Chemical Physics 303 (2004) 157–164

www.elsevier.com/locate/chemphys

Ab initio study of the singlet–triplet relative stability of2,6-dibromo-20,60-bistrifluoromethyl-diphenylmethylene

Elena Rodr�ıguez, Rosa Caballol, Mar Reguero *

Departament de Qu�ımica F�ısica i Inorg�anica, Universitat Rovira i Virgili, Pl. Imperial Tarraco 1, 43005 Tarragona, Spain

Received 16 March 2004; accepted 19 May 2004

Available online 15 June 2004

Abstract

Diphenylmethylene is the main parent system in the search of stable carbenes, singlet as well as triplet ones. The substituents of

the phenyl rings are the keys to favour one state in front of the other, but the mechanism of this influence is little known. A model of

one of the first stable triplet carbenes that has been synthesized, the 2,6-dibromo-20,60-bistrifluoromethyl-diphenylmethylene, has

been the subject of this theoretical study. Singlet–triplet energy differences have been calculated using high level ab initio methods

(CASSCF for optimum geometries and DDCI for vertical energy differences and CASPT2 and B3LYP-Broken Symmetry for

comparison purposes). For the model carbene the results showed that the triplet state, with a large carbenic angle, was more stable

than the singlet one. Two additional series of calculations have been carried out to analyze the electronic and steric influence of the

phenyls and the phenyl substituents on the singlet–triplet relative stability.

� 2004 Elsevier B.V. All rights reserved.

Keywords: Diphenylcarbene; Singlet–triplet relative stability; Correlated ab initio calculation

1. Introduction

The study of reactive intermediates at chemical and

structural levels is of prime importance for under-

standing physical organic chemistry. In this field, stable

carbenes can provide an insight into transient organicchemistry and are of considerable importance in syn-

thetic chemistry. As early as 1910 Staudinger’s studies

on the decomposition of diazo compounds led to

carbenes being recognised as reactive species [1]. Their

role as transient intermediates has become of great im-

portance in the last five decades. The ground state spin

multiplicity is determinant on the carbene reactivity, so

it is a crucial factor that must be controlled. Althoughin the 70’s a lot of experimental as well as theoretical

work was devoted to carbenes [2] the search for stable

singlet carbenes in normal conditions was only suc-

* Corresponding author. Tel.: +34-977-559718; fax: +34-977-559563.

E-mail address: reguero@quimica.urv.es (M. Reguero).

0301-0104/$ - see front matter � 2004 Elsevier B.V. All rights reserved.

doi:10.1016/j.chemphys.2004.05.013

cessful in the late 1980s, when macroscopic amounts of

these compounds were isolated at room temperature [3].

Nowadays, there is still a considerable amount of re-

search activity in this area, attempting to find singlet

species with a sufficiently long life but with the char-

acteristic reactivity of these compounds [4]. Althoughtriplet carbenes have also been known experimentally

for some decades [5] and Zimmerman did some work on

them in 1964 [6], it was only in the 1990s that stable

triplet species (diphenylmethylenes derivatives) were

first synthesized [7]. Development was fast, going from a

half life of a few seconds in special conditions at room

temperature for the 2,20,4,40,6,60-hexabromo-diphe-

nylmethylene [8] to 200 s in normal conditions for the2,20,6,60-tetrabromo-4,40-di-tert-butyldiphenylmethylene

[9] and 1 h in solution at room temperature and infinite

stability at )40 �C for the 2,6-dibromo-4-tert-butyl-

20,60-bistrifluoromethyl-40-isopropyldiphenylmethylene

1, ‘‘a triplet carbene that can almost be bottled’’ [10].

The newest triplet carbenes synthesized are stable for

hours at room temperature [11].

