896.(29) Poater, J.; Sola, M.; Bickelhaupt, F. M. Chem.sEur. J. 2006, 12,

2902.(30) GAMESS: Schmidt, M. W.; Baldridge, K. K.; Boatz, J. A.; Elbert,

S. T.; Gordon, M. S.; Jensen, J. H.; Koseki, S.; Matsunaga, N.; Nguyen,K. A.; Su, S. J.; Windus, T. L.; Dupuis, M.; Montgomery, J. A. J. Comput.Chem. 1993, 14, 1347–1363.

(31) Lehd, M.; Jensen, F. J. Comput. Chem. 1991, 12, 1089.(32) Cortes-Guzman, F.; Bader, R. F. W. Chem. Phys. Lett. 2003, 379,

183.(33) Mandado, M.; Vila, A.; Grana, A. M.; Mosquera, R. A.; Cioslowski,

J. Chem. Phys. Lett. 2003, 371, 739.(34) Bader, R. F. W. et al. AIMPAC: A Suite of Programs for the AIM

Theory; McMaster University: Hamilton, Ontario, Canada, L8S 4M1.Contact [email protected].

(35) Biegler-Konig, F. W.; Bader, R. F. W.; Nguyen-Dang, T. T.J. Comput. Chem. 1982, 3, 371.

(36) Aray, Y.; Murgich, J.; Luna, M. A. J. Am. Chem. Soc. 1991, 113,7135.

(37) Hunter, E. P.; Lias, S. G. J. Phys. Chem. Ref. Data 1998, 27, 413.(38) Mariott, S.; Topsom, R. D.; Lebrilla, C. B.; Koppel, I.; Mishima,

M.; Taft, R. W. J. Mol. Struct. 1986, 137, 133.(39) Grana, A. M.; Mosquera, R. A. Chem. Phys. 1999, 243, 17.

JP811023X



87


88

ELECTRON DENSITY ANALYSIS ON THE ALPHA ACIDITY OF NITRILES

José Luis López, Ana M. Graña, Ricardo A. Mosquera*

Dpto. Química Física, Universidade de Vigo,

Lagoas-Marcosende, 36310-Vigo, Galicia (Spain).

Abstract

24 substituded cyanocompounds and the corresponding anions obtained upon H+-

abstraction from diverse positions were subjected to an electron density analysis with

the Quantum Theory of Atoms in Molecules (QTAIM). All the electron densities were

obtained at the B3LYP/6-31++G(2d,2p) level on completely optimized geometries. -

H+ abstraction is found as the most favored one (by at least 100 kJ mol

-1 in all the

tested compounds). The presence of additional resonance electron attractors reduces

significantly the -deprotonation energy, whereas this magnitude is quite insensitive to

the inclusion of resonance electron donors. The electron density rearrangement

accompanying the deprotonation is basically in line with the predictions of the

resonance model. Thus a significant part of the electron density gained by expelling

the proton is transferred to cyano N and to other groups where significant resonance

structures delocalize the negative charge.


89

Introduction

Carbanions stabilized by mesomeric electron acceptor groups are a class of

compounds with a certain practical interest. In fact, they have been employed widely in

organic synthesis.1 Even, some important biochemical intermediates display this

chemical moiety.2 From a theoretical point of view, they are convenient systems for

testing the reliability of electron delocalization models. According to the resonance

model (RM), the negative charge of the C atom is expected to be delocalized on the

mesomeric electron acceptor, e.g. O in a carbonyl group or N in a cyano substituent. In

this context, we acknowledge the very good services provided by RM in Chemistry.3,4

Even, different possibilities to supply resonance structures with more reliable and

quantitative weighting coefficients obtained making use of modern tools of electron

density topological analysis can be explored.5 Nevertheless, since the publication of

the seminal paper by Wiberg and Laidig on the electronic origin of the esther and

amide resonance,6 it is not possible to deny that a large amount of inconsistencies

between RM predictions and computed evolutions of electron densities have been

reported.7-26

Most of these discrepancies where obtained studying protonation

processes or in nucleophilic addition reactions. In contrast, deprotonations seem to

have been much less explored.

This paper aims to get insight into the stabilization of carbanions by cyano

groups that is on the basis of the significant acidity displayed by the hydrogens of

methylenes (and other groups) that are α to CN units. In order to achieve this objective

we have performed an electron density analysis of neutral and deprotonated anionic

species of a series of substituted N≡CHRR’ cyanocompounds (R’=H in most of them)


90

(Table 1). This analysis was carried out with the Quantum Theory Atoms in Molecules

(QTAIM).27,28

As an starting point, we remember the N≡C-RR’ anions are considered to be

stabilized by delocalization of the negative charge on the N atom. This is represented

by –N≡CRR’ resonance Lewis structures. In polysubstituted nitriles, delocalizations

can be extended to other atoms of R and R’ groups where similar resonance structures

could be written. Scheme 1 shows an example of them for compound N (containing an

additional π-acceptor substituent: NO2. The opposite effect, should be expected when

the additional substituent is a π-donor like -NH2 or –OH.

C NC

N

H

O

O

-C NC

N

H

O

O

--+

-N +

C N-C

N

H

O

O

-+

Scheme 1

Computational details

QTAIM allows the partitioning of a molecule into disjoint subsystems without

resorting to hypothesis alien to Quantum Mechanics.27,28

With a few exceptions,29

each

of these subsystems consists of a nucleus, which acts as an attractor for the trajectories

of the gradient of the electron density vector field, (r), and its associated atomic

basin, throughout these trajectories spread. An atom, , is defined as the union of the

attractor and its associated basin, and is surrounded by zero flux surfaces for (r).


91

The integration of the proper density functions within these limits provides diverse

atomic properties such as the electron population, N(), or the total atomic electron

energy, E().

QTAIM also recovers main elements of molecular structure in terms of the

critical points, rc, of the electron density, (r). Prominent among them are the bond

critical points (BCPs), which are located roughly in between every pair of bonded

atoms. Although the relationship between the presence of a BCP and the existence of a

chemical bonding has become a controversial and it is still a debated point of the

theory,30-35

the electron density at a certain BCP is regarded as an indicator for bond

strength.

All the neutral (1-24) and deprotonated (1a-24a) species here considered

(Table 1) were fully optimized at the B3LYP/6-31++G(2d,2p) levels using the

Gaussian-09 program.36

Exclunding the long chain linear cyanoalkanes (14 and 15),

initial geometries were optimized for all expected conformers. The completely

antiperiplanar conformation was the only initial geometry optimized for 14 and 15.

The electron densities obtained were analyzed with the QTAIM by means of the

program AIMPAC.37

The accuracy of the integrated properties was tested using the

differences between molecular properties and those obtained by summation of the

properties of the fragments [N-N() or E-E()] (Table 1). These differences are

always smaller (in absolute value) than 2 10-3

au and 1.2 kJ/mol, respectively, which

are found to be accurate enough comparing with other works carried out at similar

theoretical levels. In the same vein, the integrated values of the Laplacian of the


92

electron density in all the atomic fragments, L(), are always smaller (in absolute

value) than 10-3

au.

Deprotonation energies, dpE, (Table 1) were calculated taken into account the

thermal and zero point vibrational corrections (unscaled) obtained for deprotonated

and neutral species. All the optimized structures were real minima as they do not

display any imaginary frequency. When more than one local minima is present in the

neutral or anionic form o certain compound dpE is computed as the different between

the lowest energy conformer found for each species.

Results and Discussion

Atomic and bond properties of neutral nitriles, as well as the 2(r) topology, have been described thoroughly in a previous HF study by Aray et al.

38 As our results for neutral molecules are in perfect agreement with theirs, we focus our discussion on the effects of deprotonation.

Deprotonation energies.

Table 1 lists the dpE energies obtained for -deprotonation of the 24 cyanocompounds here studied. For the sake of simplicity, in what follows compound 1 (cyanomethane) will be our reference, and deprotonation energies will be commented as relative values to that computed for 1 (dpE). First we notice that, in spite of

large structural changes, deprotonation energies do not span in a wide range. It is also

noticeable that positive values are scarce. Especially when we take into account that

the most positive value corresponds to LiCH2CN (compound 8), whose neutral

optimized structure is significantly different from those of the remaining species, with

the Li atom attached to the CN group and not to the methylene, denoting its ionic

character. Thus, one [CH2CN]- is already formed in neutral 8. As a consequence

abstracting a proton from it demands the largest amount of energy and this compound

can be excluded from the series because of this singular bonding structure.


