ELECTRONIC STRUCTURE OF IONIZED NON-COVALENT DIMERS:
METHODS DEVELOPMENT AND APPLICATIONS
by
Anna A. Golubeva
A Dissertation Presented to theFACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIAIn Partial Fulfillment of the
Requirements for the DegreeDOCTOR OF PHILOSOPHY
(CHEMISTRY)
May 2010
Copyright 2010 Anna A. Golubeva
Acknowledgements
I would like to mention the following people to whom I owe a great debt of gratitude.
Prof. Anna Krylov, my advisor, has contributed greatly to my development as a
researcher - curious, motivated and thinking - in the past four years. As a person truly
inspired by science, she is a perpetuum mobile of the group, never letting the research to
stop. Her motivation and enthusiasm are quite contagious. What is even more important,
however, is that Anna Krylov is a great person to work with - fair, understanding, open-
minded, patient and with a sense of humor. Not every scientist is gifted with such a
personality, but she has it all – and I’m very happy to be a part of her group.
While in graduate school, I was lucky to have some outstanding teachers. I truly
enjoyed the fun and engaging lectures on Statistical Mechanics by Prof. Chi Mak. His
class was the place where I first found out that one can model the stock market with
statistics. Prof. Wlodek Proskurowski’s class on Numerical Analysis at the Department
of Mathematics significantly broadened my knowledge of linear algebra and program-
ming. Now I know exactly how the Hamiltonian is diagonalized, and that Householder
matrix has little to do with running a household. I would also like to acknowledge
Dr. Michael Quinlan. With him as the undergraduate lab director, TAing never seemed
boring.
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My scientific work was greatly influenced by Prof. Alexander Nemukhin - my
advisor at the Moscow State University (MSU). His lectures on Quantum Mechanics
is where I first got interested in the subject of Computational Chemistry.
Many thanks go to Evgeny Epifanovsky, Vadim Mozhayskiy, Dr. Vitalii Vanovschi,
Dr. Kadir Diri, Dr. Lukasz Koziol and Dr. Kseniya Bravaya, as well as all other former
and present Electronic Structure group members.
Finally, I do believe that behind all my achievements, there is always my Family.
My husband, Anton Zadorozhnyy, made sure I never felt left alone with the difficul-
ties. He provided me with support and advice whenever I was close to collapsing. My
father, Alexey Golubev, a theoretical chemist himself, advised me to join the special-
ized computational chemistry group at MSU when I was only 17 years old. Back then
I believed that all computational chemists do is about calculating how much grams of
A is needed in order to get that much grams of B. My mother, Valentina Golubeva, an
analytical chemist, was the first to show me the pH paper and to teach me how to grow
a crystal. These experiments resulted in major excitement of me as a 10-year old girl
and, perhaps, that was why I decided to become a chemist. My sisters, Vera and Alena,
are always there for me to cheer me up. My grandparents - Galina Golubeva, Viktor
Golubev, Lubov Vinogradova and Nikolay Vinogradov - always believed in me and sup-
ported me. They also always welcomed all curious child questions from me like “Can
we see atoms using a microscope?”, providing the grounds for me becoming a scientist.
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Table of Contents
Acknowledgements ii
List of Figures vii
List of Tables xii
Abstract xvi
1 Ionized non-covalent dimers: Fascinating and challenging 11.1 Non-covalent interactions . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Ionized non-covalent dimers as model charge-transfer systems . . . . . 21.3 Methodological challenges . . . . . . . . . . . . . . . . . . . . . . . . 41.4 Equation-of-motion coupled-cluster family of methods . . . . . . . . . 61.5 Bonding in ionized non-covalent dimers: The qualitative Dimer Molec-
ular Orbitals and Linear Combinations of Atomic Orbitals framework . 81.6 Reference list . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2 Configuration interaction approximation of equation-of-motion method forionization potentials: A benchmark study 162.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.2 The IP-CISD method . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.3 Computational details . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.4 Numerical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.4.1 Equilibrium geometries and electronically excited states of theuracil cation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.4.2 Equilibrium geometries of the three isomers of the benzene dimercation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.4.3 Water dimer cation . . . . . . . . . . . . . . . . . . . . . . . . 272.4.4 Timings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292.6 Reference list . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
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3 The electronic structure, ionized states and properties of the uracil dimers 363.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.2 Computational details . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.3.1 Prerequisites: Electronic states and spectrum of the uracil cation 383.3.2 Electronic structure of the uracil dimers . . . . . . . . . . . . . 403.3.3 Vertical ionization energies of the monomer and the dimers . . . 423.3.4 The electronic spectra of dimer cations . . . . . . . . . . . . . 48
3.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533.5 Reference list . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4 Ionization-induced structural changes in uracil dimers and their spectro-scopic signatures 574.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 574.2 Computational detais . . . . . . . . . . . . . . . . . . . . . . . . . . . 574.3 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.3.1 Molecular orbital framework . . . . . . . . . . . . . . . . . . . 604.3.2 Ionization-induced structural changes: Equilibrium geometries
of the uracil dimer cations . . . . . . . . . . . . . . . . . . . . 634.3.3 Binding energies of the neutral and ionized uracil dimers: Poten-
tial and free energy calculations . . . . . . . . . . . . . . . . . 704.3.4 The electronic spectra of the uracil dimer cations . . . . . . . . 74
4.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 794.5 Reference list . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
5 Ionized states of dimethylated uracil dimers 865.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 865.2 Computational details . . . . . . . . . . . . . . . . . . . . . . . . . . . 865.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.3.1 Potential energy surface of the neutral dimers: Structures andenergetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.3.2 The effect of methylation on the ionized states of the monomerand the dimers . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5.3.3 Ionization-induced changes in the monomer and the dimers: Struc-tures and properties . . . . . . . . . . . . . . . . . . . . . . . . 96
5.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1085.5 Reference list . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
6 Ionized non-covalent dimers: Outlook and future research directions 1136.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1136.2 Conical intersections in ionized non-covalent dimers: Benzene dimer
cation revisited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
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6.3 The effect of substituents in ionized non-covalent dimers: Electronicstructure and properties . . . . . . . . . . . . . . . . . . . . . . . . . . 122
6.4 Reference list . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
Bibliography 129. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
A EOM-IP optimized geometries of Bz+2 139X-displaced isomer (XD) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139Y-displaced isomer (YD) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140T-shaped isomer (TS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141Strongly x-displaced isomer (XSD) . . . . . . . . . . . . . . . . . . . . . . . 142Strongly y-displaced isomer (YSD) . . . . . . . . . . . . . . . . . . . . . . . 143Fused isomer (FD) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
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List of Figures
1.1 The DMO-LCFMO description of the two lowest ionized states in theuracil dimer. In-phase and out-of-phase overlap between the FMOsresults in the bonding (lower) and antibonding (upper) dimer’s MOs.Changes in the MO energies, and, consequently, IEs, are demonstratedby the Hartree-Fock orbital energies (hartrees). Ionization from the anti-bonding orbital changes the bonding from non-covalent to covalent, andenables a new type of electronic transitions, which are unique to theionized dimers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1 Definitions of the geometric parameters for uracil (upper panel) andwater dimer (lower panel) at the proton-transferred geometry. . . . . . 20
2.2 Definitions of the geometric parameters for three isomers of the benzenedimer:x-displaced (top),y-displaced (middle), and t-shaped (bottom). 21
2.3 Selected bondlengths in the five lowest electronic states of the uracilcation. The corresponding values of the neutral are shown by dashedlines. The MOs from which electron is removed are shown for eachstate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.4 The CNC(2) angle in the five lowest electronic states of uracil cation.Dashed line shows the corresponding value at the geometry of neutral. . 33
2.5 The CC bond lengths of the three benzene dimer cation isomers in theground electronic state optimized with IP-CISD/6-31(+)G(d) and IP-CCSD/6-31(+)G(d). Only the values of the symmetry unique param-eters for corresponding symmetry non-equivalent fragments are shown
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.6 Selected bondlengths and angles in the two lowest electronic states ofthe water dimer cation optimized with IP-CISD and IP-CCSD with dif-ferent bases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
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3.1 π-stacking and hydrogen-bonding in DNA (top) and the geometries ofthe stacked (a) and hydrogen-bonded (b) uracil dimers. . . . . . . . . . 37
3.2 Electronic spectrum and relvant MOs of the uracil cation at the geometryof the neutral. The MO hosting the hole in the ground state of the cationis also shown (top left). Dashed lines show the transitions with zerooscillator strength. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.3 MOs and IEs (eV) of the ten lowest ionized states of the stacked uracildimer. Ionization from the highest MO yields ground electronic stateof the dimer cation, and ionizations from the lower orbitals result inelectronically excited states. . . . . . . . . . . . . . . . . . . . . . . . 41
3.4 MOs and IEs (eV) of the ten lowest ionized states of the hydrogen-bonded uracil dimer. Ionization from the highest MO yields groundelectronic state of the dimer cation, and ionizations from the lower orbitalsresult in electronically excited states. . . . . . . . . . . . . . . . . . . 42
3.5 Basis set dependence of the five lowest IEs of uracil. The shaded areasrepresent the range of the expertimental values. . . . . . . . . . . . . . 44
3.6 Vertical electronic spectrum of the stacked uracil dimer cation at thegeometry of the neutral. Dashed lines show the transitions with zerooscillator strength. MOs hosting the unpaired electron in final electronicstate, as well as their symmetries, are shown for each transition. The MOcorresponding to the initial (ground) state of the cation is shown in themiddle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.7 Vertical electronic spectra of the stacked uracil dimer cation at twodifferent geometries: the geometry of the neutral (bold lines) and therelaxed cation geometry (dashed lines). MOs hosting the unpaired elec-tron in final electronic state are shown for each transition. . . . . . . . 52
3.8 Vertical electronic spectrum of the hydrogen-bonded uracil dimer cationat the geometry of the neutral. Dashed lines show the transitions withzero oscillator strength. MOs hosting the unpaired electron in finalelectronic state, as well as their symmetries, are shown for each tran-sition. The MO corresponding to the initial (ground) state of the cationis shown in the middle. . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.1 The ten lowest ionized states of the t-shaped uracil dimer at the neutralgeometry calculated with the IP-CCSD/6-311(+)G(d,p). . . . . . . . . 62
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4.2 The geometries of the cations versus the respective neutrals for the threeuracil dimer isomers . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.3 The definitions of the intra- and inter-fragment geometric parameters foruracil dimer isomers. . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.4 Two highest occupied MOs of the three isomers of the uracil dimer atthe neutral and cation geometry. . . . . . . . . . . . . . . . . . . . . . 68
4.5 The binding energies (kcal/mol) of the three isomers of neutral uracildimer calculated at two levels of theory: IP-CCSD/6-311(+)G(d,p) (bold)andωB97X-D/6-311(+)G(d,p) (italic). . . . . . . . . . . . . . . . . . 71
4.6 The binding energies (kcal/mol) of the three isomers of uracil dimercation calculated at two levels of theory: IP-CCSD/6-311(+)G(d,p) (bold)andωB97X-D/6-311(+)G(d,p) (italic). For the proton-transfered h-bondeduracil dimer cation, the binding energies corresponding to the two dis-sociation limits are presented. . . . . . . . . . . . . . . . . . . . . . . 72
4.7 The electronic spectra (top panel) of the stacked uracil dimer cation atthe neutral (solid black) and the cation (dashed blue) geometries calcu-lated with IP-CCSD/6-31(+)G(d) and the electronic states correspond-ing to the three most intense transitions (bottom panel). . . . . . . . . . 76
4.8 The electronic spectra (top panel) of the h-bonded uracil dimer cationat the neutral (solid black), symmetric transition state (dashed blue) andthe proton-transferred cation (dash-dotted pink) geometries calculatedwith IP-CCSD/6-31(+)G(d) and the electronic states corresponding tothe three most intense transitions (bottom panel). . . . . . . . . . . . . 78
4.9 The electronic spectra (top panel) of the t-shaped uracil dimer cation atthe neutral (solid black) and the cation (dashed blue) geometries calcu-lated with IP-CCSD/6-31(+)G(d) and the electronic states correspond-ing to the three most intense transitions (bottom panel). . . . . . . . . . 81
5.1 Five isomers of the stacked neutral 1,3-dimethyluracil dimer and theirbinding energies (kcal/mol). The energy spacings (kcal/mol) betweenthe lowest-energy structure and other isomers are given in the paren-thesis. All values were obtained withωB97X-D/6-311(+,+)G(2d,2p)except for theDe value of isomer 1 shown in bold, which is the IP-CCSD/6-31(+)G(d) estimate. . . . . . . . . . . . . . . . . . . . . . . 89
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5.2 The five lowest ionized states and the molecular orbitals of dimethylu-racil (top) and uracil (bottom) calculated by IP-CCSD/6-311(+)G(d,p).