158 E. Rodr�ıguez et al. / Chemical Physics 303 (2004) 157–164

BrCF3

BrCF3

r1 r2

θ

12

3

5

64

1'2'

3'

4'

5'

6'

φ1 = < C2C1C1'C2'

78

7'8'

0

1

To control the ground state spin multiplicity, it is

necessary to know the factors that favor the stabilization

of one species or the other. In general, electronic effects

(enlargement of the electronegativity of the substituents

and inductive or mesomeric effects) stabilize the singlet

via thermodynamic stabilization, while steric effects due

to bulky substituents stabilize both singlet and triplet

species by protecting the reactive carbene center (kineticstabilization). Stabilization of the triplet relative to the

singlet state seems only to be possible by substituents

that enlarge the carbenic angle, a. Thus, if electronic

effects are negligible, steric effects determine the ground

state multiplicity [12,13].

With this in mind, it is easy to understand how it is

possible to stabilize the singlet state and isolate singlet

carbenes but it is not such an easy task to stabilize thetriplet state to get triplet stable carbenes. Although some

experiments with dialkylmethylenes have been successful

recently [13], most of the research has concentrated on

diphenylmethylenes. The sterically hindered polyhalo-

genated and polymethylated diphenylmethylenes are

potentially good parent compounds for stable triplet

carbenes [1,9,10,14] but further stabilization via new

substituents in the phenyl ring is required if a compoundis to be stable in normal conditions at room tempera-

ture. Some recent studies focus on this point [14], but

light still needs to be shed on the different possible ways

of influence of the phenyl substituents.

Likewise, little is known about the structure of triplet

diphenylmethylenes. Because the compounds of this

family synthesized so far have a short life, the X-ray

crystallographic structure is known for only one com-pound, bis(2,4,6-trichlorophenyl)methylene, trapped in

a crystal [15].

Fortunately, these gaps in knowledge are gradually

being filled by theoretical studies, which have proved to

be an essential complement to experimental studies. In

this respect, carbenes have also created considerable

early interest. The first ab initio calculations had to fo-

cus on small carbenes [16] and these systems, althoughapparently simple, have not become stale [17]. They are

still considered a challenge and used as benchmarks to

check the accuracy of new theoretical methods

[17a,17b,17i]. Larger systems with bulky substituents

have not been the subject of theoretical studies until

short ago, when several studies on phenyl- and diphe-

nylmethylenes and derivatives were carried out using

density functional theory (DFT) methods. Structures,

energies and the effects of changes on substituents and

geometry were analysed [15,18] and reactivity studied[19]. Nevertheless, because DFT methods have difficul-

ties in accurately describing some open shell structures

or systems that cannot be described at a single reference

level, it seems advisable to study some of these larger

systems with high-level multireference methods, which

provide eigenfunctions of bS2, so as to have other reliable

theoretical data for purposes of comparison. In this

paper we present a computational study of the 2,6-dib-romo-20,60-bistrifluoromethyl-diphenylmethylene, spe-

cies 2, as a model of the triplet stable carbene 1. The

differences between species 1 and 2 are expected to have

a negligible effect on the singlet–triplet energy difference.

This hypothesis will be justified later on.

BrCF3

BrCF3

r1 r2

θ

12

3

5

6 4

1'2'

3'

4'

5'6'

φ1 = < C2C1C1'C2'

0

2

The difference dedicated configuration interaction

(DDCI)method [20] is used to compute the singlet–triplet

energy gap.Thismethodhas already been tested in several

types of systems and has given very accurate energy dif-

ferences [17i,21]. In particular, when it was used to cal-

culate singlet–triplet gaps for small carbenes, thecomparison with full configuration interaction (FCI) re-

sults was highly satisfactory. Agreement with experi-

mental data was also excellent for halogenated carbenes

[17i]. We have ran complete active space self-consistent

field (CASSCF) calculations to optimize the structures

and have carried out some CASPT2 and DFT calcula-

tions for comparison purposes.Wehave also analyzed the

main factors that determine themultiplicity of the groundstate of the derivatives of the diphenylmethylene.

2. Computational details

The singlet–triplet vertical energy differences have

been evaluated with the DDCI method [20]. DDCI is a

multireference selected single and double CI methodthat uses a minimal CAS as reference space. The selec-

tion of the configurations is based on the fact that up to

second order perturbation theory all the configurations

that arise from double excitations from the doubly oc-

E. Rodr�ıguez et al. / Chemical Physics 303 (2004) 157–164 159

cupied to the virtual orbitals on top of the CAS do not

contribute to the energy difference of the electronic

states of interest and hence, can be eliminated. This

considerably reduces the computational effort in the

diagonalization of the CI space. However, the procedurestill gives rise to huge CI expansions at the DDCI level.