93

Table 1. Deprotonation energies, ΔdpE (in kJ mol-1

) and accuracy estimators for

QTAIM integrations for the RR’CH-CN molecules here studiede.

R R’ ΔdpE ΔdpE N-N()b

E-E()c

|L()|d

1 H H 1549.3 0 -0.4 (0.0)f

-0.4 (-0.2)f

0.5

2 H CN 1375.6 -173.7 0.1 (0.0) 0.1 (-0.2) 0.2

3 CN CN 1228.9 -320.4 -0.6 (0.2) -0.4 (0.0) 0.1

4 CH3-O-CO H 1402.2 -147.1 0.2 (0.4) 0.1 (0.1) 0.9

5 NO2 H 1334.4 -214.9 1.2 (1.9) 0.7 (1.2) 0.7

6 OH H 1547.3 -2 -0.3 (1.2) -0.2 (0.7) 0.8

7 NH2 H 1552.2 2.9 -1.5 (-0.3) -0.9 (-0.4) 0.1

8 Li H 1660.7 111.4 -0.1 (0.4) -0.2 (0.0) 0.7

9 SiH3 H 1472.0 -77.3 1.0 (0.2) 0.5 (-0.2) 0.9

10 F H 1526.6 -22.7 0.3 (0.7) 0.0 (0.2) 0.5

11 F F 1503.4 -45.9 -0.6 (0.2) -0.8 (0.5) 1.0

12 CH3 H 1558.8 9.5 1.0 (-0.6) -1.0 (-0.6) 0.9

13 CH3 CH3 1556.6 7.3 2.0 (0.8) 1.0 (0.1) 0.9

14 CH3(CH2)8 H 1548.0 -1.3 -0.6(0.1) -0.5(0.2) 0.4

15 CH3(CH2)9 H 1548.2 -1.1 -0.1(0.4) -0.6(0.7) 1.3

16a CH2=CH-CN - 1548.4 -0.9 -0.3 (1.2) -0.2 (0.7) 0.8

17 CH2=CH H 1458.0 -91.3 -1.5 (-0.3) -0.9 (-0.4) 0.1

18 C6H5 H 1444.2 -105.1 -0.1 (0.4) -0.2 (0.0) 0.7

19 p-NO2C6H4 H 1342.6 -206.7 0.1 (0.0) 0.1 (-0.2) 0.2

20 p-NH2C6H4 H 1469.5 -79.8 -0.6 (0.2) -0.4 (0.0) 0.1

21 m-NO2C6H4 H 1388.3 -161 -1.5 (-0.3) -0.9 (-0.4) 0.1

22 m-NH2C6H4 H 1453.5 -95.8 -0.6 (0.2) -0.8 (0.5) 1.0

23 o-NO2C6H4 H 1363.0 -186.3 -0.3 (1.2) -0.2 (0.7) 0.8

24 o-NH2C6H4 H 1455.5 -93.8 0.2 (0.4) 0.1 (0.1) 0.9 aThis compound, CH2=CH-CN, does not follow the general RR’CH-CN formula.

bValues in au multiplied by 10

3.

cin kJ mol

-1.

dMaximum absolute value of integrated L() in the neutral molecule and its protonated

species, in au multiplied by 103.

eValues for protonated species in parenthesis.

The other positive dpE values do not exceed 10 kJ mol-1

(7, 12 and 13). 12 and 13

correspond to other short alkyl chains (cyanoethane and cyano-iso-propane). The small

difference between them (Table 1) leads us to think that chain ramifications are not


94

significant to this problem. The effect of chain size is even smaller for larger alkyl

groups (14 and 15), becoming negligible.

7 should be compared with the other resonance electron donor containing compound (+R) here considered: 6. Both values are really close (slightly positive one and slightly negative the other). Thus we conclude that the inclusion of +R substituents does not really modify dpE.

-20

0

20

40

60

80

100

120

140

160

180

0 1 2 3 4 5 6 7 8 9 10 11

14 14(t)

15 15(t)

Figure 1. Relative values (in kJ mol-1

) of deprotonation energies (dpE) vs. H+-

abstraction position in compounds 14 and 15.

In contrast, significantly negative dpE values are displayed by those compounds (2-5) that include additional (CN being also one of them) resonance electron withdrawers (-R). According to the RM these compounds allow a larger delocalization of the formal negative charge formed at the C (scheme 1). A similar mechanism can be

considered for π-conjugated substituents, such as vinyl (17) of phenyl (parent, 18, or

susbtitued, 19-24) groups. In fact all these compounds (2-5, 17-24) reduce the

deprotonation energy by more than 90 kJ mol-1

with regard to the reference (1).

We have also checked that -deprotonations are preferred over other possible processes for H+-abstractions. To this end we computed all possible H-abstractions along the alkyl chain of 14 and 15 (Figure 1). Other deprotonations cost at least 100 kJ mol

-1 more than the alpha one. Moreover the only significant difference between both

points is due to the displacement (by one position) of the terminal and previous to

terminal methyl or methylene group.


95

Proton abstraction effects on atomic electron populations and bond properties in

cyanomethane.

As in the previous section, we will refer to compound 1 as our basic model to

describe the electron density change due to -deprotonation. The variations

experienced by its atomic electron populations, N(Ω), in the process are shown in

Figure 2. All the atoms increase their electron population after expelling the proton,

which means sharing 0.948 au. Whereas a little more than one half of the electron

density is kept within the CH2 unit, the electron density taken by the cyano group is

important, and there is an important transference of electron density to its N atom.

C NC

H

H 217

151

343

118

118

Figure 2. Variations of atomic electron populations in 1 upon -deprotonation,

dpN(Ω), (in au multiplied by 103).

C NC

H

H

-26.50.042 -83

+33.40.296 +87

Figure 3. Variations of most significant BCP properties in 1 upon -deprotonation:

Relative electron density values (in au and bolface) are multiplied by 103, absolute

values of ellipticities (in italics) and relative values of the total electronic energy

density (multiplied by 103).


96

In the same vein the evolutions of BCPs properties is in line with the

predictions of the RM model. Thus, we notice (Figure 3) the C-C bond is reinforced

while the C-N linkage gets weaker. At the same time the first bond shrinks by 0.08 Å,

while the later lengths by 0.03 Å. More meaningful, both bond ellipticities that are

perfectly null in the neutral compound become 0.296 and 0.042 in the anion. Finally

the values of the total energy density function become more negative for C-C in the

anion and less negative for the C-N likange, pointing to a reinforcement of covalent

character in the former and to its depletion towards a significant polarization in the

latter.

Conclusions

QTAIM analysis of the electron densities of 24 substituded cyanocompounds

and the corresponding anions obtained upon H+-abstraction allowed us to establish the

following conclusions: -deprotonation is at least favored by 100 kJ mol-1

with regard

to other deprotonation processes. While resonance electron attractors reduce

significantly the energy involved in the process, the effect of resonance electron donors

is nearly negligible. Deprotonation involves a significant variation of atomic electron

populations. Whereas hydrogen atoms are involved in this rearrangement, the role they

play is not so important as that in protonation. In contrast, those atoms where the

resonance model predicts significant delocalizations of the negative charge gain an

important part of the electron density left by the hydrogen.

Acknowledgements We are indebted to “Centro de Supercomputación de Galicia”

(CESGA) for access to their computational facilities.


97

References

(1) Trost, B. M., Ed. Comprehensive Organic Synthesis, Vol. 3, Carbon-Carbon u-

Bond Formation; Pergamon Press: Oxford, 1991.

(2) Richard, J. P. In The Chemistry of Enols; Rappoport, Z., Ed.; Wiley: New York,

1990.

(3) Carey, F. A.; Sundberg, R. J. Advanced Organic Chemistry; Kluwer Academic:

New York, 2001.

(4) Wheland, G.W. Resonance in Organic Chemistry; Wiley: New York, 1955.

(5) Ferro-Costas, D., Mosquera, R. A. Phys. Chem. Chem. Phys. 2015, 17, 7424.