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.3 The ten lowest ionized states and the corresponding MOs of the lowest-energy isomer of the neutral stacked 1,3-dimethyluracil computed withIP-CCSD/6-31(+)G(d). . . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.4 Five low-lying isomers of the 1,3-dimethyluracil dimer cation and thedissociation energies (kcal/mol). The energy spacings (kcal/mol) betweenthe lowest-energy structure and other isomers are given in the paren-thesis. All values were obtained withωB97X-D/6-311(+,+)G(2d,2p)except for theDe value of isomer 1 (shown in bold), which is the IP-CCSD/6-31(+)G(d) estimate. . . . . . . . . . . . . . . . . . . . . . . 97
5.5 The ionization-induced changes in geometry, binding energies (kcal/mol)and the MOs of isomer 1 of the stacked 1,3-dimethyluracil dimer. TheωB97X-D/6-311(+,+)G(2d,2p) optimized structures, dissociation ener-gies and the HF/6-31(+)G(d) MOs are presented. . . . . . . . . . . . . 99
5.6 The ionization-induced changes in geometry, binding energies (kcal/mol)and the MOs of isomer 2 of the stacked 1,3-dimethyluracil dimer. TheωB97X-D/6-311(+,+)G(2d,2p) optimized structures, dissociation ener-gies and the HF/6-31(+)G(d) MOs are presented. . . . . . . . . . . . . 100
5.7 The ionization-induced changes in geometry, binding energies (kcal/mol)and the MOs of isomer 3 of the stacked 1,3-dimethyluracil dimer. TheωB97X-D/6-311(+,+)G(2d,2p) optimized structures, dissociation ener-gies and the HF/6-31(+)G(d) MOs are presented. . . . . . . . . . . . . 101
5.8 The ionization-induced changes in geometry, binding energies (kcal/mol)and the MOs of isomer 4 of the stacked 1,3-dimethyluracil dimer. TheωB97X-D/6-311(+,+)G(2d,2p) optimized structures, dissociation ener-gies and the HF/6-31(+)G(d) MOs are presented. . . . . . . . . . . . . 102
5.9 The changes in geometry, binding energies (kcal/mol) and the MOs ofisomer 5 of the stacked 1,3-dimethyluracil dimer at ionization. TheωB97X-D/6-311(+,+)G(2d,2p) optimized structures, dissociation ener-gies and the HF/6-31(+)G(d) MOs are presented. . . . . . . . . . . . . 103
5.10 The electronic spectra of 1,3-dimethyluracil (left) and uracil (right) atthe vertical (solid black) and the relaxed (dashed blue) geometries cal-culated by IP-CCSD/6-31(+)G(d). . . . . . . . . . . . . . . . . . . . . 104
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5.11 The three most intense transitions in the electronic spectrum of the low-est isomer of stacked 1,3-dimethyluracil cation at vertical (solid black)and cation (dashed blue) geometries. The DMOs corresponding to theground state (framed) and excited states (regular) are shown. The posi-tions of the peaks were calculated at IP-CCSD/6-31(+)G(d) level, whilethe intensities are from the non-methylated dimer calculations. . . . . . 107
6.1 The six optimized geometries of the benzene dimer cation and the corre-sponding energy gaps calculated at the IP-CCSD(dT)/6-31(+)G(d) (italic)and IP-CCSD/6-311(+,+)G(d,p) (bold) levels of theory. . . . . . . . . . 115
6.2 The definitions of structural parameters for the benzene dimer cation.The distance between the centers of mass of the fragmentsdCOM , sepa-rationh and sliding coordinates∆ are shown. . . . . . . . . . . . . . . 116
6.3 The evolution of the four lowest electronic states of the benzene dimercation along thex- (top panel) andy- (bottom panel) displecement coor-dinates calculated with IP-CCSD/6-31(+)G(d). Two moderately (XD,YD) and two strongly-displaced (XSD, YSD) fully-optimized ground-state structures were employed. The blue arrows depict the CR tran-sitions at four geometries and the dashed lines interconnect the relatedelectronic states. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
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List of Tables
2.1 The IP-CCSD bondlengths (A) in the five electronic states of the uracilcation and absolute errors (in parenthesis) of IP-CISD relative to IP-CCSD. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.2 The IP-CCSD angles (degrees) in the five electronic states of the uracilcation and absolute errors (in parenthesis) of IP-CISD relative to IP-CCSD. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.3 IP-CCSD and IP-CISD permanent dipole moments (a.u.) of the fivelowest electronic states of the uracil cation computed at the respectiveoptimized geometries relative to the center of mass. . . . . . . . . . . . 24
2.4 The IP-CCSD and IP-CISD excitation energies (eV) and transition dipolemoments (a.u.) of the uracil cation at the equilibrium geometries of theneutral and the cation. . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.5 The bondlengths (A), angles (degrees), interfragment distances and slid-ing displacements (A) in the ground state of thex-displaced,y-displacedand t-shaped benzene dimer cations calculated with IP-CISD/6-31(+)G(d).For thex- andy-displaced structures, geometric parameters for only oneof the benzene fragments are provided (the fragments are equivalent bysymmetry). Absolute errors of IP-CISD relative to IP-CCSD are pre-sented in parenthesis. Average absolute errors are calculated using thedata for symmetry unique parameters. . . . . . . . . . . . . . . . . . . 26
2.6 The IP-CCSD bondlengths (A) and angles (degrees) in the two elec-tronic states of the water dimer cation and absolute errors (in parenthe-sis) of IP-CISD relative to IP-CCSD calculated with different bases. . . 28
3.1 Five lowest verical IEs (eV) of the uracil monomer calculated withEOM-IP-CCSD. The number of basis functions (b.f.) is given for eachbasis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
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3.2 Excitation energies, transition dipole moments and oscillator strengthsof the electronic transitions in the uracil cation calculated with EOM-IP-CCSD with different bases. . . . . . . . . . . . . . . . . . . . . . . 45
3.3 Ten lowest vertical IEs (eV) of the stacked uracil dimer calculated withEOM-IP-CCSD. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.4 Ten lowest verical IEs (eV) of the hydrogen-bonded uracil dimer calcu-lated with EOM-IP-CCSD. . . . . . . . . . . . . . . . . . . . . . . . . 47
3.5 Ten lowest verical IEs (eV) of the stacked dimer calculated with EOM-IP-CCSD/6-311(+)G(d,p) versus the energy-additivity scheme resultsestimated using 6-31(+)G(d). . . . . . . . . . . . . . . . . . . . . . . 48
3.6 Ten lowest vertical IEs (eV) of the hydrogen-bonded uracil dimer calcu-lated with EOM-IP-CCSD/6-311(+)G(d,p) versus the energy-additivityscheme results estimated from 6-31(+)G(d). . . . . . . . . . . . . . . . 49
3.7 Oscillator strengths and transition dipole moments for the electronictransitions in the ionized stacked uracil dimer calculated with EOM-IP-CCSD/6-31(+)G(d) at the geometry of the neutral. . . . . . . . . . . 51
3.8 Oscillator strengths and transition dipole moments for the electronictransitions in the ionized stacked uracil dimer calculated with EOM-IP-CCSD/6-31(+)G(d) at the equilibrium geometry of the ionized dimer.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.1 The values of optimized structural parameters (A, Degree) of the frag-ments in the stacked, h-bonded, h-transfered h-bonded and t-shapeduracil dimer cations. The differences (A, Degree) w.r.t. the equilibriumgeometry of the respective neutral complex are also given showing theionization-induced changes in geometry. See Fig. 4.3 for the definitionsof the parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.2 The values of inter-fragment structural parameters (A, Degree) of thestacked, h-bonded, h-transfered h-bonded and t-shaped uracil dimer cations.The differences (A, Degree) w.r.t. the equilibrium geometry of the respec-tive neutral complexes are given in parenthesis. See Fig. 4.3 for thedefinitions of the parameters. . . . . . . . . . . . . . . . . . . . . . . 67
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4.3 Total (Etot, hartree) and dissociation (De, kcal/mol) energies of the fourisomers of the uracil dimer in the neutral and ionized states computedby CCSD/IP-CCSD with 6-311(+)G(d,p). Relevant total energies of theuracil monomer are also given. The relaxation energies (∆E, kcal/mol)defined as the difference in total energies of the cation at the neutral andrelaxed cation geometries are also shown. For HU+
2 (PT) dissociationenergies corresponding to the U0 + U+ / (U - H)0 + UH+ channels aregiven. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.4 The dissociation energies (kcal/mol) and standard thermodynamic quan-tities of the neutral and the cation uracil dimers calculated at theωB97X-D/6-311(+)G(d,p) level. For the proton-transfered cation the values cor-responding to the two different dissociation limits are given. . . . . . . 73
4.5 The excitation energies (∆E, eV), transition dipole moments (< µ2 >,a.u.) and oscillator strengths (f ) of the stacked dimer cation at the geom-etry of the neutral and cation, IP-CCSD/6-31(+)G(d). . . . . . . . . . . 77
4.6 The excitation energies (∆E, eV), transition dipole moments (< µ2 >,a.u.) and oscillator strengths (f ) of the symmetric h-bonded dimercation at the geometry of the neutral and cation, IP-CCSD/6-31(+)G(d). 79
4.7 The excitation energies (∆E, eV), transition dipole moments (< µ2 >,a.u.) and oscillator strengths (f ) of the h-bonded dimer cation at theoptimized proton-transferred geometry, IP-CCSD/6-31(+)G(d). . . . . 80
4.8 The excitation energies (∆E, eV), transition dipole moments (< µ2 >,a.u.) and oscillator strengths (f ) of the t-shaped dimer cation at thegeometry of the neutral and cation, IP-CCSD/6-31(+)G(d). . . . . . . . 82
5.1 The total (hartree) and dissociation energies (kcal/mol) of the neutraland ionized 1,3-dimethyluracil monomer and dimers calculated at theωB97X-D/6-311(+,+)G(2d,2p) level of theory. . . . . . . . . . . . . . 90
5.2 The total (hartree) and dissociation energies (kcal/mol) of the neutraland ionized 1,3-dimethyluracil and its dimer (lowest energy isomer) cal-culated at the IP-CCSD/6-31(+)G(d) level of theory. For the monomerand the dimer cations, the relaxation energy (∆ECCSD
relax , kcal/mol) isprovided.a The uracil and uracil dimer IP-CCSD/6-31(+)G(d) resultsb
are included for comparison. . . . . . . . . . . . . . . . . . . . . . . . 91
xiv
5.3 The five lowest ionized states and the corresponding IEs (eV) of the 1,3-dimethyluracil at the vertical geometry calculated by IP-CCSD with the6-31(+)G(d) and 6-311(+)G(d,p) bases. The IE shifts (eV) with respectto the uracil values are given in parenthesis. . . . . . . . . . . . . . . . 94
5.4 The electronic spectrum of the 1,3-dimethyluracil cation at the verticaland relaxed geometries calculated at the IP-CCSD/6-31(+)G(d) level. . 105
5.5 The ionization energies (eV) and the DMO charactera corresponding tothe ten lowest ionized states of the stacked 1,3-dimethyluracil dimer atthe vertical geometry (isomer 1) calculated at the IP-CCSD/6-31(+)G(d)level. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
6.1 The ground state total energies (in hartree) of the six isomers of Bz+2 cal-
culated at three levels of theory: IP-CCSD/6-31(+)G(d), IP-CCSD(dT)/6-31(+)G(d) and IP-CCSD/6-311(+,+)G(d,p)+FNO(99.25%) . . . . . . . 116
6.2 The characteristic geometric parameters of the six ground-state struc-tures of the benzene dimer cation. The distances between the centersof mass of the fragmentsdCOM (in A), separationh (in A) and slidingcoordinate∆ (in A) values are presented. . . . . . . . . . . . . . . . . 117
6.3 The six lowest symmetry-allowed transitions in the electronic spectrumof the benzene dimer cation at the XD and XSD optimized geometries.Calculated with IP-CCSD/6-31(+)G(d). . . . . . . . . . . . . . . . . . 120
6.4 The six lowest symmetry-allowed transitions in the electronic spectrumof the benzene dimer cation at the YD and YSD optimized geometries.Calculated with IP-CCSD/6-31(+)G(d). . . . . . . . . . . . . . . . . . 121
6.5 Theoretical estimates of the lowest VIE (in eV) of the nucleobase monomersandπ-stacked dimers. . . . . . . . . . . . . . . . . . . . . . . . . . . 125
xv
Abstract
Several prototypical ionized non-covalent dimers - the uracil, 1,3-dimethylated uracil
and benzene dimer cations - are studied by high-level ab initio approaches including the
equation-of-motion coupled cluster method for ionization potentials (EOM-IP-CC). The
qualitative Dimer Molecular Orbitals as Linear Combinations of Fragment Molecular
Orbitals (DMO-LCFMO) framework is used to interpret the results of calculations.