To overcome this difficulty, we used the dedicated mo-

lecular orbitals (DMO) strategy [22] to truncate the MO

set. As has been pointed out, the orbital energies are not

a good criterion for cutting the orbital space and suc-

cessive truncations give a poor convergence with the size

of the MO space. Instead, a sound hierarchic order of

the MOs can be obtained by diagonalizing the differenceof the two density matrices associated to the two states

involved in the energy difference. The resulting orbitals

are known as dedicated orbitals and the corresponding

eigenvalues, the so called participation numbers, give an

indication of how important each dedicated orbital is in

the magnetic coupling. In this way, the MO space can be

reduced with almost no loss of accuracy. A final re-

finement to the method prevents the results from de-pending on the starting MOs by improving them

iteratively (IDDCI) [23] to better describe the transition

studied.

When DFT calculations have been carried out, we

have used the broken symmetry (BS) approach [24].

DES–T has to be calculated as

DES–T ¼ 2 EBS � ETð Þ2� S2h i ; ð1Þ

where hS2i is the expectation value of cS2 .

CASSCF and geometry optimization calculations

have been carried out with the MOLCAS package (5.4version) [25] and DFT, B3LYP and UB3LYP (Broken

Symmetry) calculations with the GAUSSIANAUSSIAN 98 package

[26]. The DDCI calculations have been performed with

the casdi code [27] and dedicated and IDDCI orbitals

were obtained with the natural program [28]. For

CASSCF and DDCI calculations of all compounds a

minimal basis set was used for all C, H and F atoms

except for the carbenic carbon, for which an extendedbasis set, (10s6p4d)/[5s3p2d] was used. Goddard et al.

[29] have shown that to minimize the correlation error

due to basis set limitation, it is much more effective to

extend the basis on the central C than on the substitu-

ents. For Br atoms the effective core potential of Ba-

randiaran and Seijo (Cowan–Griffin relativistic ab initio

core Potential type) [30] was used with a (9s8p4d)/

[1s1p2d] basis set for the external electrons. For theUB3LYP (Broken Symmetry) calculations, the aim of

which was to make comparisons with other published

DFT results, we used the same basis set as in these

previous calculations, that is, the Pople triple-f split

valence set, 6-311G(d,p) [31]. The geometry of species 2

was optimized without any restriction. The use of ef-

fective core potentials for Br atoms precludes the pos-

sibility of carrying out frequency calculations (in the

Molcas 4.1 package), so ZPE corrections could not be

taken into account for this compound.

In all the DDCI calculations the core orbitals were

frozen. For compound 2, the largest system studied here,21 orbitals were frozen, which yielded around 2� 106

determinants for the DDCI wave functions. For com-

pounds 3a, 3b, 4 and 5, the 1s orbitals of the C, Br and F

atoms were frozen. When the Dedicated-MO DDCI

approximation was used with a threshold of 10�3 for the

participation number, approximately 20% of the mo-

lecular orbitals were discarded and the number of de-

terminants of the wave function reduced to 106

approximately.

3. Results and discussion

The hypothesis of the negligible influence of the

substituents in 4 and 40 positions in species 1 is based on

some recent experimental work that systematicallystudied the effect of para substituents on diphenylm-

ethylenes [14]. This work showed that para substituents

do not modify the geometry of the carbene but, when

the unpaired electron on the p orbital of the triplet

carbene is delocalized, the triplet is stabilized thermo-

dynamically. But as the authors pointed out, this is not

the case for the para-t-butyl group, which stabilizes the

singlet and triplet carbenes equally, only at the kineticlevel, because it hinders any possible dimerization in the

para position. The same effect is expected of the para-

isopropyl substituent. For this reason it is expected that

para substituents will not affect the singlet–triplet energy

difference. In fact, as our results will show later, the

ground state of compound 2 is also the triplet, like in

compound 1.