(6) Wiberg, K.B.; Laidig, K.E. J. Am. Chem. Soc. 1987, 109, 5935-5943.

(7) Wiberg, K.B.; Breneman, C.M. J. Am. Chem. Soc. 1992, 114, 831.

(8) Slee, T.S.; MacDougall, P.J. Can. J. Chem. 1988, 66, 2961.

(9) Laidig, K.E. J. Am. Chem. Soc. 1992, 114, 7912.

(10)Laidig, K.E.; Cameron, L.M. J. Am. Chem. Soc. 1996, 118, 1737.

(11)Glaser, R. J. Phys. Chem. 1989, 93, 7993.

(12)Glaser, R.; Choy, G.S.-C. J. Am. Chem. Soc. 1993, 115, 2340.

(13)Speers, P.; Laidig, K.E.; Streitwieser, J. Am. Chem. Soc. 1994, 116, 9257.

(14)Vila, A.; Mosquera, R.A. Tetrahedron 2001, 57, 9415.

(15)González Moa, M.J.; Mosquera, R.A. J. Phys. Chem. A 2003, 107, 5361.

(16)González Moa, M.J.; Mosquera, R.A. J. Phys. Chem. A 2005, 109, 3682.

(17)González Moa, M.J.; Mandado, M.; Mosquera, R.A. Chem. Phys. Lett. 2006, 428,

255.

(18)López, J.L.; Graña, A.M.; Mosquera, R.A. J. Phys. Chem. A 2009, 113, 2652-

2657.

(19)Mandado, M.; Van Alsenoy, C.; Mosquera, R.A. J. Phys. Chem. A 2004, 108,

7050.

(20)Graña, A.M.; Hermida-Ramón, J.M.; Mosquera, R.A. Chem. Phys. Lett. 2005,

412, 106.

(21)Mandado, M.; Mosquera, R.A.; Graña, A.M. Chem. Phys. Lett. 2004, 386, 454.


98

(22)Mandado, M.; Van Alsenoy, C.; Mosquera, R.A. Chem. Phys. Lett. 2005, 405, 10.

(23)Mandado, M.; Van Alsenoy, C.; Mosquera, R.A. J. Phys. Chem. A 2005, 109,

8624.

(24)Otero, N.; González Moa, M. J.; Mandado, M.; Mosquera, R. A Chem. Phys. Lett.

2006, 428, 249.

(25)Otero, N.; Estévez, L.; Mandado, M.; Mosquera, R. A. Eur. J. Org. Chem. 2012,

12, 2403.

(26)Estévez, L.; Mosquera, R. A. Chem. Phys. Lett. 2008, 451, 121.

(27)Bader, R. F. W. Atoms in Molecules: A Quantum Theory Oxford University Press:

New York, 1990.

(28)Bader, R. F. W. Chem. Rev. 1991, 91, 893.

(29) Alcoba, D. R.; Lain, L.; Torre, A.; Bochicchio, R. C. Chem. Phys. Lett. 2005, 407,

379.

(30) Cioslowski, J.; Mixon, S. T. Can. J. Chem. 1992, 70, 443.

(31) Bader, R. F. W. J. Phys. Chem. A 1998, 102, 7314.

(32) Haaland, A.; Shorokhov, D. J.; Tverdova, N. V. Chem. Eur. J. 2004, 10, 4416.

(33) Poater, J.; Solà, M.; Bickelhaupt, F. M. Chem. Eur. J. 2006, 12, 2889.

(34) Bader, R. F. W. Chem. Eur. J. 2006,12, 2896.

(35) Poater, J.; Solà, M.; Bickelhaupt, F. M. Chem. Eur. J. 2006, 12, 2902.

(36) G. W. T. M. J. Frisch, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R.

Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G. A. Petersson, H. Nakatsuji, M.

Caricato, X. Li, H. P. Hratchian, A. F. Izmaylov, J. Bloino, G. Zheng, J. L.

Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T.

Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, J. A. Montgomery, Jr., J. E.

Peralta, F. Ogliaro, M. Bearpark, J. J. Heyd, E. Brothers, K. N. Kudin, V. N.

Staroverov, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J. C. Burant, S.

S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J. M. Millam, M. Klene, J. E. Knox, J. B.

Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev,

A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, R. L. Martin, K. Morokuma, V.

G. Zakrzewski, G. A. Voth, P. Salvador, J. J. Dannenberg, S. Dapprich, A. D. Daniels,


99

Ö. Farkas, J. B. Foresman, J. V. Ortiz, J. Cioslowski, and D. J. Fox, Gaussian, Inc.,

Wallingford CT, 2009.

(37) Bader, R. F. W. et al. AIMPAC: A suite of programs for the AIM theory; Mc

Master University, Hamilton, Ontario, Canada L8S 4M1. Contact

[email protected]

(38) Aray, Y.; Murgich, J.; Luna, M. A. J. Am. Chem. Soc. 1991, 113, 7135.

(39) Stutchbury, N. C. J.; Cooper, D. L. J. Chem. Phys. 1983, 79, 4967.

mailto:[email protected]


100

QTAIM STUDY OF REARRANGEMENT REACTIONS IN NITROGENATED

COMPOUNDS

José Luis López, Ricardo A. Mosquera, Ana M. Graña*

Dpto. Química Física, Universidade de Vigo,

Lagoas-Marcosende, 36310-Vigo, Galicia (Spain)

ABSTRACT

The variations of the geometries, the electron density and atomic charges along the

reaction path of rearrangement reactions were studied by B3LYP/6-311++G**

methods. The reaction paths were studied for the Curtius rearrangement of

formaldehyde oxime, the step of rearrangement of the Hofmann reaction of

acetamide and the step of rearrangement of the Beckmann reaction of propanone

oxime. The atomic and bond properties for the minima, the transition states and

selected points along the reaction coordinated were analysed, including atomic and

bond properties obtained from QTAIM analysis of the electron density. The results

show similar patterns for all the three reactions: the new bonds are built when the old

ones break, after the reactions go through the transition state. Regarding to the

electron transfer during the reaction, a similar behaviour is found for the Curtius and

the Beckmann rearrangements: only the atoms involved in the migration (the atom

that moves and the two atoms bonded to it in the reagent and the product) exhibit

large variation of charge along the path, i.e., the electron charge transfer happen

among them. For the Hofmann reaction the Br atom is also involved in the charge

transfer, because is the atom which moves away as an anion. The study of the

reagent, transition state and product structures reveals that the usual resonance forms

representing the geometries do not correspond to the obtained results for bond

lengths and atomic charges.

KEYWORDS: QTAIM; Density functional calculations; Electron density analysis;

Reaction mechanisms


101

INTRODUCTION

Rearrangement reactions are an important group of reactions in which an atom or a

bond moves from a site in the reagent to a different site in the product. These

reactions may occur in a concerted manner or through a step-wise mechanism.

In this paper, we have studied three different rearrangement reactions: Curtius

rearrangement of formaldehyde oxime, the step of rearrangement of the Hofmann

reaction of acetamide and the step of rearrangement of the Beckmann reaction of

propanone oxime. From the mechanism of these reactions we have selected the step

which involves the migration of one atom in order to study how the geometries and

the different atomic and bond properties, specifically atomic charges, change along

the reaction path.

The Curtius rearrangement[1]

allows us to obtain isocyanates from acyl-azides:

Scheme 1

The mechanism for this reaction remained unknown for years. The main point in

discussion was if the reaction takes place in one stage or if it occurs in several steps

with acylnitrenes (RC(O)N:) as intermediates.

Different theoretical studies [2]

[3-6]

[4]

[5]

[6]

[7]

[8]

on aryl and acyl azides show that the

syn conformers with respect to the C-N bond are more stable than the anti ones and

that for syn conformers Curtius rearrangement occurs in one stage. The barriers for


102

syn- anti isomerization achieve 7-9 kcal mol-1

whereas the barriers for the

transformation of syn compounds into isocyanates are considerably lower than the

barriers corresponding to the rearrangement of anti compounds into isocyanates. For

this reason the Curtius reaction occurs by a concerted mechanism as shown in

Scheme I.