As the simplest model systems, the neutral and ionized non-covalent dimers, such as
π-stacked and H-bonded nucleobase dimers, can shed some light on the complex mech-
anism of the charge transfer in DNA. The correct treatment of non-covalent interactions
is challenging to the ab initio methodology, therefore the special attention is given to the
development and benchmarking of the new methods.
First, we introduce and benchmark the cost-saving configuration-interaction variant
of the EOM-IP-CCSD method: EOM-IP-CISD. The computational scalling of EOM-
IP-CISD in N5, as opposed to the N6 scalling of EOM-IP-CCSD. The EOM-IP-CISD
structures for the open-shell systems are of a similar quality as the HF geometries of
well-behaved closed-shell molecules, while the excitation energies are of a semiquanti-
tative value. The performance of promising Density Functional Theory developments,
i.e. the novel long-range and dispersion-corrected functionals, is also assessed through-
out this work.
xvi
Next, the potential energy surfaces, electronic structure and properties of uracil
dimer and 1,3-dimethylated uracil dimer cations are investigated. The electronic struc-
ture of dimers is explained by DMO-LCFMO. Non-covalent interactions lower the ver-
tical ionization energies by up to 0.35 eV, the largest red-shift is observed for the stacked
and t-shaped structures. Ionization induces significant changes in bonding patterns,
structures and binding energies. In the cations the interaction between the fragments
becomes more covalent and the binding energies are 1.5-2.0 times larger than in the
neutrals. The relaxation of the cation structures is governed by two different mecha-
nisms: the hole delocalization and the electrostatic stabilization. The electronic spectra
of dimer cations exhibit significant changes upon relaxation, which can be exploited
to experimentally monitor the ionization-induced dynamics. The position and inten-
sity of the charge-resonance transitions can be used as spectroscopic probes in such
experiments. Finally, we investigate the effect of substituents on the electronic struc-
ture of non-covalent dimers. For weak perturbations, i.e. the CH3 group, the effect of
substituents can be incorporated into the qualitative DMO-LCFMO picture as constant
shifts of the dimers and the monomers levels.
Future research topics, such as the conical intersections in the benzene dimer cations
and the electronic structure of the chemically-modified nucleobase dimers, are discussed
in the last chapter.
xvii
Chapter 1
Ionized non-covalent dimers:
Fascinating and challenging
1.1 Non-covalent interactions
From the chemist’s perspective, there are two types of molecular interactions - cova-
lent and non-covalent. Covalent interactions giving rise to chemical bonds arise when
two atoms share the electrons. In the electronic structure terms, covalent interaction
originate in the atomic orbital overlap, which increases the electron delocalization and,
thus, lowers electronic energy. Non-covalent interactions are everything beyond the
covalent definition. They include the electrostatic, induction and dispersion intermolec-
ular forces, the latter being also known as van der Waals interactions. Hydrogen bond
straddles the two domains, as it includes partial electron sharing, but also a degree of
electrostatic interaction. The non-covalent interactions are weak relative to the covalent
or pure ionic ones. Typical stabilization energies for a chemical bond are of the order
of hundred kilocalories per mole, whereas the hydrogen-bonded and dispersion inter-
acting systems are bound by tenth to several kilocalories per mole, respectively. Nev-
ertheless, the importance of non-covalent interactions for chemistry cannot be overes-
timated. Condensed-phase chemistry, biochemistry, surface chemistry, catalysis, poly-
mer science - these are just several fields of modern chemistry that are defined by the
non-covalent interactions to a considerable degree [1–3]. For instance, the 3D structure
of one of the most important molecules in biochemistry - the DNA double helix - is
1
a result of a network of hydrogen-bonding andπ-stacking interactions that are of the
non-covalent nature. Other examples include protein secondary and tertiary structure,
enzyme-substrate binding, and more.
1.2 Ionized non-covalent dimers as model charge-
transfer systems
In recent years, significant efforts were directed towards investigating charge transfer
(CT) in DNA, which is related to the DNA damage processes. The DNA’s photo- and
oxidizing damage is of great importance to the biology and medicine, as it is likely to
be realted to some of the serious deseases [4].
Under the oxidizing or photoionizing conditions, the hole is injected in the DNA
molecule, in particular, in its easiest-to-ionize guanine site. The hole then migrates
through the DNA strand over large distances of more than 100A, which was experi-
mentally observed for both pure DNA/DNA [5, 6] and mixed DNA/RNA duplexes [7].
In addition to the biological significance of this process, this nano-scale conductivity of
DNA and RNA is attractive for the molecular electronics applications [8–10]. Despite
its importance, the CT phenomenon is not yet fully understood and the progress requires
joint experimental and theoretical efforts.
Several mechanisms of CT in DNA have been proposed [11–16], but none of them
offers a complete description of the process. Different factors were shown to be impor-
tant: the DNA sequence and composition (in particular, the percentage of GC and AT
Watson-Crick base pairs), thermally-induced chain fluctuations, the presence of Na+
counterions [17]. Moreover, the non-covalent interactions between the bases, especially
2
theπ-stacking, appear to be crucial for this process [18–20]. The study of ionized nucle-
obase dimers - the simpliest model systems for the CT in DNA - can shed some light at
this complex phenomenon.
While ionization energies (IEs) of nucleic acid bases in the gas phase have been
characterized both experimentally [21–27] and computationally [28–31], much less is
known about the effects of interactions present in realistic environments, likeπ-stacking
and h-bonding, on the ionized states of nucleobases.
We characterized the electronic structure of the ionized uracil dimers [32, 33] and
dimethylated uracil dimers [34]. Other ionized nucleobase dimers, like the adenine and
thymine homo- and hetero-dimers [35] and cytosine dimers [36] were also investigated
recently. Calculations [32–36] and VUV measurements [35,36] demonstrated that non-
covalent interactions lower vertical ionization energies (VIEs) by as much as 0.7 eV
(in cytosine dimers). Interestingly, the magnitude and origin of the effect are different
for different isomers. The largest drop in IEs was observed in the symmetric stacked
and non-symmetric h-bonded dimers. In the former case, the IE is lowered due to the
hole delocalization over the two fragments, while in the latter case the stabilization is
achieved by the electrostatic interaction of hole with the “neutral” fragment. Therefore,
non-covalent interactions seem to reduce the gaps in IEs of purines and pyrimidines,
which may play an important role in hole migration through DNA.
Earlier studies of the effects ofπ-stacking on IEs of nucleobases include Hartree-
Fock and DFT estimates using Koopmans theorem [37–41], MP2 (Møller-Plesset per-
turbation theory) and CASPT2 (perturbatively-correcte d complete active space self-
consistent field) calculations [28,30,42].
3
1.3 Methodological challenges
The correct treatment of non-covalent interactions is difficult for ab initio methodology
[1, 3, 43], especially for the systems dominated by dispersion interactions. Dispersion
forces originate in correlated motion of the electrons, so highly-correlated approaches,
such as coupled cluster methods, are required for reliable results. However, theN6-N8
scalling of these methods quickly rules out their application to large systems (i.e., more
than 40-50 atoms). A less expensive alternative to the traditional correlated wave func-
tion based methods, Density Functional Theory (DFT), fails to account for dispersion
interaction when used with standard functionals [44, 45]. The reason is the local and
semi-local character of the approximate exchange-correlation functional (εXC). For a
cluster AB, where charge densities on A and B fragments do not overlap:
εXC(AB) = εXC(A) + εXC(B), (1.1)
whereεXC(A) andεXC(B) depend solely on the densities (or the density and its gra-
dient) on fragments A and B, respectively. Such model cannot account for the long-
range attractive dispersion and fails to adequately describe non-covalent systems at large
separations, when the dispersion forces dominate. Moreover, the situation is far from
prefect at short-range where the attractive dispersion interaction is underestimated by
DFT due to the incorrect asymptotic behavior of standard functionals [44]. The latest
developements of the semi-empirical dispersion-corrected functionals [46,47], where an
empiricalR−6 term is included to account for the long-range dispersion interaction, are
promising; however, they do not provide a universal solution. Other problems include
the shallow potential energy surfaces (PES) of non-covalent complexes and technical
issues such as Basis Set Superposition Error (BSSE) [1]. Thus, even a closed-shell
4
system is a challenge for modern computational chemistry when it is dominated by non-
covalent interactions.
With the open-shell systems such as ionized non-covalent dimers additional issues
emerge. The single-reference post-HF approaches, e.g. MP2 and CCSD, are plagued by
the spin-contamination, symmetry-breaking and imbalanced description of the closely-
lying multiple electronic states. The former follows from the fact that the HF variational
solution (i.e., the unrestricted HF solution) is generally not an eigenfunction of the〈S2〉
operator. Consequently, the UHF wave function is a mixture of states of different multi-
plicity. The correct spin symmetry can be enforced in HF by restricting the spatial parts
of the orbitals to be equal for the electrons with different spin (the restricted open-shell
HF). However, this solution problem is not optimal from variational principle point of
view, as it is higher in energy.
The imbalance originates in the multi-configurational character of the open-shell
wave functions, which can be accounted for by correlated multi-reference (MR)
approaches, like CASPT2 or MR-CISD. However, some of the imbalance is still present
in the MR wave function, because the configurations of similar importance are not
treated on the same footing. Other disadvantages that limit the applications of MR meth-
ods are the high cost and inconvenience resulting from the need to choose the relevant
configurations manually.
The DFT description of the ionized non-covalent systems suffers from self-
interaction erorrs (SIE) in addition to the issues mentioned previously [48]. Because
of the approximate character of the exchange-correlation functional, the exchange and
repulsion terms do not cancel out for one electron in DFT. This results in unphysical
situation when the electron interacts with itself. The SIE is responsible for the incorrect
behavior at the dissociation limit for the symmetric dimer cations, for instance, the ion-
ized rare gas and nucleobase dimers [48]. The total energy of the dissociating system
5
becomes much lower than the sum of the total energies of the products. The resulting
potential energy profiles instead of levelling off at infinite separations exhibit a char-
acteristic downward curve. This behaviour is suppressed if the Hartree-Fock exchange
is used, which is exploited in the long-range corrected (LC) functionals. One of the
promising functionals isωB97X-D [49], which includes both LR Hartree-Fock and dis-
persion correction. TheωB97X-D shows significant improvement over traditional DFT
functionals when applied to non-covalent systems.
1.4 Equation-of-motion coupled-cluster family of meth-
ods
The equation-of-motion coupled-cluster (EOM-CC) methods [50–60] offer an original
solution to open-shell problems. Instead of dealing with the symmetry-broken and spin-
contaminated wave function of the open-shell state of interest, the EOM-CC accesses
the target states via a well-behaved reference state employing various excitation oper-
ators. The reference state is chosen such that it is free from spin-contamination and
symmetry-breaking at the Hartree-Fock level. Thus, the EOM methods do not suffer
from these common flaws of traditional wave function approaches. When used properly,
they yield balanced wave functions that include all the important configurations from the
target manifold. Other advantages of the EOM approach include embedded dynamical
correlation effects and elegant formalism. The EOM-CC methods are universal and
can be successfullly applied to diverse open-shell situations, including the open-shell
cations, anions, di- and tri-radicals, bond-breaking, exactly and nearly-degenerate elec-
tronic states.
6
The wave function of the target state in EOM-CC is represented as follows:
ΨEOM−CC = ReT Φ0, (1.2)
where Φ0 is Hartree-Fock determinant of the closed-shell reference state,T is the
coupled-cluster operator andR is the appropriate excitation operator generating the tar-
get configurations from the reference CCSD wave function. Depending on an EOM-CC
model, different excitation operators are used. For instance, in the EOM model for
ionization potentials (EOM-IP) [58], which is an appropriate choice for ionized non-
covalent systems, the operatorR is ionizing and generates all1h (one hole) and2h1p
(two hole one particle) determinants from the reference configuration. This model is
capable of accessing the doublet states of the radical cations from the neutral reference.