The geometry optimization of the singlet and tripletstates of 2 was first performed at the CASSCF(2,2) level

with no restrictions. The main geometrical parameters

are shown in Table 1. In both states the two aromatic

rings are almost perpendicular to each other, one nearly

in the plane of the carbene (/1ðsingletÞ ¼ 20�,/1ðtripletÞ ¼ 13�), and the other nearly perpendicular to

it (/2ðsingletÞ ¼ 77�, /2ðtripletÞ ¼ 80�). In a series of

calculations carried out later on, a simplified Cs geom-etry was used. Table 1 also shows the reoptimized pa-

rameters of this geometry with a symmetry plane

ð/1 ¼ 0�, /2 ¼ 90�Þ.In the CASSCF optimized geometry of 2, the triplet

state has a central bond angle of 146�, larger than the

singlet state angle of 127�. In the singlet geometry the

bond distance from the central carbon to the bromine-

substituted ring is slightly shorter than the distance tothe trifluormethyl-substituted one due to the orientation

of the first aromatic ring that allows the electron

donation from the ring to the empty p orbital of the

Table 1

Main geometrical parameters calculated for 2 (C1 and Cs geometries) and 1 (C1 geometry) and measured experimentally for bis(2,4,6-trichloro-

phenyl)methylene

State h dC0–C1dC0–C10 /

2-C1 CASSCF(2,2)a T 145.9 1.395 1.406 82.5

S 127.5 1.396 1.404 80.1

2-Cs CASSCF(2,2)a T 143.0 1.400 1.409 90.0

S 129.3 1.388 1.397 90.0

1-C1 B3LYPb T 176.3 1.368 1.368 90.7

S 134.2 1.393 1.403 79.1

Experimentalc T 142.0 1.437 1.423 76.0

Angles in (�), bond distances in (�A).a This study.bRef. [18a].c Ref. [15].

160 E. Rodr�ıguez et al. / Chemical Physics 303 (2004) 157–164

carbenic center and consequently the bond order is in-

creased. In the triplet state the two atomic orbitals of the

carbene center are singly occupied, so the interactionwith both aromatic rings is similar and the bond dis-

tances dC0–C1and dC0–C10 are also similar.

The accuracy of the geometries obtained cannot be

directly judged, as there are no experimental data for

this system. The structural parameters obtained can only

be compared with the DFT geometry calculated for 1

[18a] at the B3LYP/6-311G(d,p) level (see Table 1 for

the main geometrical parameters) and with the X-raycrystallographic data of the triplet state of the bis(2,4,6-

trichlorophenyl)methylene trapped in a crystal [15] (see

Table 1). The geometrical parameters obtained in this

study are nearer the experimental values than those of

the DFT calculations. In particular the DFT triplet state

gives an almost linear structure for the central carbene.

This unexpected result can be imputed to the flatness of

the triplet surface obtained in [18a].Absolute energies and energy gaps are collected in

Table 2. Vertical energy differences were calculated with

CASSCF(2,2), CASPT2(2,2) and DDCI methods at the

Table 2

Vertical singlet–triplet energy differences (in kcalmol�1) at the optimized ge

Method State Absolute energies

Triplet minimum S

CASSCF(2,2)a S )1193.3343 )T )1193.3731 )

CASPT(2,2)a S )1194.5962 )T )1194.6447 )

B3LYP(BS)b S )6322.6575 )T )6322.6677 )

DDCIa S )1193.4788 )T )1193.5081 )

DDCI-DMOsa S )1193.4767 )T )1193.5063 )

IDDCI-DMOsa S )1193.4992 )T )1193.5231 )

aWith core potentials.bAll electron.

singlet and triplet minima. The triplet state is more

stable than the singlet one and, consequently, the energy

differences are smaller at the singlet minimum. Only atthe IDDCI and DFT B3LYP(BS) level do the energy

curves cross and the singlet state is slightly more stable

than the triplet one (by around 1.5 kcalmol�1) at the

singlet minimum.