The Hofmann rearrangement[9]

allows us to obtain amines from amides following a

multi-stage mechanism shown in Scheme 2. One of the steps in the mechanism

involves the migration of a methyl group in a similar way that in the Curtius reaction.

This step appears in scheme into a box. To the best of our knowledge the only

theoretical study[10]

of this reaction was performed into a study about the mechanism

of the synthesis of oxazolidines, which includes a Hofmann rearrangement as the

most important step of the reaction. This study does not include the evolution of the

reaction and the obtained value for the energy barrier (ΔG at 298 K is 123.4 kJ mol-1

,

from DFT calculations with chloroform as a solvent) is not comparable to our results

as the size and structure of the molecules are very different.


103

Scheme 2

The Beckmann rearrangement [11]

[12]

[13]

is an acid-catalysed reaction to obtain

amides from oximes. The mechanism, shown in Scheme 3, includes one stage that

involves the migration of a methyl group. The Beckmann rearrangement has been

widely studied by experimental methods [14]

[15]

[16]

. Specifically, the ciclohexanone

oxime into ε-caprolactam, which is an important compound for the fabrication of

Nylon-6 and other resines.

Different theoretical [17]

[18]

[19]

[20]

[21]

[22]

studies have been performed on the

mechanism of the Beckmann rearrangement in the gas phase. Nguyen et al[18]

[19]

[20]

studied the reaction catalysed by a proton, as a model of the rearrangement under a

strong acid condition. The first step, where the O-protonated complex is obtained,


104

was found to be the rate-limiting step. An important number of studies have been

performed [23]

[17]

by using different heterogeneous catalyst for this reaction.

Scheme 3

COMPUTATIONAL METHODS

All calculations were performed by using B3LYP method in Gaussian09 [24]

with 6-

311++G** basis set. For the three reactions, intrinsic coordinate (IRC) calculations

were carried out. All the optimized structures were characterized as minima in the

frequencies calculation The wavefunctions were obtained for reagents, products,

transition states and selected points of the path. On these wavefunctions we

performed QTAIM[25]

[26]

topological electron density analysis by using the

AIMPAC package[27]

of programs in order to obtain bond and atomic properties.

The value of the electron density at the bond critical points, (rc ) are employed as an

indicator for bond strength. Electron populations, N(Ω), were calculated by

numerical integration of the respective density function. The absolute values

achieved for the integrated values of the laplacian of the electron density in all the

atomic fragments, L(Ω), were smaller than 1.0∙10-3

au. The differences between total

electron population and that obtained by summation of properties of the fragments

[N-ΣN(Ω)], were always smaller (in absolute value) than 2.0∙10-3

au.


105

RESULTS

1. Curtius rearrangement

Figure 1 shows the energy profile for the reaction:

The energy barrier is 114.9 kJ mol-1

in agreement with previous DFT results (114.5

kJ mol-1

) for the non-catalytic reaction¡Error! Marcador no definido.. After

including the ZPVE value the barrier is 100.8 kJ mol-1

in agreement with

experimental and theoretical values for Curtius rearrangements (95-115 kJ mol-1

). [7,

28]

Table 1 shows the main geometrical parameters for the critical points in the path:

Bond/Angle Reactive TS Product

O2-C1 1.202 1.208 1.167

N3-C1 1.417 1.301 1.210

H4-C1 1.097 1.151 1.986

N5-N3 1.250 1.77

N6-N5 1.123 1.098 1.095

H4-N3 2.057 1.761 1.008

N3-C1-H4 109.1 91.6 23.9

C1-N3-N5 115.1 105.2


106

Table 1. Main geometrical parameters. Distances in Å and angles in degrees.

The geometric parameters are in good agreement with the those obtained from both

previous theoretical and experimental studies [29]

[30]

[31]

[32]

. For the reagent,

different bond distances are found from N5 to N3 and N6. The N5-N6 distance is

closer to the distance in N2 while the N3-N5 length is larger. From these values it

seems that the resonance form in Scheme 1 showing two double bonds could not

represent the structure of the molecule. It is confirmed when the values of the atomic

charges for N5 and N6 are considered (-0.099 and 0.186 au respectively). They are

small values for the charges which do not agree with the partial charges in the

proposed resonance form.

In the transition state the H4 atom is bonded to C1 and N3, taking into account the

existence of a bond critical point in both cases. The bond to C1 is very close to that

in the reactive, increasing 0.054 Å the reagent value. The bond to N3 is also closer to

that in the reagent but the difference is 0.293 Å. The N5-N6 distance is in the

transition state very similar to that in N2 molecule. The geometry for the transition

state, with small angles involving C1, causes the high energy barrier of the reaction.

Figure 2 exhibits the variations of the main bonds involved in the reaction: C1-H4,

N3-H4 and N3-N5 considering the length of the bonds and the value of the electron

density in the critical point.


107

Figure 2

The C1-H4 distance increases along the reaction path showing the most important

variation in the central part of the path, after the transition state. The electron density

decreases as the distance increases and a critical point for the electron density of the

bond, is found after the transition state until a value about 0.87 Å. The N3-H4

distance increases during the reaction and a critical point for the electron density

appears after the transition state (for distances shorter than 1.24 Å). There is a point

where he distances from H4 to C1 and N3 arise the same value. In that point there is

a bond to C1 (considering the existence of a critical point for the electron density)

but there is not a bond to N3. The N3-N5 bond becomes larger and a critical point for

ρ, is found along the whole path, but the values are smaller than 0.1 au for lengths

larger than 1.91 Å.


108

Figure 3

The evolution of the charges of the atoms involved in the rearrangement, is shown in

Figure 3. The charge for N5 scarcely changes along the reaction, it is slightly

negative in the reagent and the first points of the reaction and it becomes virtually

zero (within the margin of error of the calculation) at the end of the reaction when

the N2 molecule is obtained. The values of the charges for C1 and H4 increase

(atomic populations decrease) during the reaction with maximum differences of 0.47

and 0.38 au, respectively. On the contrary, charge for N3 becomes more negative

along the path and this atom gains 0.79 au along the path from C1 and H4 (they lost

0.85 au). The O atom charge remains almost constant during the process with a

maximum difference smaller than 0.03 au. The most important variations in the

values of the charges happen after the transition state when the H4-N3 distance

experiences the largest change.


109

2. Hofmann rearrangement

The energy profile for the step involving migration is shown in Figure 4. The barrier

for this reaction is 74.2 kJ mol-1

(66.9 kJ mol-1

when ZPVE is included). As it was

mentioned above the only theoretical study available [10]

for this step of the reaction

corresponds to large molecules with different electronic and steric effects and it

results in a value of ΔG at 298 K of 123.4 kJ mol-1

to be compared to the value of

63.7 kJ mol-1

obtained in this work.

Figure 4

The most important geometric parameters for reagent, product and transition state

appear in Table 2.

The geometry found for the reagent does not agree with the resonance form in

Scheme 2. The C-N distance is larger than the typical value in C=N bonds while the

C-O distance is shorter than the typical C-O single bond[33]

.

In the transition state, the C1 atom is bonded to C5 but there is not bond to N6, as a

bond critical point could not be found. The bond distances exhibit in both cases


110

intermediate vales between reagent and product, but they are closer to the value in

the reagent. The distance between O atom and C5 as well as the distance between N6

and C5 show smaller differences but they are in the transition state closer to those in

the product of the reaction.

Bond/Angle Reactant TS Product

C5-C1 1.550 1.844 2.540

N6-C1 2.336 2.021 1,456

O7-C5 1.246 1.199 1.186

N6-C5 1.328 1.247 1.188

Br8-N6 1.985 2.591

C1-C5-N6 108.2 79.1 17.9

N6-C5-O7 133.7 162.4 174.3


The evolution of the main distances between atoms and the electron density in the

bond critical point, is shown in Figure 5.

The distance between Br and C5 increases almost linearly from a standard value for

bonded atoms. The bond critical point is not found when the distance is higher than

2.27 Å. In the transition state, the C1 atom is bonded to the C5 but there is no bond

to N6 atom. The bond critical point for C1-N6 appears when the one for C1-C5

disappears, so in the point where both distances equals, there is a bond between C1

and C5 but there is not a bond between C1 and N6.