The second-quantization expressions forR andT operators for one of the extensions of
the EOM-IP model with single and double substitutions (EOM-IP-CCSD) are:
R = R1 + R2 (1.3)
R1 =∑
i
rii (1.4)
R2 =1
2
∑ija
raija
+ji (1.5)
T = T1 + T2 (1.6)
T1 =∑ia
tai a+i (1.7)
T2 =1
4
∑ijab
tabij a
+b+ij (1.8)
wheretai , tabij andri, ra
ij are the unknown amplitudes of the coupled-cluster and EOM
excitation operators. The EOM-CC solutions are obtained in a two-step procedure. First,
the coupled-cluster equations for the reference state are solved and the amplitude vector
7
for the operatorT is obtained in a procedure that scales asN6. Second, the EOM states
(or equivalently the left and right amplitude vectors of operatorR for EOM states) are
found by the diagonalization of the similarity-transformed HamiltonianH = e−THeT
at theN5 cost.
HR = ER (1.9)
LH = ER (1.10)
LIRJ = δij (1.11)
Other EOM-CC models include the electron atachment (EA) [57], spin flip (SF)
[55, 56] and electron excitations (EE) [54] variants. These ideas can be implemented
within the CI approach [61] and one of the methods, EOM-IP-CISD, is described in
Section 2.2.
1.5 Bonding in ionized non-covalent dimers: The qual-
itative Dimer Molecular Orbitals and Linear Com-
binations of Atomic Orbitals framework
The DMO-LCFMO (Dimer Molecular Orbital Linear Combination of Fragment Molec-
ular Orbitals) framework [62] enables the qualitative prediction of the bonding and
properties of non-covalent dimers. Within this framework, the electronic structure of
the dimer is described in terms of the fragment (i.e. monomer) molecular orbitals
(FMOs). Symmetric and non-symmetric dimers are treated analogously to the famil-
iar MO-LCAO approach to of homo- and hetero-nuclear diatomics [63].
8
ν(F1) = πCC(F1) ν(F2) = πCC(F2)
ψ+(ν)
-0.361
-0.384-0.372 -0.372
ψ-(ν)
Figure 1.1: The DMO-LCFMO description of the two lowest ionized states in the uracildimer. In-phase and out-of-phase overlap between the FMOs results in the bonding(lower) and antibonding (upper) dimer’s MOs. Changes in the MO energies, and, con-sequently, IEs, are demonstrated by the Hartree-Fock orbital energies (hartrees). Ioniza-tion from the antibonding orbital changes the bonding from non-covalent to covalent,and enables a new type of electronic transitions, which are unique to the ionized dimers.
As illustrated in Figure 1.1, the dimer molecular orbitals (DMOs) are symmetric and
antisymmetric linear combinations of the FMOs:
ψ+(ν) =1√
2(1 + sνν)(ν(F1) + ν(F2)) (1.12)
ψ−(ν) =1√
2(1− sνν)(ν(F1)− ν(F2)) (1.13)
whereν(F1) andν(F2) are the FMOs centered on two equivalent fragments F1 and
F2, ψ+(ν) andψ−(ν) denote the bonding and antibonding orbitals with respect to the
interfragment interaction andsνν = 〈ν(F1) | ν(F2)〉 is the overlap integral. Folowing
9
the MO-LCAO reasoning, the energy splitting between the bonding and antibonding
orbitals is proportional to the overlapsνν [63]. Therefore, the dimer system ionizes
at lower ionization energies relative to the monomer and the decrease in dimer IE is
proportional to the FMO overlap. From Figure 1.1 we can also predict the behaviour
of the ionization-induced changes in the dimer system. As the electron is ejected from
the dimer, the formal bond order changes from0 to 12
and the interfragment interaction
increases.
Twice as many ionized states appear in dimer relative to the monomer. In the elec-
tronic spectrum of the dimer cation, all transitions can be classified into two categories:
the charge resonance (CR) and the local excitations (LE). The CR transitions are defined
as transitions between the ionized states corresponding to the in- and out-of-phase com-
bined FMOs of the same character, i.e.ψ−(ν) → ψ+(ν). The LE are the transitions
between the DMOs combined out of FMOs of different character, i.e.ψ−(ν) → ψ+(ζ)
orψ−(ν) → ψ−(ζ). The CR transitions are unique to the dimer, whereas LE are similar
to the transitions present in the electronic spectrum of monomer cation. It can be shown
that the intensity of the CR transitions is sensitive to the FMO overlap and interfragment
separation:
I(ψ−(ν) → ψ+(ν)) ∝ RF1···F2√1− sνν
(1.14)
wheresνν = 〈ν(F1) | ν(F2))〉. When the cation relaxes from the vertical geometry,
the FMO overlap increases (sν(F1)ν(F2) → 1), and the CR band intensity rises in the
electronic spectrum. Therefore, the CR transitions can be used to probe the structural
changes occuring in the dimer cation.
In non-symmetric dimers, the transitions corresponding to charge-transfer between
the fragments become important.
10
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[36] O. Kostko, K.B. Bravaya, A.I. Krylov, and M. Ahmed, Ionization of cytosinemonomer and dimer studied by VUV photoionization and electronic structure cal-culations, Phys. Chem. Chem. Phys. (2010), In press, DOI: 10.1039/B921498D.
[37] A.-O. Colson, B. Besler, and M.D. Sevilla, Ab initio molecular orbital calculationson DNA base pair radical ions: Effect of base pairing on proton-transfer energies,electron affinities, and ionization potentials, J. Phys. Chem.96, 9787 (1992).
13
[38] A.-O. Colson, B. Besler, and M.D. Sevilla, Ab initio molecular orbital calculationson DNA radical ions. 4. Effect of hydration on electron affinities and ionizationpotentials of base pairs, J. Phys. Chem.97, 13852 (1993).
[39] H. Sugiyama and I. Saito, Theoretical studies of GC-specific photocleavage ofDNA via electron transfer: Significant lowering of ionization potential and 5’-localization of HOMO of stacked GG bases in B-form DNA, J. Am. Chem. Soc.118, 7063 (1996).
[40] F. Prat, K.N. Houk, and C.S. Foote, Effect of guanine stacking on the oxidation of8-oxoguanine in B-DNA, J. Am. Chem. Soc.120, 845 (1998).
[41] S. Schumm, M. Prevost, D. Garcia-Fresnadillo, O. Lentzen, C. Moucheron, andA. Krisch-De Mesmaeker, Influence of the sequence dependent ionization poten-tials of guanines on the luminescence quenching of Ru-labeled oligonucleotides:A theoretical and experimental study, J. Phys. Chem. B106, 2763 (2002).
[42] D. Roca-Sanjuan, M. Merchan, and L. Serrano-Andres, Modelling hole-transferin DNA: Low-lying excited states of oxidized cytosine homodimer and cytosine-adenine heterodimer, Chem. Phys.349, 188 (2008).
[43] G.S. Tschumper,Reviews in Computational Chemistry, chapter Chapter 2: Reli-able electronic structure computations for weak noncovalent interactions in clus-ters, pages 39–90. Jon Wiley & Sons, 2009.
[44] S. Kristyan and P. Pulay, Can (semi)local density functional theory account for theLondon dispersion forces?, Chem. Phys. Lett.229, 175 (1994).
[45] P. Hobza, J.Sponer, and T. Reschel, Density functional theory and molecularclusters, J. Comput. Chem.16, 1315 (1995).
[46] S. Grimme, Accurate description of van der Waals complexes by density func-tional theory including empirical corrections, J. Comput. Chem.25, 1463 (2004).
[47] S. Grimme, Semiempirical GGA-type density functional constructed with a long-range dispersion correction, J. Comput. Chem.27, 1787 (2006).
[48] Y. Zhang and W. Yang, A challenge for density functionals: Self-interaction errorincreases for systems with a noninteger number of electrons, J. Chem. Phys.109,2604 (1998).
[49] J.-D. Chai and M. Head-Gordon, Long-range corrected hybrid density functionalswith damped atom-atom dispersion interactions, Phys. Chem. Chem. Phys.10,6615 (2008).
14
[50] D.J. Rowe, Equations-of-motion method and the extended shell model, Rev. Mod.Phys.40, 153 (1968).
[51] K. Emrich, An extension of the coupled-cluster formalism to excited states (I),Nucl. Phys.A351, 379 (1981).
[52] H. Sekino and R.J. Bartlett, A linear response, coupled-cluster theory for excitationenergy, Int. J. Quant. Chem. Symp.26, 255 (1984).
[53] J. Geertsen, M. Rittby, and R.J. Bartlett, The equation-of-motion coupled-clustermethod: Excitation energies of Be and CO, Chem. Phys. Lett.164, 57 (1989).
[54] J.F. Stanton and R.J. Bartlett, The equation of motion coupled-cluster method.A systematic biorthogonal approach to molecular excitation energies, transitionprobabilities, and excited state properties, J. Chem. Phys.98, 7029 (1993).
[55] A.I. Krylov, Size-consistent wave functions for bond-breaking: The equation-of-motion spin-flip model, Chem. Phys. Lett.338, 375 (2001).
[56] S.V. Levchenko and A.I. Krylov, Equation-of-motion spin-flip coupled-clustermodel with single and double substitutions: Theory and application to cyclobuta-diene, J. Chem. Phys.120, 175 (2004).
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[58] S. Pal, M. Rittby, R.J. Bartlett, D. Sinha, and D. Mukherjee, Multireferencecoupled-cluster methods using an incomplete model space — application toionization-potentials and excitation-energies of formaldehyde, Chem. Phys. Lett.137, 273 (1987).
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15
Chapter 2
Configuration interaction
approximation of equation-of-motion
method for ionization potentials: A
benchmark study
2.1 Overview
A configuration interaction variant of EOM-IP-CCSD method is introduced. The per-
formance and capabilities of the new approach are demonstrated by application to the
uracil cation, water dimer and benzene dimer cations by benchmarking against more cor-
related EOM-IP-CCSD. The formal introduction of IP-CISD is given in Section 2.2, its
performance and errors for structural parameters and excitation energies are discussed
in Section 2.4.1, 2.4.2 and 2.4.3.
2.2 The IP-CISD method
The IP-CISD wave function for state can be written as:
ΨIP−CISD = RΦ0, (2.1)
16
In this equationΦ0 is the Hartree-Fock determinant of the reference closed-shell system
and the operatorR = R1 + R2 is the familiar EOM-IP excitation operator:
R1 =∑
i
rii (2.2)
R2 =1
2
∑ija
raija
+ji (2.3)
(2.4)
In other words,R1 andR2 generate the linear combinations of all possible ionized (i.e.,
1h) and ionized-excited (2h1p) determinants with appropriate spin-projection (either
Ms=12
orMs = −12) from the reference HF wave function.
The equations for the amplitudes ofR of the electronic state K are derived by apply-
ing the variational principle to the CI energy functional:
EK =< ΨIP−CISD(K)|H|ΨIP−CISD(K) >
< ΨIP−CISD(K)|ΨIP−CISD(K) >(2.5)
and are:
(H − E0)R = RΩ, (2.6)
whereH is the matrix of the Hamiltonian in the basis of the1h and2h1p determinants,
matrix R contains the amplitudes,Ω is a matrix composed of the energy differences
with respect to the reference state,ωk = EK − E0, andE0 =< Φ0|H|Φ0 >. Thus, the
amplitudes and target states’ energies are found by diagonalization of the Hamiltonian
in the1h, 2h1p space.
HSS − E0 HSD
HDS HDD − E0
R1(K)
R2(K)
= ωK
R1(K)
R2(K)
(2.7)
(2.8)
17
whereHSS,HDS, andHDD denote1h− 1h, 2h1p− 1h, and2h1p− 2h1p blocks of the
Hamiltonian matrix, respectively.
The key advantages of a more correlated EOM-IP-CCSD method are common to
its less-expensive configuration-interaction approximation. For the closed-shell refer-
ences, the set of ionized and ionized-excited determinants is spin-complete and multiple
ionized states are treated on the same footing in IP-CISD.