At first sight, the discrepancy of the CASPT2 results

is surprising. To know if it is due to the limited size of

the active space, several calculations at the 2-Cs triplet

geometry were run with enlarging active spaces. Anenergy criterion was used to choose the active orbitals

until the whole p system of both aromatic rings were

included in the active space (Table 3). The stability of

the vertical energy difference rules out the size of the

active space as the source of the poor results of the

CASPT2 methods and confirms the validity of our

DDCI calculations based on a (2,2) active space. Other

authors (Schaefer in [19b], Borden in [19e]) have alreadystated the failure of the CASPT2 methods in this kind of

calculations where the electronic configuration of the

states to be compared have different type of orbital oc-

ometries of the singlet and triplet states for 2

DES–T

inglet minimum Triplet minimum Singlet minimum

1193.3561 24.4 2.96

1193.3608

1194.6162 30.4 10.8

1194.6334

6322.6533 13.4 )1.56322.6516

1193.4869 18.4 0.8

1193.4882

1193.4848 18.5 1.0

1193.4864

1193.5049 15.0 )1.41193.5027

Table 3

CASPT2 vertical singlet–triplet energy differences (in kcalmol�1) at the

triplet 2-Cs geometry for different sizes of active space

Active space DES–T

2,2 25.7

4,4 26.8

12,12 26.1

14,14 26.2

E. Rodr�ıguez et al. / Chemical Physics 303 (2004) 157–164 161

cupancy. In the particular case of diphenylmethylene theerror in the adiabatic S–T energy difference is assumed

to be of almost 10 kcalmol�1 [19e] and it is attributed to

an overestimation of the delocalization energy of the

triplet [19b].

The DMO approximation of the DDCI performs

very satisfactorily. The energy differences between these

results and the standard DDCI ones are less than 0.2

kcalmol�1, while the CI space is reduced to almost halfits size when 13 orbitals for the singlet and 15 orbitals

for the triplet are eliminated. With this truncated MO

set, the iterative IDDCI procedure, which improves the

active orbitals, modifies the energy differences stabilizing

the singlet relative to the triplet by 3.5 kcalmol�1 at the

triplet minimum and by 2.4 kcalmol�1 at the singlet one.

This latter change is enough to make the singlet more

stable than the triplet at this geometry.B3LYP (BS) calculations were run with a 6-

311G(d,p) basis set so that they could be compared with

previous DFT results [18a]. The energy differences were

obtained using Eq. (1) and hS2i values of 1.04 and 0.53

for the BS state at the triplet and BS minima, respec-

tively. The geometries optimized at the CASSCF(2,2)

level were used because the BS minimum does not nec-

essarily coincide with the singlet minimum. ET þ DEBS–T

should be optimized if the DFT methods are to give

accurate adiabatic S–T energy gaps, but this is beyond

the scope of this paper. The B3LYP (BS) results show

the best agreement with the IDDCI gaps in spite of the

fact that the basis set used in the calculations was dif-

ferent. We determined the adiabatic S–T energy differ-

ence so that comparisons could be made with previous

DFT results. To do so we had to add the energy dif-ference between the singlet and triplet geometries at the

triplet state to the vertical energy difference at the singlet

geometry. The result is a gap of 8.7 kcalmol�1. Wood-

cock et al. [18a] report an adiabatic S–T energy differ-

ence of 12.0 kcalmol�1 for system 1 calculated at the

B3LYP/6-311G(d,p) level. There were some differences

between these DFT calculations: the DFT results of [15]

were obtained for compound 1 while ours were forcompound 2 and we used the optimized CASSCF(2,2)

geometries). Even so the agreement should be better.

The discrepancy must be due to the different description

of the states. The BS solution may be expressed as

WBS ¼ cSWS þ cTWT;

where WS is the pure closed shell description. It can be

shown that the hS2i values correspond to cT ¼ 0:51 and

0.72 at the BS and T minimum, respectively, which in-dicates that the open shell character is not negligible at

all and consequently that the closed shell wavefunction

is not a suitable description. Furthermore, the descrip-

tion is not consistent along the energy curve since the

spin contamination varies. This poor description of the

singlet state must be the source of the mentioned dis-

crepancy and may also be the source of the errors found

by Tomioka and co-workers [15] in B3LYP results of S–T energy gaps in carbenes which they attribute to an

overestimation of the triplet stability.