111


112

Figure 5

Figure 6

Figure 6 shows the variation of the atomic charges for the most important atoms in

the molecules. The charges for oxygen and hydrogen atoms remain almost constant

during the reaction with maximum differences smaller than 0.1 au for oxygen and

0.05 au for hydrogen atoms. The value for Q(C1) changes after the transition state:

from the reagent to the transition state changes less than 0.02 au and from the

transition state to the product the variation is 0.39 au. A similar pattern is found for

the evolution of the charge of N6, with a difference between the value in the

transition state and the value in the product of -0.51 au. It suggest a charge transfer

between these atoms in this stage of the reaction. The results show a continuous

decrease of the charge of C5 from the reagent to the product with an intermediate

values in the transition state. The Br atomic charge becomes gradually more negative

although the change is slightly more important before the transition state. After the

transition state C5 charge decreases 0.24 au (becomes more positive) and Br charge

increases 0.28 au (becomes more negative). So, the electron transfer happen from C5

to Br through N6 and from C1 to N6. The negative atomic charge of the oxygen atom

decreases during the reaction less than 0.1 au showing values between -1.22 and -

1.13 au from reagent to product. So, the differences in the charge of this atom in

reagent, transition state and product structures confirm the results for the C-O bond

length and show that the resonance forms in Scheme 2 are not representative of the

structures of the molecules.

3. Beckmann rearrangement

Figure 7 shows the value of the energy along the reaction path for this reaction. The

value of the barrier for this step of the reaction is 23.7 kJ mol-1

(12.5 kJ mol-1

taking

into account the ZPVE correction). It is lower than that found from DFT

calculations[18]

for formaldehyde oxime (44 kJ mol-1

) but higher to those found Chu


113

et al in a DFT study[23]

of the activation barriers of the rearrangement step of the

Beckmann reaction over solid acid catalyst. They studied the dependence of the

barrier values on Brønsted acid strength and they found values between 3.9 and 9.4

kJ mol-1

.

Figure 7. Evolution of the energy along the reaction path

The main geometric values for the minima and the transition state of the reaction

appear in Table 3:

Bond/Angle Reagent TS Product

C1-N2 1.256 1.194 1.143

C1-C5 1.530 1.719 2.576

N2-C5 2.255 1.946 1.433

C1-C9 1.493 1.467 1.440

N2-O3 1.764 2.437 3.334

C5-C1_N2 107.6 81.7 1.3

C9-C1-N2 132.4 154.0 179.8

C1-N2-O3 108.5 94.4 62.8



114

The reagent exhibits a CN bond with a C=N typical value, whereas in the product the

CN bond is closer to the experimental (1.157 Å) or to the DFT calculated (1.149 Å)

value of CN in acetonitrile. So, it could be inferred that the most important resonance

structure in the product should be that with a CN triple bond. However, when the

values of the atomic charges are analysed for this structure they are not compatible

with the expected positive charge on the N atom. So, the value for Q(C1) is +1.05 au

and the value for Q(N2) is -1.29 au. Although there is a hydrogen bond between the

oxygen of the water molecule and one of the H atoms bonded to C9, the charge for

the H2O molecule is 0.01 au and the charge for C9 is 0.09 au. However, the charge of

all the hydrogen atoms bonded to C5 and C9 is larger than 0.1 au and the total charge

of the methyl group bonded to N atom is 0.72 au. These results agree with those

obtained for the resonance forms and atomic charges in CN-protonated molecules [34]

with structures more compatible with a H+-N≡C-R Lewis structure than with the H-

N+≡C-R and H-N=C

+-R ones.

The main parameters of the geometry of the transition state show values intermediate

between the values in the reagent and the product, except for C1-N2 bond and C5-

C1-N2 angle with values closer to those in the reactive.

Figure 8 shows the evolution of the main bond distances during the reaction as well

as the value for the electron density in the bond critical point. The bond length

between C1 and C5 decreases whereas the distance between N2 andC5 increases by a

similar amount. The bond critical point for N2-C5 bond appears when the ones for

C1-C5 and N2-O3 disappear, after the transition state for the reaction. At the point

where the C1-C5 and N2-C5 arises the same value C5 is bonded to C1 but it is not

bonded to N2. The N2-C3 bond is always a weak bond with values of (rc) in the

bond critical point less than 0.12 au. The lowest values of (rc) for C1-C5 and N2-C5

in Figure 8 are larger than the highest value for N2-C3.


115

Figure 8

Figure 9 shows the variation of the atomic charges of the atoms involved in the

rearrangement and the H2O structure during the reaction.

The value of the charge for the H2O fragment is positive at the beginning of the

reaction but becomes almost zero after the transition state, although a hydrogen bond

from O to one of the H atoms bonded to C9 appears at the end of the reaction. This

result agrees with the resonance form for the reagent in Scheme 3 which shows a

positive charge on this fragment, although the positive values of the atomic charge

correspond to the hydrogen atoms of the fragment with a negative charge on the O

atom.

The atomic charges for C1 and C5 increase following a parallel pattern with

maximum differences between reagent and product of 0.400 and 0.331 au

respectively. At the beginning of the reaction, the charge of C5 atom scarcely


116

changes and the charge transfer happen from C1 to N2. After the transition state, this

charge is transferred to N2, which exhibits a maximum difference between reagent

and product of 0.670 au. During the first part of the reaction, before the transition

state, the hydrogens bonded to the C atoms transfer charge to the H2O fragment: the

hydrogen atoms lost 0.281 au and the water fragment gains 0.310 au. The C9 atomic

charge scarcely changes during the reaction and remains in values below 0.1 au

along the reaction.

Figure 9

CONCLUSIONS

For the three reactions studied (Curtius, Hofmann and Beckmann rearrangements) a

concerted mechanism with a same pattern was found. At the transition state of the

reaction the original bond present in the reagent molecule exists and the new one

does not. After the transition state the new bond is formed, when the old one breaks.

Regarding to the electron transfer during the reaction, a similar behaviour is found

fort the Curtius and the Beckmann rearrangements: only the atoms involved in the

migration (the atom that moves and the two atoms bonded to it in the reagent and the


117

product) exhibit large variation of charge along the path, i.e., the electron charge

transfer happen among them. For the Hofmann reaction the Br atom is also involved

in the charge transfer, because is the atom which moves away as an anion. The study

of the reagent, transition state and product structures reveals that the usual resonance

forms representing the geometries do not correspond to the obtained results for bond

lengths and atomic charges.

ACNOWLEDGEMENTS

We thank CESGA for acces to their computational facilities.

REFRENCES

[1] T. Curtius, Berichte der deutschen chemischen Gesellschaft 1890, 23, 3023-

3033.

[2] N. P. Gritsan, M. S. Platz, W. T. Borden, Computational Methods in

Photochemistry 2005, 13, 235-356.

[3] M. V. Zabalov, R. P. Tiger, Russian Chemical Bulletin 2012, 61, 1694-1704.

[4] J. Liu, S. Mandel, C. M. Hadad, M. S. Platz, Journal of Organic Chemistry

2004, 69, 8583-8593.



[7] V. Tarwade, O. Dmitrenko, R. D. Bach, J. M. Fox, Journal of Organic

Chemistry 2008, 73, 8189-8197.

[8] R. Kakkar, S. Zaidi, R. Grover, International Journal of Quantum Chemistry

2009, 109, 1058-1069.

[9] E. S. Wallis, J. F. Lane, in Organic Reactions, John Wiley & Sons, Inc.,

2004.


118

[10] A. Duan, L. Peng, D. Peng, F. L. Gu, Journal of Organic Chemistry 2013, 78,

12585-12592.

[11] E. Beckmann, Berichte der deutschen chemischen Gesellschaft 1886, 19,

988-993.

[12] A. H. Blatt, Chemical Reviews 1933, 12, 215-260.

[13] W. Z. Heldt, Journal of Organic Chemistry 1961, 26, 1695-1702.

[14] V. R. R. Marthala, Y. Jiang, J. Huang, W. Wang, R. Gläser, M. Hunger,

Journal of the American Chemical Society 2006, 128, 14812-14813.

[15] B. M. Reddy, G. K. Reddy, K. N. Rao, L. Katta, 2009, 306, 62-68.