2.3 Computational details
Equilibrium geometries of the five lowest ionized states of uracil were optimized using
analytic gradients underCs constraint at the IP-CCSD and IP-CISD levels with the 6-
31+G(d) basis set [1]. The cation excitation energies and transition properties were
computed at the neutral uracil geometry (optimized by RI-MP2/cc-pVTZ, see Ref. 24),
and at the optimized geometry of the lowest electronic state of the cation using the 6-
31+G(d) and 6-311+G(d,p) bases [1,2], with the core electrons frozen.
Permanent dipole moments were computed at the respective optimized geometries
using fully relaxed IP-CCSD and IP-CISD one-particle density matrices. Since the
dipole moments of charged systems are not origin-invariant, all the dipoles were com-
puted relative to the center of mass of the cations.
In water dimer calculations, the geometries of the neutrals from Ref. 70 were
employed. The cation geometries were optimized by IP-CISD and IP-CCSD with
the 6-311(+,+)G(d,p), 6-311(2+,+)G(d,p), 6-311(2+,+)G(2df) and aug-cc-pVTZ basis
sets [1–3] with symmetry constraint.
Benzene dimer calculations were carried out with IP-CISD and IP-CCSD with 6-
31(+)G(d) basis and under symmetry constraint, as in Ref. 6. The wave functions for
18
the t-shaped were analyzed using the Natural Bond Orbitals (NBO) [4] procedure and
the charge of the individual fragments was calculated.
All optimizations were conducted using defaultQ-CHEM optimization thresholds:
the gradient and energy tolerance were set to3 · 10−4 and1.2 · 10−3 respectively; maxi-
mum energy change was set to1 · 10−6. The IP-CCSD geometries of the benzene dimer
isomers were computed using tighter thresholds [5].
All electrons were correlated in the uracil, water dimer and benzene dimer geometry
optimizations and properties calculations.
Figs. 2.1 and 2.2 provide the definitions of the geometric parameters for uracil, water
dimer and three benzene dimer isomers.
2.4 Numerical results
2.4.1 Equilibrium geometries and electronically excited states of the
uracil cation
Uracil has eight different bonds between heavy atoms, as depicted in Fig. 2.1. Fig. 2.3
shows the values of the CC(1), CO(1), CO(2), and CN(2) bondlengths for the five low-
est electronic states of the cation, as well as the corresponding values in the neutrals.
The MOs hosting the unpaired electron are also shown. In agreement with molecular
orbital considerations, ionization results in significant changes in some bond lengths,
which vary from state to state. For example, the CC(1) bond becomes much longer in
the first ionized state derived by ionization from theπCC orbital, whereas the CO bonds
undergo significant changes in the states derived by ionization from the respective oxy-
gen lone pairs. As one can see from Fig. 2.3, IP-CISD systematically underestimates the
19
CC(1)
CN(1)NC(1)
CN(2)
NC(2) CC(2)
CO(1)
CO(2)
CCN(1)
CNC(1)
NCN(1)
CNC(2)
NCC(1)
CCC(1)
H1
O1H2
O2
H3
H4
O1O2
Figure 2.1: Definitions of the geometric parameters for uracil (upper panel) and waterdimer (lower panel) at the proton-transferred geometry.
bond lengths, probably because of the uncorrelated Hartree-Fock reference. However, it
reproduces the trends, such as structural differences between the states, very well.
The absolute errors of IP-CISD versus IP-CCSD are summarized in Table 2.1.
For the bondlengths, the IP-CISD errors are always negative. The table also presents
average absolute errors and standard deviations for each state, which are around 0.014-
0.016A and 0.007-0.010A, respectively. Absolute average error and standard deviation
20
C1 C2
C3
C4C5
C6
C1C2
C3
C4 C5
C6
Fragment 2
C2h x-displaced isomer
Fragment 1 Fragment 1
Fragment 2
C2h y-displaced isomer
C1C2
C3C4 C5
C6
C1 C2
C3C4C5
C6
Fragment 1
Fragment 2
C2v t-shaped isomer
C1C2
C3C4 C5
C6
C1
C2
C3C4
C5
C6
Figure 2.2: Definitions of the geometric parameters for three isomers of the benzenedimer:x-displaced (top),y-displaced (middle), and t-shaped (bottom).
for these eight bonds in five electronic states are 0.015A and 0.008A, respectively.
The results for six bond angles are summarized in Table 2.2. The results are similar to
the bondlengths behavior — IP-CISD reproduces the trend in structural changes very
well. Average absolute error and standard deviation for all angles in the five states are
0.343 and 0.266 degrees, respectively. Fig. 2.4 visualizes changes in CNC(2) angle
upon ionization. The computed permanent dipole moments in the center of mass frame
are given in Table 2.3. The IP-CCSD and IP-CISD values are very similar indicating
that IP-CISD reproduces well both the equilibrium structures and electron distributions.
IP-CISD values are systematically 0.1-0.2 a.u. too large. Thus, IP-CISD wave func-
tions inherit limitations of the uncorrelated Hartree-Fock reference and are too ionic,
21
Table 2.1: The IP-CCSD bondlengths (A) in the five electronic states of the uracil cationand absolute errors (in parenthesis) of IP-CISD relative to IP-CCSD.
Bonds 12A′′ 12A′ 22A′′ 22A′ 32A′′
CC(1) 1.403 (0.017) 1.365 (0.009) 1.352 (0.014) 1.345 (0.014) 1.375 (0.013)
CN(1) 1.321 (0.005) 1.357 (0.013) 1.390 (0.012) 1.392 (0.010) 1.471 (0.028)
NC(1) 1.460 (0.027) 1.386 (0.009) 1.358 (0.011) 1.351 (0.010) 1.371 (0.017)
CN(2) 1.386 (0.011) 1.427 (0.021) 1.416 (0.032) 1.351 (0.013) 1.398 (0.009)
NC(2) 1.403 (0.016) 1.341 (0.003) 1.426 (0.029) 1.387 (0.007) 1.425 (0.009)
CC(2) 1.469 (0.012) 1.423 (0.010) 1.444 (0.001) 1.459 (0.003) 1.473 (0.005)
CO(1) 1.215 (0.020) 1.286 (0.024) 1.231 (0.018) 1.236 (0.028) 1.204 (0.027)
CO(2) 1.199 (0.021) 1.199 (0.024) 1.226 (0.017) 1.272 (0.025) 1.230 (0.023)
average abs. error 0.016 0.014 0.017 0.014 0.016
standard deviation 0.007 0.008 0.010 0.009 0.009
as compared to more correlated IP-CCSD ones. Table 2.4 presents vertical excitation
energies and transition dipole moments of the uracil cation at two different geometries,
i.e., the geometry of the neutral and the equilibrium geometry of the lowest ionized
state. IP-CISD errors are 0.1-0.3 eV and they are consistently larger for the low-lying
states. Overall, the order of states is reproduced correctly, however, IP-CISD excitation
energies are of semi-quantitative accuracy only. Intensities of transitions are in qualita-
tive agreement. Most importantly, both methods agree which states are dark and which
are bright, indicating that the underlying wave functions are qualitatively similar. Other
important trends, e.g., the lowering of the transition dipoles for the two highest states
upon geometric relaxation (from the neutral to the cation), are also reproduced.
The basis set dependence of the errors is small, as evidenced by the results in two
different bases.
22
Tabl
e2.
2:T
heIP
-CC
SD
angl
es(d
egre
es)
inth
efiv
eel
ectr
onic
stat
esof
the
urac
ilca
tion
and
abso
lute
erro
rs(in
pare
nthe
sis)
ofIP
-CIS
Dre
lativ
eto
IP-C
CS
D.
Bon
ds12A
′′12A
′22A
′′22A
′32A
′′
CC
N(1
)11
9.21
7(0
.156
)12
2.52
9(0
.078
)12
2.64
8(0
.280
)12
1.82
6(0
.223
)12
0.74
5(0
.728
)
CN
C(1
)12
5.63
6(0
.152
)12
4.33
4(0
.232
)12
3.33
3(0
.621
)12
1.30
9(0
.101
)12
2.44
6(0
.027
)
NC
N(1
)11
3.07
7(0
.496
)11
2.38
1(0
.584
)11
3.97
7(1
.260
)11
8.07
9(0
.225
)11
4.01
8(0
.215
)
CN
C(2
)12
6.73
3(0
.533
)12
4.29
1(0
.383
)12
6.22
4(0
.556
)12
4.31
5(0
.099
)12
9.40
9(0
.318
)
NC
C(2
)11
5.21
4(0
.463
)12
0.78
1(0
.046
)11
4.48
1(0
.644
)11
6.35
2(0
.105
)11
3.36
5(0
.222
)
CC
C(1
)12
0.12
3(0
.429
)11
5.68
4(0
.093
)11
9.33
7(0
.447
)11
8.12
0(0
.145
)12
0.01
6(0
.430
)
aver
age
abs.
erro
r0.
372
0.23
60.
635
0.15
00.
323
stan
dard
devi
atio
n0.
172
0.21
20.
334
0.06
00.
239
23
Table 2.3: IP-CCSD and IP-CISD permanent dipole moments (a.u.) of the five lowestelectronic states of the uracil cation computed at the respective optimized geometriesrelative to the center of mass.
12A′′ 12A′ 22A′′ 22A′ 32A′′
IP-CCSD 2.509 1.474 1.144 1.384 2.641
IP-CISD 2.632 1.602 1.279 1.511 2.759
2.4.2 Equilibrium geometries of the three isomers of the benzene
dimer cation
Geometrical parameters (see Fig. 2.2) for the three isomers of the benzene dimer cation
are summarized in Table 2.5 and visualized in Fig. 2.5. On this example, we investigate
how well IP-CISD reproduces the structures of the ionized non-covalent dimers. Ioniza-
tion of such systems changes the bonding from non-covalent to covalent, which results
in significant structural changes, in particular the interfragment distance. For example,
the interfragment distance shrinks from 3.9 to 3.3A in the sandwich isomers. IP-CISD
overestimates the interplanar separation in the displaced sandwich isomers by approxi-
mately 0.2A, while the sliding displacement is reproduced quite accurately. Similarly,
the separation between the rings in the t-shaped structure is overestimated.
In the t-shaped structure the two fragments are nonequivalent, and the charge is
unevenly distributed between the rings. The degree of charge distribution determines
the intensity of charge resonance bands, which can be used to probe the structure and
dynamics of the system. The NBO analysis of the IP-CISD densities for the states
involved in this transition yields an 0.888 and 0.101 partial charge on fragment 1 (stem),
which is in excellent agreement with the IP-CCSD values [6] of 0.880 and 0.099, respec-
tively. Charge-resonance transition energies are 0.71 and 0.81 eV for EOM-IP-CCSD
and IP-CISD, respectively.
24
Table 2.4: The IP-CCSD and IP-CISD excitation energies (eV) and transition dipolemoments (a.u.) of the uracil cation at the equilibrium geometries of the neutral and thecation.
neutral cation
6-31(+)G(d,p) IP-CCSD IP-CISD IP-CCSD IP-CISD
E µ2 E µ2 E µ2 E µ2
12A′ 0.668 0.000 0.367 0.000 1.175 0.000 0.820 0.000
22A′′ 1.063 0.000 0.867 0.000 1.809 0.000 1.577 0.000
22A′ 1.647 0.790 1.427 0.819 2.385 0.611 2.156 0.613
32A′′ 3.566 1.342 3.627 0.955 4.209 0.940 4.223 0.611
average abs. error 0.195 0.208
neutral cation
6-311(+)G(d,p) IP-CCSD IP-CISD IP-CCSD IP-CISD
E µ2 E µ2 E µ2 E µ2
12A′ 0.642 0.000 0.335 0.000 1.144 0.000 0.785 0.000
22A′′ 1.037 0.000 0.848 0.000 1.779 0.000 1.557 0.000
22A′ 1.614 0.786 1.388 0.820 2.349 0.603 2.112 0.611
32A′′ 3.543 1.358 3.613 0.968 4.187 0.952 4.209 0.620
average abs. error 0.198 0.211
The changes in intramolecular parameters are reproduced by IP-CISD very well
— average absolute error in bond lengths for all three isomers is 0.01A. Note that
Jahn-Teller displacements in the t-shaped isomer are also accurately described. The
contraction of the interfragment distance is reproduced correctly, however, the distance
is overestimated. We interpret this by the absence of dispersion in uncorrelated Hartree-
Fock reference employed by IP-CISD. The absolute error is slightly larger owing to the
larger distance.
25
Tabl
e2.