Our results, in particular the variability of the hS2ivalue of the BS eigenfunction, show that it is not pos-

sible to generalize when describing the electronic struc-

ture of carbenes as a whole. Any method with little

flexibility in the wavefunction must be used with extreme

care or only in those cases in which previous knowledgeof the electronic structure ensures its applicability.

It would be interesting to know what the main factors

are that make the triplet state of carbene 1 so stable. In

an attempt to determine these factors, we planned two

series of calculations. The first one focuses on how the

substituents affect the singlet–triplet energy gap. The

second one analyzes the influence of the geometry on

this energy difference.In the first calculations, the DES–T was obtained (at

the DDCI level) for different fragments of compound 2.

To lower the cost of the calculations and eliminate ef-

fects other than the electronic ones, the geometries of the

fragments were taken from an optimized geometry of

the triplet state of species 2 but constrained to Cs sym-

metry. That is, the phenyl rings were on the plane of the

central carbene or perpendicular to it. The fragments,shown in Fig. 1, were methylene, phenylmethylene in

two conformations (3-a and 3-b in Fig. 1), diphenylm-

ethylene, 2,6-dibromo-phenylmethylene (4), 2,6-bis(tri-

fluormethyl)-phenylmethylene (5) and species 2 in a Cs

geometry (2-Cs). In all these calculations an active space

of two electrons in two orbitals was used.

The results for the energy differences are shown in

Table 4. Given that for these compounds the triplet stateis always more stable than the singlet one, DES–T will be

smaller for the species where the singlet state is relatively

more stable. In our previous study of small halocarbenes

and halosilylenes [17i], we found a kind of additive be-

havior: that is to say, in general, the change in DES–T

from CH2 to CX2 was almost twice the change from

CH2 to CHX. This is not the case here. The substitution

of an H atom by a phenyl ring hardly changes the energydifference, independently of the orientation of the ring

(from methylene to 3a or 3b), but when the two H atoms

are substituted the energy gap decreases around

Fig. 1. Fragments of compound 2: phenylmethylene, planar confor-

mation (3a); phenylmethylene, perpendicular conformation (3b);

2,6-dibromo-phenylmethylene, planar conformation (4); 2,6-bis(triflu-

oromethyl)-phenylmethylene, perpendicular conformation (5).

-0.92

-0.91

-0.90

-0.89

-0.88

-0.87

85 95 105 115 125 135 145angle

En

erg

y +

38 (

a.u

.)

S

T

Fig. 2. Potential energy curves for the singlet and triplet states of

methylene when angle h changes from the FCI optimized geometries.

Energies calculated at the CASSCF(2,2)6-311G(d,p) level.

Table 4

Singlet–triplet vertical energy difference at the DDCI level for different

fragments of compound 2

Structure DES–T

(kcalmol�1)

Methylene 22.2

Planar phenylmethylene (3a) 22.3

Perpendicular phenylmethylene (3b) 23.3

Diphenylmethylene (Cs geometry) 17.5

2,6-Dibromo-phenylmethylene (4) 28.3

2,6-Bis(trifluoromethyl)-phenylmethylene (5) 18.3

2,6-Dibromo-20,60-bistrifluoromethyl-

diphenylmethylene (2-Cs)

14.5

DES–T in kcalmol�1.

162 E. Rodr�ıguez et al. / Chemical Physics 303 (2004) 157–164

4.7 kcalmol�1 (from methylene to diphenylmethylene).

The substituents of both phenyl rings, contrary to what

could be expected, have opposite effects: while the bro-

mine substituents stabilize the triplet relative to the

singlet by 6.0 kcalmol�1 (from 3a to 4), the trifluo-

romethyl substituents destabilize the triplet by 5.0

kcalmol�1 (from 3b to 5). The effect of both on diphe-

nylmethylene (to 2-Cs) is a relative destabilization of thetriplet of 3.0 kcalmol�1.