[16] J. C. Jochims, S. Hehl, S. Herzberger, Synthesis-Stuttgart 1990, 1128-1133.

[17] J. Sirijaraensre, T. N. Truong, J. Limtrakul, The Journal of Physical

Chemistry B 2005, 109, 12099-12106.

[18] M. T. Nguyen, G. Raspoet, L. G. Vanquickenborne, Journal of the American

Chemical Society 1997, 119, 2552-2562.

[19] M. T. Nguyen, G. Raspoet, L. G. Vanquickenborne, Journal of the Chemical

Society-Perkin Transactions 2 1997, 821-825.

[20] G. Raspoet, M. T. Nguyen, L. G. Vanquickenborne, Bulletin Des Societes

Chimiques Belges 1997, 106, 691-697.

[21] J. Sirijaraensre, J. Limtrakul, Physical Chemistry Chemical Physics 2009, 11,

578-585.

[22] N. An, B.-X. Tian, H.-J. Pi, L. A. Eriksson, W.-P. Deng, Journal of Organic

Chemistry 2013, 78, 4297-4302.

[23] Y. Chu, P. Ji, X. Yi, S. Li, P. Wu, A. Zheng, F. Deng, Catalysis Science &

Technology 2015, 5, 3675-3681.

[24] G. W. T. M. J. Frisch, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman,

G. Scalmani, V. Barone, B. Mennucci, G. A. Petersson, H. Nakatsuji, M. Caricato,

X. Li, H. P. Hratchian, A. F. Izmaylov, J. Bloino, G. Zheng, J. L. Sonnenberg, M.

Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y.

Honda, O. Kitao, H. Nakai, T. Vreven, J. A. Montgomery, Jr., J. E. Peralta, F.

Ogliaro, M. Bearpark, J. J. Heyd, E. Brothers, K. N. Kudin, V. N. Staroverov, R.

Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J. C. Burant, S. S. Iyengar, J.


119

Tomasi, M. Cossi, N. Rega, J. M. Millam, M. Klene, J. E. Knox, J. B. Cross, V.

Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J.

Austin, R. Cammi, C. Pomelli, J. W. Ochterski, R. L. Martin, K. Morokuma, V. G.

Zakrzewski, G. A. Voth, P. Salvador, J. J. Dannenberg, S. Dapprich, A. D. Daniels,

Ö. Farkas, J. B. Foresman, J. V. Ortiz, J. Cioslowski, and D. J. Fox, Gaussian, Inc.,

Wallingford CT, 2009.

[25] R. W. F. Bader, Atoms in Molecules: A Quantum Theory Oxford University

Press: New York, 1990.

[26] R. F. W. Bader, Chemical Reviews 1991, 91, 893-928.

[27] F. W. Bieglerkonig, R. F. W. Bader, T. H. Tang, Journal of Computational

Chemistry 1982, 3, 317-328.

[28] C. Wentrup, H. Bornemann, European Journal of Organic Chemistry 2005,

4521-4524.

[29] K. Yokoyama, S. Takane, T. Fueno, Bulletin of the Chemical Society of

Japan 1991, 64, 2230-2235.

[30] A. M. Mebel, A. Luna, M. C. Lin, K. Morokuma, Journal of Chemical

Physics 1996, 105, 6439-6454.

[31] W. A. Shapley, G. B. Bacskay, Journal of Physical Chemistry A 1999, 103,

6624-6631.

[32] A. L. L. East, W. D. Allen, Journal of Chemical Physics 1993, 99, 4638-

4650.

[33] P. J. a. M. Linstrom, W. G., Eds., NIST Chemistry WebBook, NIST

Standard Reference Database Number 69, National Institute of Standards

and Technology, Gaithersburg MD, 20899, http://webbook.nist.gov.

[34] J. Luis Lopez, A. M. Grana, R. A. Mosquera, Journal of Physical Chemistry

a 2009, 113, 2652-2657.

http://webbook.nist.gov/


120

5. CONCLUSIONES

El análisis QTAIM de la densidad electrónica de varias series de

cianocompuestos considerados como inertes o sometidos a procesos

ácido-base, así como el estudio de la evolución de la densidad electrónica

en varias transposiciones que tienen asiento en compuestos

nitrogenados, han permitido establecer las siguientes conclusiones:

El grupo CN de los cianoalcanos lineales presenta valores

transferibles para todas sus propiedades atómicas y de enlace si

se exceptúa la energía atómica, que muestra una dependencia

del tamaño molecular. Este efecto, encontrado en otras series

homólogas, es un artificio debido a los diferentes valores del

cociente virial. Por el contrario, la energía cinética electrónica

atómica si presenta valores transferibles.

Se han encontrado varios tipos de átomos transferibles, propios

de la serie de cianoalcanos lineales:

i. Los átomos C y N del grupo CN.

ii. C en α respecto al grupo CN.

iii. C en β respecto al grupo CN.


121

Los siguientes átomos presentan un comportamiento específico

en los cianoalcanos lineales:

i. El C en posición α en los nitrilos de metilo y etilo.

ii. El C en posición β en los nitrilos de etilo y propilo.

iii. El C y el N del grupo CN en los cianuros de hidrógeno y

metilo.

El resto de los carbonos de la cadena presentan un

comportamiento similar a los correspondientes de los n-alcanos,

sean estos: internos, terminales o previos al C terminal.

El número de grupos CH2 que se puede distinguir en un

cianoalcano crece cuando se tienen en cuenta simultáneamente

propiedades atómicas y de enlace de todos los átomos

(incluyendo a los hidrógenos) y el conjunto de datos se trata con

criterios estadísticos rigurosos. Así, se pueden considerar hasta

12 grupos CH2 diferentes en los cianoalcanos lineales de cadena

larga. Estos son los metilenos situados a hasta 8 enlaces del

grupo CN, el CH2 interno y los CH2 α, β y γ al metilo terminal. Los

cuatro últimos grupos son comunes con la serie de n- alcanos.


122

La influencia mutua entre grupos CN (efecto de proximidad) sólo

puede considerarse despreciable cuando están separados por

más de 14 grupos CH2. No obstante, los efectos debidos a la

presencia de dos grupos CN pueden considerarse aditivos salvo

en compuestos CN(CH2)nCN con n<4.

La rotación del enlace central de un dicianoalcano modifica

sensiblemente las propiedades de los grupos CH2 situados entre

posiciones α y δ al enlace.

En los cianocompuestos N-protonados, el protón conserva una

elevada carga positiva. Por ello, lo representa más

adecuadamente la estructura de Lewis H+N≡CR que las

estructuras: HN+≡CR o HNC+R tradicionalmente

empleadas. También favorece la prioridad de dicha estructura el

hecho de que tras la protonación, en el enlace C≡N, aumenta la

densidad π y disminuye la ς.

La N-protonación de un nitrilo no conjugado origina

transferencias electrónicas que afectan a toda la molécula, tal

como sucede en las O- y N-protonaciones de otros compuestos


123

alifáticos. Sin embargo, en las protonaciones de nitrilos

conjugados las variaciones de población electrónica son

fundamentalmente de tipo π.

La desprotonación está significativamente favorecida frente a

las restantes en todos los cianocompuestos estudiados. Cuando

la molécula presenta sustituyentes adicionales que retiran

densidad electrónica por efecto resonante la energía de

desprotonación se reduce significativamente. No se observa un

efecto opuesto cuando la molécula incorpora dadores por

efecto resonante. Por el contrario, las energías de

desprotonación son muy semejantes a las del cianometano.

Tampoco tiene efectos significativos: el tamaño y la ramificación

del grupo alquilo o la inclusión de átomos electronegativos.

En general el modelo de resonancia proporciona predicciones

compatibles con las variaciones de población electrónica

atómica que acompañan a la desprotonación de un nitrilo. Así,

se observa un importante aumento de la población electrónica

del N del grupo ciano.


124

Las etapas de migración de las reacciones de transposición de

Curtius, Hofmann y Beckmann son elementales.

Estas reacciones transcurren siguiendo un patrón similar: el

nuevo enlace se forma después del estado de transición cuando

ya se ha roto el enlace original. En ningún punto intermedio de

la reacción coexisten los enlaces originales y los que se forman

durante la misma.