5:T
hebo
ndle
ngth
s(
A),
angl
es(d
egre
es),
inte
rfra
gmen
tdi
stan
ces
and
slid
ing
disp
lace
men
ts(
A)
inth
egr
ound
stat
eof
thex
-dis
plac
ed,y
-dis
plac
edan
dt-
shap
edbe
nzen
edi
mer
catio
nsca
lcul
ated
with
IP-C
ISD
/6-3
1(+
)G(d
).F
orth
ex
-an
dy-
disp
lace
dst
ruct
ures
,ge
omet
ricpa
ram
eter
sfo
ron
lyon
eof
the
benz
ene
frag
men
tsar
epr
ovid
ed(t
hefr
agm
ents
are
equi
vale
ntby
sym
met
ry).
Abs
olut
eer
rors
ofIP
-CIS
Dre
lativ
eto
IP-C
CS
Dar
epr
esen
ted
inpa
rent
hesi
s.A
vera
geab
solu
teer
rors
are
calc
ulat
edus
ing
the
data
for
sym
met
ryun
ique
para
met
ers.
Par
amet
er(n
umbe
r)x
-dis
plac
edy-d
ispl
aced
t-sh
aped
(fra
gmen
t1)
t-sh
aped
(fra
gmen
t2)
CH
bond
rang
e1.
075
(0.0
13)
-1.
076
(0.0
14)
1.07
4(0
.014
)-
1.07
6(0
.013
)1.
073
(0.0
09)
-1.
077
(0.0
12)
1.07
5(0
.014
)
C1C
21.
373
(0.0
10)
1.38
5(0
.011
)1.
419
(0.0
10)
1.39
3(0
.012
)
C2C
31.
408
(0.0
11)
1.41
4(0
.011
)1.
376
(0.0
01)
1.38
7(0
.012
)
C3C
41.
400
(0.0
11)
1.38
4(0
.011
)1.
414
(0.0
11)
1.39
3(0
.012
)
C4C
51.
379
(0.0
10)
1.38
4(0
.011
)1.
414
(0.0
11)
1.39
3(0
.012
)
C5C
61.
400
(0.0
11)
1.41
4(0
.011
)1.
376
(0.0
01)
1.38
7(0
.012
)
C6C
11.
408
(0.0
11)
1.38
5(0
.011
)1.
419
(0.0
10)
1.39
3(0
.012
)
Ave
rage
abs.
erro
r0.
011
0.01
10.
007
0.01
2
C1C
2C
311
9.56
9(0
.032
)12
0.47
3(0
.009
)11
9.42
8(0
.018
)11
9.93
3(0
.009
)
C2C
3C
412
0.80
7(0
.026
)12
0.30
7(0
.010
)11
9.28
2(0
.096
)11
9.93
3(0
.009
)
C3C
4C
511
9.60
7(0
.012
)11
9.30
1(0
.041
)12
1.51
4(0
.120
)12
0.13
3(0
.015
)
C4C
5C
611
9.60
7(0
.012
)12
0.30
7(0
.010
)11
9.28
2(0
.096
)11
9.93
3(0
.009
)
C5C
6C
112
0.80
7(0
.026
)12
0.47
2(0
.010
)11
9.42
8(0
.018
)11
9.93
3(0
.009
)
C6C
1C
211
9.56
9(0
.032
)11
9.09
2(0
.051
)12
1.06
5(0
.108
)12
0.13
3(0
.015
)
Ave
rage
abs.
erro
r0.
023
0.02
00.
078
0.01
1
inte
rfr.
dist
ance
3.31
/3.0
83.
31/3
.07
4.81
/4.5
8
sl.
disp
lace
men
t1.
04/1
.07
1.03
/1.1
0-
26
2.4.3 Water dimer cation
Table 2.6 summarizes geometrical parameters (see Fig. 2.1) for the two lowest electronic
states of the water dimer cation. Selected bondlengths and angles are visualized in
Fig. 2.6. The errors for the intramolecular parameters are similar to those in uracil and
benzene dimers. The trends in intramolecular distances are similar to the benzene
dimer cations, however, in this case ionization introduces even stronger perturbation
to electronic structure and leads to the proton-transfer and formation of OH· · ·H3O+
complex, as evident from the value of O1H2 distance in Table 2.6. The OO bondlength
shortens by about 0.3A in the lowest ionized state relative to the neutral. The values of
the OO distance between the two lowest ionized states differ by about 0.06A. IP-CISD
reproduces these trends and structural differences between the different ionized states
correctly.
The absolute errors for the intermolecular parameters are slightly larger, e.g., 0.05-
0.06A for the OO distance, however, one should keep in mind that the value of this bond
is about 2.5A. As in the benzene dimer example, IP-CISD overestimates the intramolec-
ular distances.
An important result is that the errors of IP-CISD relative to IP-CCSD are not very
sensitive to the basis set, as one might expect in view of different amount of correlation
included in the latter. The absolute average errors in bondlengths for two electronic
states are 0.043, 0.044, 0.037 and 0.040A in the 6-311(+,+)G(d,p), 6-311(2+,+)G(d,p),
6-311(2+,+)G(2df) and aug-cc-pVTZ bases, respectively.
2.4.4 Timings
To demonstrate gains in computational cost, we present timings for IP-CCSD and IP-
CISD calculations of the uracil dimer on a Xeon 3.2 GHz Linux machine using parallel
27
Tabl
e2.
6:T
heIP
-CC
SD
bond
leng
ths
(A
)an
dan
gles
(deg
rees
)in
the
two
elec
tron
icst
ates
ofth
ew
ater
dim
erca
tion
and
abso
lute
erro
rs(in
pare
nthe
sis)
ofIP
-CIS
Dre
lativ
eto
IP-C
CS
Dca
lcul
ated
with
diffe
rent
base
s.
6-31
1(+
,+)G
(d,p
)6-
311(
2+,+
)G(d
,p)
6-31
1(2+
,+)G
(2df
)au
g-cc
-pV
TZ
Par
amet
er12A
′′12A
′12A
′′12A
′12A
′′12A
′12A
′′12A
′
H1O
10.
978(
0.01
2)0.
973(
0.01
0)0.
978(
0.01
2)0.
973(
0.01
0)0.
977(
0.01
2)0.
973(
0.01
0)0.
975(
0.01
0)0.
970(
0.00
8)
O1H
21.
425(
0.12
7)1.
525(
0.08
1)1.
423(
0.12
8)1.
522(
0.08
3)1.
526(
0.08
2)1.
592(
0.08
3)1.
429(
0.11
5)1.
519(
0.07
9)
H3O
20.
970(
0.01
4)0.
971(
0.01
5)0.
970(
0.01
4)0.
971(
0.01
5)0.
972(
0.01
6)0.
973(
0.01
5)0.
968(
0.01
3)0.
970(
0.01
4)
O2H
40.
970(
0.01
4)0.
971(
0.01
5)0.
970(
0.01
4)0.
971(
0.01
5)0.
972(
0.01
6)0.
973(
0.01
5)0.
968(
0.01
3)0.
970(
0.01
4)
O1O
22.
475(
0.08
2)2.
532(
0.06
0)2.
474(
0.08
2)2.
529(
0.06
2)2.
549(
0.05
4)2.
592(
0.06
2)2.
478(
0.07
4)2.
524(
0.06
1)
H1O
1H
212
3.71
3(6.
795)
176.
809(
0.52
2)12
3.48
5(6.
881)
176.
520(
0.67
1)12
6.14
1(2
.966
)17
6.85
8(0
.671
)12
0.55
3(6.
235)
177.
434(
0.16
9)
H3O
2H
410
9.87
4(2.
495)
111.
259(
2.27
9)10
9.81
6(2.
517)
111.
187(
2.28
7)11
0.25
6(1
.302
)11
1.25
0(2
.287
)10
9.90
2(2.
287)
111.
147(
1.97
6)
Ave
rage
abs.
erro
rs
Bon
ds0.
050
0.03
60.
050
0.03
70.
036
0.03
70.
045
0.03
5
Ang
les
4.64
51.
400
4.69
91.
479
2.13
41.
479
4.19
81.
073
28
version (threaded over two processors) of the CCSD and EOM code (the Hartree-Fock
and integral transformation modules were not parallelized). The symmetry of the dimer
is C2, and two lowest states in each irrep were requested. In 6-31+G(d) basis (320
basis functions), the wall time for total (including SCF and integral transformation) IP-
CCSD and IP-CISD calculations was 5.82 and 1.50 hours, respectively. The IP-CISD
calculation in 6-311+G(2d,p) basis (480 basis functions) took only 10.5 hours.
2.5 Conclusions
The benchmark study of the novel configuration-interaction variant of EOM-IP-CCSD
method is reported. The method is naturally spin-adapted, variational, and size-
intensive. The computational scaling isN5, in contrast to theN6 scaling of EOM-
IP-CCSD, which results in significant computational savings. The performance of the
method was tested on the uracil cation (five electronic states), water dimer cation (two
electronic states), and three isomers of the benzene dimer cation (ground electronic
state). The results demonstrate that the equilibrium geometries of the ionized states are
reproduced reasonably well. Using symmetry unique parameters from these ten struc-
tures optimized in a modest basis set, we computed average absolute error and standard
deviation for bond lengths and angles relative to the IP-CCSD values. For bondlengths,
average absolute error and standard deviation are 0.014 and 0.007A, respectively, and
for angles — 0.255 and 0.264 degrees. It is informative to compare these numbers with
mean absolute errors and standard deviations of the HF and CCSD methods for well-
behaved closed-shell molecules relative to the experiment [7]. For bondlengths, the
CCSD/cc-pVTZ and CCSD/cc-pVDZ values are 0.0064/0.0066 and 0.0119/0.0076A,
respectively [7]. The HF errors and standard deviations in cc-pVTZ and cc-pVDZ are
0.0263/0.0223 and 0.0194/0.0225A, respectively [7]. Thus, IP-CISD structures are of
29
similar quality as HF geometries of closed-shell molecules. Inheriting limitations of the
underlying Hartree-Fock reference, IP-CISD systematically underestimates bondlengths
and overestimates interfragment distances. Most importantly, IP-CISD correctly repro-
duces structural changes induced by ionization and structural differences between dif-
ferent ionized states.
Molecular properties such as permanent and transition dipole moments and charge
distributions are reproduced very well demonstrating that IP-CISD wave functions are
qualitatively correct. Ionization energies cannot be computed by IP-CISD because of the
use of uncorrelated Hartree-Fock description of the neutral, however, energy differences
between the ionized states are of semi-quantitative accuracy (errors of about 0.3 eV
relative to IP-CCSD).
Our results suggest that IP-CISD is most useful as an economical alternative for
geometry optimization in the ionized systems. Using IP-CISD structures, more accurate
energy differences can be computed with more expensive IP-CCSD. Moreover, IP-CISD
wave functions may be employed as zeroth-order wave functions in subsequent pertur-
bative treatment.
2.6 Reference list
[1] W.J. Hehre, R. Ditchfield, and J.A. Pople, Self-consistent molecular orbital meth-ods. XII. Further extensions of gaussian-type basis sets for use in molecular orbitalstudies of organic molecules, J. Chem. Phys.56, 2257 (1972).
[2] R. Krishnan, J.S. Binkley, R. Seeger, and J.A. Pople, Self-consistent molecularorbital methods. XX. A basis set for correlated wave functions, J. Chem. Phys.72,650 (1980).
[3] T.H. Dunning, Gaussian basis sets for use in correlated molecular calculations. I.The atoms boron through neon and hydrogen, J. Chem. Phys.90, 1007 (1989).
30
[4] E.D. Glendening, J.K. Badenhoop, A.E. Reed, J.E. Carpenter, J.A. Bohmann, C.M.Morales, and F. Weinhold, NBO 5.0., Theoretical Chemistry Institute, Universityof Wisconsin, Madison, WI, 2001.
[5] P.A. Pieniazek, S.E. Bradforth, and A.I. Krylov, Charge localization and Jahn-Tellerdistortions in the benzene dimer cation, J. Chem. Phys.129, 074104 (2008).
[6] P.A. Pieniazek, S.A. Arnstein, S.E. Bradforth, A.I. Krylov, and C.D. Sherrill,Benchmark full configuration interaction and EOM-IP-CCSD results for prototyp-ical charge transfer systems: Noncovalent ionized dimers, J. Chem. Phys.127,164110 (2007).
[7] T. Helgaker, P. Jørgensen, and J. Olsen,Molecular electronic structure theory.Wiley & Sons, 2000.