These data do not show a trend and, what is more,

the smallest stability of the triplet relative to the singlet

occurs at the whole system, species 2-Cs, when no geo-

metrical parameters are changed. We can conclude that

the stability of the triplet of species 2 is not governed by

electronic factors.

To understand the steric effect of the substituents on

the relative stability of the triplet and singlet states the

strategy followed here has been different. One must keep

in mind the shape of the potential energy curves (PEC)

when angle h changes. For this purpose, the curves of

the singlet and triplet states of methylene are illustrated

in Fig. 2. They were obtained by using the optimized

Full CI geometry [32] as the starting point and bychanging only angle h between 90� and 140�. Energieswere calculated at the CASSCF(2,2)/6-311G(d,p) level.

These curves show the effect of angle h on the singlet and

triplet energies. If bulky substituents are added and only

steric effects are taken into account (i.e., it is assumed

that the substituents will not affect the electronic dis-

tribution), a positive energy caused by the steric repul-

sion of the substituents must be added to the curves.This energy will be larger for smaller angles, so the

minimum of the singlet will be more affected than the

minimum of the triplet and both will be displaced to

larger h angles. The whole effect of the bulky substitu-

ents will be to stabilize the triplet minimum relative to

the singlet one.

Kinetic stabilization has not been taken into account

here because of the static nature of the study. In anycase, this factor will modify the half-life time of species

in the ground state and will make them more or less

stable in normal conditions, but will have no influence

on the relative energy of the different states.

4. Conclusions

The DDCI method has been used to calculate the S–T

energy differences of 2 as a suitable model for carbene 1

and analyze the factors that make of this compound a

stable triplet species.

E. Rodr�ıguez et al. / Chemical Physics 303 (2004) 157–164 163

The CASSCF(2,2) calculations carried out to opti-

mize the geometries predict a nearly Cs geometry for the

two low lying singlet and triplet states. For the triplet

state the carbenic angle is 146� and the two bond dis-

tances of the central carbene are almost equal. For thesinglet state the carbenic angle is smaller, 127�. The

carbon–carbon bond distance to the bromine substi-

tuted ring is smaller in this state.

When energy differences are calculated at the DDCI

level the triplet is found to be the ground state, with a

vertical gap to the singlet state of 15.0 kcalmol�1 at the

absolute minimum. The use of DMO’s reduces sub-

stantially the DDCI space and the computational effortpreserving the quality of the results.

The effect of the carbene substituents on the relative

stability of the low-lying states has been analyzed through

the singlet–triplet energy differences of several fragments

of the parent molecule. In the phenylmethylene, the ori-

entation of the aromatic ring hardly has any effect on the

relative stability because the effect on the singlet and

triplet states is similar. The effect of the substituents of thephenyl ring is most important in the case of trifluorom-

ethyl, that leads to a relative stabilization of the singlet

state. The two aromatic rings in diphenylmethylenes

stabilize the singlet relative to the triplet.

To understand the effect of the steric impediments we

must take into account that bulky substituentswill always

destabilize the carbene, in a larger extent when the car-

benic angle is smaller. A schematic strategy is to add thiseffect to the potential energy curves of the singlet and

triplet states of the methylene where no steric impedi-

ments are present, without taking into account the pos-

sible electronic effects of the substituents. It is obvious

that on top of a displacement of both minima to larger

carbenic angles, the singlet minimum, located at a smaller

angle, will be destabilized relative to the triplet one.

It can be concluded that the substituents of the2,6-dibromo-20,60-bistrifluoromethyl-diphenylmethylene

decrease the singlet–triplet energy difference at the

electronic level, but the steric effects of these substituents

act in the opposite way and the global effect is a favored

triplet ground state.

Acknowledgements

This work has been supported by DGSIC of the

Ministerio de Educaci�on y Ciencia, Spain (Project No.

BQU2002-04029-C02-02), and by CIRIT of the Gener-

alitat de Catalunya (Grant 2001SGR-00315).

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