La transferencia de carga a lo largo de las reacciones de

transposición se produce esencialmente entre los átomos

implicados en la transposición: el átomo que migra y los

enlazados a él en el reactivo y el producto. En la transposición

de Hofmann también está implicado en la transferencia de carga

el Br que se separa como anión.


125


126

6. BIBLIOGRAFÍA

1. A. M. Graña, R. A. Mosquera, J. Chem. Phys. 110 (1999) 6606. 2. A. M. Graña, R. A. Mosquera, J. Chem. Phys. 113 (2000) 1492. 3. A. Vila, E. Carballo, R. A. Mosquera, Can. J. Chem. 78 (2000) 1535. 4. A. Vila, R. A. Mosquera, J. Chem. Phys. 115 (2001) 1564. 5. M. J. González Moa, R. A. Mosquera, J. Phys. Chem. A 107 (2003) 5361. 6. M. J. González Moa, R. A. Mosquera, J. Phys. Chem. A 109 (2005) 3682. 7. A. M. Graña, J. M. Hermida-Ramón, R. A. Mosquera, Chem. Phys. Lett. 412 (2005) 106. 8. M. Mandado, C. Van Alsenoy, R. A. Mosquera, J. Phys. Chem. A 108 (2004) 7050. 9. M. Mandado, R. A. Mosquera, A. M. Graña, Chem. Phys. Lett. 386 (2004) 454. 10. M. Mandado, C. Van Alsenoy, R. A. Mosquera, Chem. Phys. Lett. 405 (2005) 10. 11. A. Vila, R. A. Mosquera, J. Phys. Chem. A 109 (2005) 6985. 12. R. F. W. Bader, Atoms in Molecules a Quantum Theory, Oxford University Press, 1990. 13. R. F. W. Bader, Chem. Rev. 91 (1991) 893. 14. R. F. W. Bader, Acc. Chem. Res. 18 (1985) 9. 15. P. L. A. Popelier, Atoms in Molecules: An Introduction, Prentice & Hall, 2000. 16. C. Gatti, P. Macchi, Modern Charge-Density Analysis, Springer Verlag, 2012. 17. R. F. W. Bader, Can. J. Chem. 77 (1999) 86. 18. R. F. W. Bader, Int. J. Quantum Chem. 94 (2003) 173. 19. R. F. W. Bader, P. Becker, Chem. Phys. Lett. 148 (1988) 452. 20. J. Riess, W. Münch, Theor. Chmi. Acta 58 (1981) 295. 21. J. L. López, M. Mandado, A. M. Graña, R. A. Mosquera Int. J. Quantum Chem. 86 (2002) 190. 22. J. L. López, M. Mandado, M. J. González Moa, R. A. Mosquera Chem. Phys. Lett. 422 (2006) 558. 23. J. L. López, A. M. Graña, R. A. Mosquera J. Phys. Chem. A 113 (2009) 2652. 24. J. L. López, A. M. Graña, R. A. Mosquera Roy. Soc. Adv. Para ser sometido (2015). 25. J. L. López, R. A. Mosquera, A. M. Graña Eur. J. Org. Chem. Par ser sometido (2015). 26. M. Mandado, A. M. Graña, R. A. Mosquera J. Mol. Struct. (THEOCHEM) 584 (2002) 221. 27. L. Lorenzo, R. A. Mosquera Chem. Phys. Lett. 356 (2002) 305. 28. M Mandado, A. Vila, A. M. Graña, R. A. Mosquera, J. Cioslowski Chem. Phys. Lett. 371 (2003) 739. 29. F. Cortés-Guzmán, R. F. W. Bader Chem. Phys. Lett. 379 (2003) 183. 30. R. F. W. Bader, D. Bayles, J Phys. Chem. A 104 (2000) 5579. 31. R. F. W. Bader, Ting-Hua Tang, Y. Tal, F. W. Biegler-König J. Am. Chem. Soc. 104 (1982) 940. 32. R. F. W. Bader, Ting-Hua Tang, Y. Tal, F. W. Biegler-König J. Am. Chem. Soc. 104 (1982) 946. 33. H. V. Kehiaian Fluid Phase Equilibria 13 (1983) 243. 34. C. E. Shannon The Bell System Technical Journal 27 (1948) 379. 35. M. Hô, V. H. Smith Jr., D. F. Weaver, C. Gatti, R. P. Sagar, R. O. Esquivel J. Chem. Phys. 108 (1998) 5469.


127

36. M. Hô, B. J. Clark, V. H. Smith Jr., D. F. Weaver, C. Gatti, R. P. Sagar, R.O. Esquivel J. Chem. Phys. 112 (2000) 7572. 37. A. Vila, R. A. Mosquera Chem. Phys. Lett. 332 (2000) 474. 38. A. Vila, R. A. Mosquera Tetrahedron 57 (2001) 9415. 39. M. J. González Moa, M. Mandado, R. A. Mosquera Chem. Phys. Lett. 428 (2006) 255. 40. N. Otero, M. J. González Moa, M. Mandado, R. A. Mosquera Chem. Phys. Lett. 428 (2006) 249. 41. N. C. J. Stutchbury, D. L. Cooper J. Chem. Phys. 79 (1983) 4967. 42. S. Arseniyadis, K. S. Kyler, D.S. Watt, Org. React. 31 (1984) 1. 43. T. Curtius Chem. Ber. 23 (1890) 3023. 44. E. Beckmann, Chem. Ber. 19 (1886) 988. 45. A. W. v. Hofman, Chem. Ber. 14 (1881) 2725. 46. J. Liu, S. Mandel, C. M. Hadad, M. S. Platz, J. Org. Chem. 69 (2004) 8583. 47. M. V. Zabalov, R. P. Tiger, Russ. Chem. Bull. (Int. Ed.) 54 (2005) 2270. 48. M. V. Zabalov, R. P. Tiger, Russ. Chem. Bull. (Int. Ed.) 56 (2007) 7. 49. V. Tarwade, O. Dmitrenko, R. D. Bach, J. M. Fox, J. Org. Chem. 73 (2008) 8189. 50. J. Shorter, en S. Patai, Z. Rapport (eds.) The Chemistry o f Triple-Bonded Functional Groups, Wiley, 1994, capítulo 5. 51. P. Botschwina, M. Horn, M. Matuschewski, E. Schick, P. Sebals, J. Mol. Struct. (THEOCHEM) 400 (1997) 119. 52. F. H. Allen, S. E. Garner, en S. Patai, Z. Rapport (eds.) The Chemistry o f Triple-Bonded Functional Groups, Wiley, 1994, capítulo 2. 53. W. M. Irvine, Space Sci. Rev. 90 (1999) 203. 54. D. H. Rouvray Topics. Curr. Chem. 173 (1995) 1. 55. R. Carbó, L. Leyda, M. Arnau Int. J. Quantum Chem. 17 (1980) 1185. 56. J. Cioslowski, A. Nanayakkara J. Am. Chem. Soc. 115 (1993) 11213. 57. J. Cioslowski, B. B.Stefanov, P. J. Constans J. Comput. Chem. 17 (1996) 1352. 58. R. F. W. Bader Pure Appl. Chem. 60 (1988) 145. 59. J. Schwinger Phys. Rev. 82 (1951) 914. 60. R. F. W. Bader Can. J. Chem. 77 (1998) 86. 61. R. F. W. Bader, P. L. A. Popelier, T. A. Keith Angew. Chem. Int. Ed. Engl. 33 (1994) 620. 62. S. Srebenik, R. F. W. Bader J. Chem. Phys. 63 (1975) 3945. 63. S. I. Sandler, Models for Thermodynamic and Phase Equilibria Calculations, Marcel Dekker, 1994. 64. S.-T. Lin, S. I. Sandler, J. Phys. Chem. A 104 (2000) 7099. 65. D. González-Salgado, C. A. Tovar, C. A. Cerdeiriña, E. Carballo, L. Romaní, Fluid Phase Equilibria 199 (2002) 121. 66. S. Delcros, J. R. Quint, J. P. E. Grolier, H. V. Kehiaian Fluid Phase Equilibria 113 (1995) 1. 67. A. Vila, E. Carballo, R. A. Mosquera, J. Mol. Struct. (THEOCHEM) 617 (2002) 219. 68. A. E. Aliev, K. D. M. Harris, P. H. Champkin J. Phys. Chem. B 109 (2005) 23342. 69. K. D. M. Harris, en: J. L. Atwood, J. W. Steed (eds.) Encyclopedia of Supramolecular Chemistry, vol. 2, Marcel Dekker, 2004, pp. 1538–1549. 70. F. A. Carey, R. J.Sundberg Advanced Organic Chemistry, Kluwer Academic, 2001. 71. G.W. Wheland Resonance in Organic Chemistry, Wiley, 1955. 72. K. B. Wiberg, K. E. Laidig J. Am. Chem. Soc.109 (1987) 5935. 73. K. B. Wiberg, C. M. Breneman, J. Am. Chem. Soc. 114 (1992) 831.