31
Fig
ure
2.3:
Sel
ecte
dbo
ndle
ngth
sin
the
five
low
este
lect
roni
cst
ates
ofth
eur
acil
catio
n.T
heco
rres
pond
ing
valu
esof
the
neut
ral
are
show
nby
dash
edlin
es.
The
MO
sfr
omw
hich
elec
tron
isre
mov
edar
esh
own
for
each
stat
e.
1.33
1.34
1.35
1.36
1.37
1.38
1.39
1.40
1.41
CC(1) bond length, Angstrom
Ele
ctro
nic
Stat
e
IP-C
ISD
IP-C
CS
D
12A
˝
12A
´
22A
´
22A
˝
32A
˝
1.18
1.20
1.22
1.24
1.26
1.28
1.30
CO(1) bond length, Angstrom
Ele
ctro
nic
Sta
te
IP-C
ISD
IP-C
CSD
12A
˝
12A
´
22A
´
22A
˝
32A
˝
1.17
1.18
1.19
1.20
1.21
1.22
1.23
1.24
1.25
1.26
1.27
1.28
IP-C
ISD
IP-C
CS
D
CO(2) bond length, Angstrom
Ele
ctro
nic
Stat
e
12A
˝
12A
´
22A
´
22A
˝
32A
˝
1.33
1.34
1.35
1.36
1.37
1.38
1.39
1.40
1.41
1.42
1.43
CN(2) bond length, Angstrom
Ele
ctro
nic
Stat
e
IP-C
ISD
IP-C
CS
D
12A
˝
12A
´
22A
´
22A
˝
32A
˝
32
123.0
123.5
124.0
124.5
125.0
125.5
126.0
126.5
127.0
127.5
128.0
128.5
129.0
129.5
130.0
CN
C(2
) ang
le, D
egre
e
Electronic State
IP-CISD IP-CCSD
12A˝
12A´
22A´
22A˝32A˝
Figure 2.4: The CNC(2) angle in the five lowest electronic states of uracil cation.Dashed line shows the corresponding value at the geometry of neutral.
33
Fig
ure
2.5:
The
CC
bond
leng
ths
ofth
eth
ree
benz
ene
dim
erca
tion
isom
ers
inth
egr
ound
elec
tron
icst
ate
optim
ized
with
IP-C
ISD
/6-3
1(+
)G(d
)an
dIP
-CC
SD
/6-3
1(+
)G(d
).O
nly
the
valu
esof
the
sym
met
ryun
ique
para
met
ers
for
corr
espo
ndin
gsy
m-
met
ryno
n-eq
uiva
lent
frag
men
tsar
esh
own
1.37
0
1.37
5
1.38
0
1.38
5
1.39
0
1.39
5
1.40
0
1.40
5
1.41
0
1.41
5
1.42
0CC bond length, Angstrom
Par
amet
er
x-d
ispl
aced
isom
er, I
P-C
ISD
/6-3
1(+)
G*
x-d
ispl
aced
isom
er, I
P-C
CS
D/6
-31(
+)G
*
C1C
2C
2C3
C3C
4C
4C5
1.38
0
1.38
5
1.39
0
1.39
5
1.40
0
1.40
5
1.41
0
1.41
5
1.42
0
1.42
5
CC bond length, Angstrom
Para
met
er
y-d
ispl
aced
isom
er, I
P-C
ISD
/6-3
1(+)
G*
y-d
ispl
aced
isom
er, I
P-C
CS
D/6
-31(
+)G
*
C1C
2C
2C3
C3C
4
1.37
0
1.38
0
1.39
0
1.40
0
1.41
0
1.42
0
1.43
0
CC bond length, Angstrom
Par
amet
er
t-sh
aped
isom
er, f
ragm
ent 1
, IP
-CIS
D/6
-31(
+)G
* t-
shap
ed is
omer
, fra
gmen
t 1, I
P-C
CS
D/6
-31(
+)G
*
C1C
2C
2C3
C3C
41
21.
380
1.38
2
1.38
4
1.38
6
1.38
8
1.39
0
1.39
2
1.39
4
1.39
6
1.39
8
1.40
0
1.40
2
1.40
4
CC bond length, Angstrom
Par
amet
er
t-sh
aped
, fra
gmen
t 2, I
P-C
ISD
/6-3
1(+)
G*
t-sh
aped
, fra
gmen
t 2, I
P-C
CS
D/6
-31(
+)G
*
C1C
2C
2C3
34
60 80 100 120 140 160 180 2001.4
1.6
1.8
2.0
2.2
2.4
2.6
Bond
leng
th, A
ngst
rom
Number of basis functions
O1H2 / 12A'' / IP-CISD
O1O2 / 12A" / IP-CISD
O1H2 / 12A' / IP-CISD
O1O2 / 12A' / IP-CISD
O1H2 / 12A" / IP-CCSD
O1O2 / 12A" / IP-CCSD
O1H2 / 12A' / IP-CCSD
O1O2 / 12A' / IP-CCSD
60 80 100 120 140 160 180 200
110
120
130
140
150
160
170
180
Ang
le, D
egre
e
Number of basis functions
H1O1H2 / 12A" /IP-CISD
H3O2H4 / 12A" /IP-CISD
H1O1H2 / 12A' /IP-CISD
H3O2H4 / 12A' /IP-CISD
H1O1H2 / 12A" / IP-CCSD
H3O2H4 / 12A" / IP-CCSD
H1O1H2 / 12A' / IP-CCSD
H3O2H4 / 12A' / IP-CCSD
Figure 2.6: Selected bondlengths and angles in the two lowest electronic states of thewater dimer cation optimized with IP-CISD and IP-CCSD with different bases.
35
Chapter 3
The electronic structure, ionized states
and properties of the uracil dimers
3.1 Overview
The electronic structure and spectral properties of ionized uracil andπ-stacked and h-
bonded uracil dimers are characterized by EOM-IP-CCSD. In Sections 3.3.1 and 3.3.2
we discuss the electronic structure of uracil and uracil dimers, respectively. Section 3.3.3
presents the calculated vertical ionization energies for five lowest electronic states of the
monomer and ten lowest electronic states of the dimers. Special attention is given to
the monomer basis set effect (Section 3.3.3) as well as the proposed cost-saving energy-
additivity scheme (Section 3.3.3). Lastly, we present the electronic spectra of the two
uracil dimer cations calculated at the neutral and relaxed geometries (Section 3.3.4).
3.2 Computational details
In all calculations of vertical IEs, we employ the uracil dimer structures presented in
Fig. 3.1 from the S22 set of Hobza and coworkers [1]. The monomer calculations are
carried out using the RI-MP2/cc-pVTZ optimized neutral’s geometry. For the calcula-
tions of IEs and electronic spectrum of the stacked uracil dimer at the cation geometry,
its structure was relaxed with DFT/6-311(+)G(d,p) with 50-50 functional (i.e., equal
mixture of the following exchange and correlation parts: 50% Hartree-Fock + 8 %
36
C2hC2
(a) (b)
Figure 3.1:π-stacking and hydrogen-bonding in DNA (top) and the geometries of thestacked (a) and hydrogen-bonded (b) uracil dimers.
Slater + 42 % Becke for exchange, and 19% VWN + 81% LYP for correlation). Differ-
ent isomers were located on the cation potential energy surface, e.g., the t-shaped and
stacked-like structures. Here we focus on just one of the stacked uracil dimer isomers.
37
The optimized structures and relative energies of the other isomers will be discussed
elsewhere [2].
IEs of the dimers and the monomer were calculated at the EOM-IP-CCSD level
using several Pople bases [3, 4], i.e., 6-31(+)G(d), 6-311(+)G(d,p), and others. In the
monomer calculations, we also employed the 6-31G(d) and 6-31+G(d) bases with a
modifiedd-function exponent (0.2 instead of 0.8) as in Ref. 10. The core orbitals were
frozen in the IE calculations.
Electronic spectra of the cations were computed at the EOM-IP-CCSD/6-31(+)G(d)
level. The monomer spectrum was also calculated with a bigger cc-pVTZ basis set [5].
The molecular structures and relevant total energies are given in the supplementary
materials of Ref. 25. All calculations were conducted using theQ-CHEM electronic
structure package [6].
3.3 Results and Discussion
3.3.1 Prerequisites: Electronic states and spectrum of the uracil
cation
We begin with a brief overview of the electronic structure of uracil. It is a planar closed-
shell molecule ofCs symmetry. The five lowest electronic states of the uracil cation
correspond to ionizations from the five MOs shown in Fig. 3.2. Among these orbitals,
there are twoπ orbitals ofa′′ symmetry corresponding to the C—C and C—O double
bonds of uracil; two orbitals ofa′ symmetry corresponding to the oxygen lone pairs,
and onea′′ orbital of a mixed character. The highest occupied molecular orbital isπCC .
Vertical IEs of the five lowest ionized states of uracil are presented in Table 3.1, and
the corresponding electronic spectrum of the uracil cation is shown in Fig. 3.2. The
38
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00.00
0.02
0.04
0.06
0.08
0.10
0.12
Osc
illat
or S
treng
th
Energy, eV
πCC / a''
lp(O2) / a'
lp(O) + lp(N) / a''
lp(O1) / a'
lp(N) + πCC+ πCO / a''
Figure 3.2: Electronic spectrum and relvant MOs of the uracil cation at the geometry ofthe neutral. The MO hosting the hole in the ground state of the cation is also shown (topleft). Dashed lines show the transitions with zero oscillator strength.
ground state of the cation corresponds toπCC (or 1a′′) orbital being singly occupied (the
corresponding orbital is shown in the picture). Four excited cation states are derived
from ionization from the1a′, 2a′′, 2a′ or 3a′′ orbitals. All four electron transitions are
symmetry allowed, but their intensity is different: the parallel (allowed inx, y-direction)
A′′ → A′′ transitions are intense and the perpendicular (allowed inz-direction)A′′ → A′
transitions are weak due to unfavorable orbital overlap. Overall, the calculated vertical
IEs (e.g., with cc-pVTZ) for the monomer are in agreement with the experimentally
determined values [7–9], with the exception of the32A′′ transition, for which the calcu-
lated IE value at 13 eV is outside the experimental range of 12.5-12.7 eV. This difference
is within the EOM-IP-CCSD error bars (0.2-0.3 eV). The absolute differences between
EOM-IP-CCSD/cc-pVTZ and CASPT2 IEs from Ref.10 are within 0.13-0.49 eV range
39
Table 3.1: Five lowest verical IEs (eV) of the uracil monomer calculated with EOM-IP-CCSD. The number of basis functions (b.f.) is given for each basis.
Basis b.f. 12A′′ 12A′ 22A′′ 22A′ 32A′′
6-31G(d) 128 9.13 9.75 10.17 10.75 12.71
6-31G(d)a 128 9.11 9.72 10.11 10.69 12.73
6-31(+)G(d) 160 9.38 10.05 10.44 11.03 12.95
6-31(+)G(d)a 160 9.28 9.92 10.30 10.92 12.88
6-31(2+)G(d) 192 9.39 10.05 10.45 11.03 12.95
6-311(+)G(d,p) 200 9.48 10.11 10.51 11.09 13.02
6-31(2+)G(d,p) 204 9.41 10.07 10.47 11.04 12.97
6-31(+)G(2d) 208 9.45 10.13 10.52 11.10 12.99
6-31(+)G(2d,p) 220 9.46 10.13 10.53 11.11 13.00
6-311(2+,+)G(d) 224 9.43 10.09 10.47 11.07 12.97
6-311(+)G(2d) 228 9.49 10.20 10.57 11.16 13.02
6-311(2+)G(d,p) 232 9.48 10.12 10.52 11.09 13.02
6-311(2+,+)G(d,p) 236 9.48 10.12 10.52 11.09 13.02
6-31(+)G(2df) 284 9.60 10.30 10.69 11.26 13.13
cc-pVTZ 296 9.55 10.21 10.62 11.17 13.08
Exp.b 9.45-9.6 10.02-10.13 10.51-10.56 10.90-11.16 12.50-12.70
CASPT2c 9.42 9.83 10.41 10.86 12.59a Modified d-orbital exponent.
b Experimental results are from Refs. 7–9c Empirically corrected (IPEA=0.25) CASPT2/ANO-L 431/21 from Ref. 10
and are slightly larger than the discrepancies between the EOM-IP-CCSD and the exper-
imental values. Note that the CASPT2 results shown in Table 3.1 are obtained using the
empirical IPEA correction [10], which improves the agreement with the experiment
(e.g., not IPEA corrected CASPT2 value [10] for the lowest IE is 9.22 eV, which is 0.23
eV below the experimental range).