128

74. R. Glaser, G. S. K. Choy J. Am. Chem. Soc. 115 (1993) 2340. 75. C. L. Perrin J. Am. Chem. Soc. 113 (1991) 2865. 76. K. E. Laidig J. Am. Chem. Soc. 114 (1992) 7912. 77. C. Gatti, P. Fantucci J. Phys. Chem. 97 (1993) 11677. 78. F. L. Hirshfeld, Theor. Chim. Acta 44 (1977) 129. 79. F. De Proft, C. Van Alsenoy, A. Peeters, W. Langenaker, P. J. Geerlings, J. Comput. Chem. 23 (2002) 1198. 80. L. H. Thomas Proc. Camb. Phil. Soc. 23 (1926) 542. 81. E. Fermi, Zeits. für Phys. 48 (1928) 73. 82. W. Kohn, L. Sham Phys. Rev. A 140 (1965) 1133. 83. R.G. Parr, W. Yang Density Functional Theory of Atoms and Molecules, Oxford University Press, 1989. 84. E. S. Kryachko, E. V. Ludeña, Energy Density Functiona Theory of Atoms in Molecules, Kluwer Academic Publishres, 1990. 85. P. Hohenberg, W. Kohn Phys. Rev. B 136 (1964) 864. 86. J. F. Janak, Phys. Rev. B 18 (1978) 7165. 87. A. Strowasser, R. Hoffman J. Am. Chem. Soc. 121 (1999) 3414. 88. G. E. Scuseria, V. N. Staroverov en: Theory and Application of Computational Chemistry: The First 40 Years. C. E. Dykstra, G. Frenking, K. S. Kim, G. E. Scuseria, (eds.) Elsevier, 2005; p. 669. 89. Y. Zhao, N. E. Schultz, D. G. Truhlar J. Chem. Theory Comput. 2 (2006) 364. 90. Y. Zhao, D. G. Truhlar Theor. Chem. Acc. 120 (2008) 215. 91. Y. Zhao, D. G. Truhlar Acc. Chem. Res. 41 (2008) 157. 92. J. Tao, J. P. Perdew. V. N. Staroverov, G. E. Scuseria Phys. Rev. Lett. 91 (2003) 146401. 93. X. Xu, W. A. Goddard, III, Proc. Natl. Acad. Sci. U.S.A. 101 (2004) 2673. 94. J. P. Perdew, K. Schmidt en Density Functional Theory and Its Applications to Materials, V. Doren, C. Van Alsenoy, P. Geerlings.(eds.) American Institute of Physics 2001. 95. A. E. MattssonScience 298 (2002) 759. 96. R. Van Leeuwen, E. Baerends J. Phys. Rev. A 49 (1994) 2421. 97. A. D. Becke, J. Chem. Phys. 109 (1998) 2092. 98. P. Mori-Sanchez, A. J. Cohen, W. Yang J. Chem. Phys. 124 (2006) 91102. 99. A. D. Becke J. Chem. Phys. 98 (1993) 5648. 100. J. Perdew, A. Ruzsinszky, J. Tao, V. N. Staroverov, G. E. Scuseria, G. I. Csonka J. Chem. Phys. 123 (2005) 62201. 101. Q. Wu, P. W. Ayers, W. Yang, J. Chem. Phys. 119 (2003) 2978. 102. M. Dion, H. Rydberg, E. Schroder, D. C. Langreth, B. I. Lundqvist Phys. Rev. Lett. 92 (2004) 246401. 103. T. Sato, T. Tsuneda, K.; Hirao, J. Chem. Phys. 123 (2005) 4307. 104. E. R. Johnson, A. D. Becke, J. Chem. Phys. 124 (2006) 174104 105. S. Grimme, J. Comput. Chem. 27 (2006) 1787. 106. T. Sato, T. Tsuneda, K. Hirao, J. Chem. Phys. 126 (2007) 234114. 107. P. Jurecka, J. Cerny, P. Hobza, D. R. Salahub J. Comput. Chem. 28 (2007) 555. 108. C. Lee, W. Yang, R. G. Parr, R. G. Phys. Rev. B 37 (1988) 785. 109. A. D. Becke Phys. Rev. A 38 (1988) 3098. 110. W. Kohn, Y. Meir, D. E. Makarov Phys. Rev. Lett. 80 (1998) 4153. 111. T. V. Mourik, R. J. Gdanitz, J. Chem. Phys. 116 (2002) 9620.


129

112. Y. Zhao, D. G. Truhlar J. Phys. Chem. A 108 (2004) 6908. 113. A. D. Becke, J. Chem. Phys. 104 (1996) 1040. 114. B. J. Lynch, P. L. Fast, M. Harris, D. G. Truhlar J. Phys. Chem. A 104 (2000) 4811. 115. P. A. M. Dirac Proc. Cambridge Philos. Soc. 26 (1930) 376. 116. J. C. Slater Quantum Theory of Matter, McGraw-Hill, 1968. 117. C. Adamo, V. Barone, J. Chem. Phys. 108 (1998) 664. 118. B. J. Lynch, D. G. Truhlar J. Phys. Chem. A 107 (2003) 8996. 119. N. Castillo, C. F. Matta, R. Boyd J. Chem. Phys. Lett. 409 (2005) 265. 120. J. Poater, M. Solà, F. M. Bickelhaupt, Chem. Eur. J. 12 (2006) 2889. 121. R. F. W. Bader Chem. Eur. J. 12 (2006) 2896. 122. A. Haaland, D. J. Shorokhov, N. V. Tverdova, Chem. Eur. J. 10 (2004) 4416; Chem. Eur. J. 10 (2004) 6210 (Corrigendum). 123. R. F. W. Bader, F. De-Cai, J. Chem. Theory Comput. 1 (2005) 403. 124. J. Cioslowski, S. T. Mixon, Can. J. Chem. 70 (1992) 443. 125. J. Cioslowski, S. T. Mixon, J. Am. Chem. Soc. 114 (1992) 4382. 126. R. F. W. Bader J. Phys. Chem. A 102 (1998) 7314. 127. F. W. Biegler-König, J. Schönbohm, D. Bayles J. Comp. Chem. 22 (2001) 545. 128. P. B. Quiñónez, A. Vila, A. M. Graña, R. A. Mosquera Chem. Phys. 287 (2003) 227. 129. A. Vila, R. A. Mosquera Chem. Phys. Lett. 345 (2001) 445. 130. M. Lehd, F. Jensen J. Comput. Chem. 12 (1991) 1089. 131. M. Mandado, A. M. Graña, R. A. Mosquera Chem. Phys. Lett. 355 (2002) 529. 132. T. S. Slee, P. J. MacDougall Can. J. Chem. 66 (1988) 2961. 133. K. E. Laidig, L. M. Cameron J. Am. Chem. Soc. 118 (1996) 1737. 134. R. Glaser J. Phys. Chem. 93 (1989) 7993. 135. P. Speers, K. E. Laidig, A. Streitwieser J. Am. Chem. Soc. 116 (1994) 9261. 136. A. Vila, R. A. Mosquera Chem. Phys. Lett. 371 (2003) 540. 137. N. Otero, L. Estévez, M. Mandado, R. A. Mosquera, Eur. J. Org. Chem. 12 (2012) 2403. 138. L. Estévez, R. A. Mosquera, Chem. Phys. Lett. 451 (2008) 121.

UNIVERSIDAD DE VIGO TESIS DOCTORAL

Documents

Transcript of UNIVERSIDAD DE VIGO TESIS DOCTORAL