3.3.2 Electronic structure of the uracil dimers
Fig. 3.3 displays the calculated Hartree-Fock MOs corresponding to the ten lowest ion-
ized states of the stacked uracil dimer and the corresponding ionization energies (IEs)
40
calculated with EOM-IP-CCSD/6-311(+)G(d,p). The ten highest occupied orbitals of
the stacked dimer are symmetric and antisymmetric combinations of the five highest
occupied FMOs. The biggest splitting (0.53 eV) is between the states derived from
bonding and antibonding combinations of theπ-like FMOs, whereas the combinations
of FMOs of the lone pair character are almost degenerate. As Fig. 3.4 shows, the elec-
9.14 9.6610.14 10.20
10.5210.47
11.07 11.0212.96
12.67
Orb
ital e
nerg
y
State energy
Figure 3.3: MOs and IEs (eV) of the ten lowest ionized states of the stacked uracil dimer.Ionization from the highest MO yields ground electronic state of the dimer cation, andionizations from the lower orbitals result in electronically excited states.
tronic structure of hydrogen-bonded dimer exhibits similar trends, i.e., the FMOs of
the same character are combined to produce bonding and anti-bonding DMOs. The
important difference is that the overlap between the FMOs is the biggest for the in-
plane orbitals, resulting in the biggest splitting for the DMOs formed from FMOs cor-
responding to the lone pairs on the two neighboring oxygens. Overall, the splittings are
smaller than in theπ-stacked dimer, i.e., the largest splitting is 0.35 eV, and the splittings
between the two lowest states is only 0.10 eV.
41
9.35 9.47
10.20
10.69
10.25
10.72
11.5511.19
12.83 12.95
Orb
ital e
nerg
y State energy
Figure 3.4: MOs and IEs (eV) of the ten lowest ionized states of the hydrogen-bondeduracil dimer. Ionization from the highest MO yields ground electronic state of the dimercation, and ionizations from the lower orbitals result in electronically excited states.
Note that the orbital splitting does not change state ordering in the dimers relative to
the monomer.
3.3.3 Vertical ionization energies of the monomer and the dimers
Monomer ionization energies, transition dipoles, and the basis set effects
We investigate the basis set effects using monomer IEs to choose an optimal basis
set for the dimer calculations. Basis set convergence is illustrated in Fig. 3.5. The
range of the experimental IEs is shown by the shaded areas. As one can see, beyond
the 6-311(+)G(d,p) basis the variations in IEs are less than 0.12 eV. The analysis of
42
the data in Table 3.1 leads to the following conclusions. Firstly, the triple-ζ qual-
ity basis is desirable, as double-ζ and triple-ζ IEs differ by up to 0.07 eV — com-
pare, for example, 6-31(2+)G(d,p) vs. 6-311(2+)G(d,p), and 6-31(+)G(2d) vs. 6-
311(+)G(2d) results. Secondly, the polarization on hydrogens and additional polar-
ization on heavy atoms have a noticeable effect on IEs: for example switching from
6-31(2+)G(d) to 6-31(2+)G(d,p) results in a just 0.02 eV change; yet the difference
between 6-311(2+,+)G(d) and 6-311(2+,+)G(d,p) values is 0.05 eV. Difference between
the 6-31(+)G(2df) and 6-31(+)G(2d) values is 0.17 eV. Lastly, adding diffuse func-
tions on hydrogens and extra diffuse functions on heavy atoms has a negligible effect
on IEs — compare, for example, 6-31(+)G(d) vs. 6-31(2+)G(d); 6-311(+)G(d,p) vs.
6-311(2+)G(d,p); and 6-311(2+)G(d,p) vs. 6-311(2+,+)G(d,p). Thus, we choose 6-
311(+)G(d,p) as an optimal basis for the dimers. The results with the modified d-orbital
exponent [10] do not show systematic improvement over the values obtained with the
standard polarization function. Overall, calculated vertical IEs for the monomer are in
agreement with the experimentally determined values, with the exception of the32A′′
transition, for which the calculated IE value at 13 eV is outside the experimental range
of 12.5-12.7 eV. The difference is within the EOM-IP-CCSD error bars (0.2-0.3 eV).
Another observation is that both the state ordering and the energy gaps between the
states do not depend on the basis set, i.e., the curves in Fig. 3.5 are almost parallel.
This suggests that cost-reducing energy-additivity schemes can be employed for the IE
calculations.
Finally, Table 3.2 contains monomer excitation energies and oscillator strengths
calculated with different bases ranging from 6-31(+)G(d) to cc-pVTZ. Interestingly, the
energies, transition dipole values and oscillator strengths change only slightly with the
basis set increase, and the 6-31(+)G(d) basis set appears to be sufficient for the transition
property calculations.
43
6-31G*
6-31(+)G*
6-311(+)G**
6-31(+)G(2d)
6-31(+)G(2df)
cc-pVTZ6-311G(2+,+)**
120 140 160 180 200 220 240 260 280 3009.0
9.5
10.0
10.5
11.0
11.5
12.0
12.5
13.0
X 2A''
1 2A'
2 2A''
3 2A'
4 2A''
Ioni
zatio
n en
ergy
, eV
Number of basis functions
Figure 3.5: Basis set dependence of the five lowest IEs of uracil. The shaded areasrepresent the range of the expertimental values.
Dimer IEs and the energy additivity scheme
The monomer results from Sec. 3.3.3 suggest to employ the 6-311(+)G(d,p) basis for
the dimer IE calculations together with energy-additivity schemes. Here we investi-
gate whether these results apply for the dimers, whose description may require a basis
larger than 6-311(+)G(d,p), i.e., augmented by additional diffuse functions, to accurately
describe theπ-stacking or hydrogen-bonding interaction.
Tables 3.3 and 3.4 contain calculated IEs for the ten lowest ionized states of the
stacked and hydrogen-bonded complexes, respectively. The IE data in Table 3.3 exhibit
similar basis set effects as in the monomer. Additional sets of diffuse functions on heavy
atoms or hydrogens have negligible effect on IEs, whereas extra polarization leads to
noticeable changes in IEs. Overall, the results from Tables 3.3 and 3.4 confirm that the
44
Table 3.2: Excitation energies, transition dipole moments and oscillator strengths of theelectronic transitions in the uracil cation calculated with EOM-IP-CCSD with differentbases.
Property Basis 12A′ 22A′′ 22A′ 32A′′
∆E, eV 6-31(+)G(d) 0.668 1.647 1.063 3.566
6-311(+)G(d,p) 0.642 1.614 1.037 3.543
cc-pVTZ 0.664 1.627 1.069 3.533
< µ2 >, a.u. 6-31(+)G(d) 0.0003 0.0000 0.7888 1.3419
6-311(+)G(d,p) 0.0003 0.0000 0.7859 1.3586
cc-pVTZ 0.0002 0.0000 0.7378 1.3306
f 6-31(+)G(d) 0.0000 0.0000 0.0205 0.1172
6-311(+)G(d,p) 0.0000 0.0000 0.0200 0.1180
cc-pVTZ 0.0000 0.0000 0.0193 0.1152
6-311(+)G(d,p) basis is indeed an optimal choice for the stacked dimer in terms of accu-
racy versus computational cost. Surprisingly, a single set of diffuse functions is suf-
ficient for adequate representation of the ionizedπ-stacked dimer, although additional
diffuse functions might become more important at shorter interfragment distances.
The stacked dimer IEs from Table 3.3 demonstrate that, similarly to the monomer,
the energy spacing between the ionized states remains almost constant in different bases,
thus suggesting that energy-additivity schemes can be employed.
IEs for the hydrogen-bonded dimer are collected in Table 3.4 and exhibit the same
trends as in the stacked dimer.
Finally, we describe a simple energy-additivity scheme for the dimer IE calculations.
As the IE curves remain parallel both in the monomer and dimer, we approximate the
target dimer IEs calculated with a large basis,IED,largeEOM−IP−CCSD, using the dimer IEs
calculated with a smaller basis,IED,smallEOM−IP−CCSD, and the monomer IEs calculated with
the large and small bases (IEM,largeEOM−IP−CCSD andIEM,small
EOM−IP−CCSD, respectively):
45
Tabl
e3.
3:Te
nlo
wes
tver
tical
IEs
(eV
)of
the
stac
ked
urac
ildi
mer
calc
ulat
edw
ithE
OM
-IP
-CC
SD
.
Sta
te6-
31G
(d)
6-31
(+)G
(d)
6-31
(2+
)G(d
)6-
31(2
+)G
(d,p
)6-
311(
+)G
(d,p
)6-
311(
++
)G(d
,p)
6-31
1(2+
)G(d
,p)
X2B
8.81
9.03
9.04
9.06
9.14
9.14
9.14
12A
9.31
9.56
9.56
9.59
9.66
9.66
9.66
22B
9.77
10.0
610
.06
10.0
710
.14
10.1
410
.14
22A
9.81
10.1
210
.12
10.1
310
.20
10.1
910
.19
32B
10.1
110
.38
10.3
910
.41
10.4
710
.47
10.4
7
32A
10.1
510
.44
10.4
410
.46
10.5
210
.52
10.5
2
42B
10.6
710
.94
10.9
410
.96
11.0
211
.02
11.0
2
42A
10.7
210
.99
10.9
911
.00
11.0
711
.06
11.0
6
52B
12.3
812
.61
12.6
112
.63
12.6
712
.69
12.6
8
52A
12.6
512
.88
12.8
812
.91
12.9
612
.96
12.9
6
b.f.
256
320
384
408
416
424
480
46
Table 3.4: Ten lowest verical IEs (eV) of the hydrogen-bonded uracil dimer calculatedwith EOM-IP-CCSD.
State 6-31G(d) 6-31(+)G(d) 6-311(+)G(d,p)
X2Au 9.01 9.26 9.35
12Bg 9.11 9.37 9.47
12Bu 9.84 10.13 10.20
12Ag 9.89 10.17 10.25
22Bg 10.37 10.62 10.69
22Au 10.35 10.65 10.72
22Bu 10.85 11.12 11.19
22Ag 11.20 11.49 11.55
32Au 12.53 12.76 12.83
32Bg 12.63 12.87 12.95
IED,largeEOM−IP−CCSD ≈ IED,small
EOM−IP−CCSD + (IEM,largeEOM−IP−CCSD − IEM,small
EOM−IP−CCSD)
(3.1)
As follows from the data from Tables 3.5 and 3.6, this scheme yields the results that
are very close to the exact calculation. All IEs estimated from the dimer 6-31(+)G(d)
values are within 0.01-0.02 eV from the full EOM-IP-CCSD/6-311(+)G(d,p) dimer
results for both complexes. This difference is negligible compared to the 0.2-0.3 eV
error bars of EOM-IP-CCSD. To rationalize the excellent performance of the energy-
additivity scheme, let us rewrite Eq. (3.1) separating the dimer and monomer terms as
follows:
IED,largeEOM−IP−CCSD − IED,small
EOM−IP−CCSD ≈ IEM,largeEOM−IP−CCSD − IEM,small
EOM−IP−CCSD
(3.2)
47
Table 3.5: Ten lowest verical IEs (eV) of the stacked dimer calculated with EOM-IP-CCSD/6-311(+)G(d,p) versus the energy-additivity scheme results estimated using 6-31(+)G(d).
State IED6−31(+)G(d) ∆IEM
6−311(+)−6−31(+)G(d) IED,estimated6−311(+)G(d,p) IED
6−311(+)G(d,p) Abs. Error
X2B 9.03 0.10 9.13 9.14 0.01
12A 9.56 0.10 9.66 9.66 0.00
22B 10.06 0.07 10.13 10.13 0.00
22A 10.12 0.07 10.19 10.19 0.00
32B 10.38 0.07 10.45 10.46 0.01
32A 10.44 0.07 10.51 10.52 0.01
42B 10.94 0.06 11.00 11.00 0.00
42A 10.99 0.06 11.05 11.05 0.00
52B 12.61 0.08 12.69 12.67 0.02
52A 12.88 0.08 12.96 12.96 0.00
Eq. (3.2) thus implies that the basis set correction is the same for the monomer, stacked
or hydrogen-bonded dimer and the splitting between the overlapping FMOs is well
reproduced even in a relatively small basis set, i.e., 6-31(+)G(d).
3.3.4 The electronic spectra of dimer cations
This Section compares the electronic spectra of the monomer and the dimer cations
calculated by EOM-IP-CCSD. The transitions are between the states of the cation cor-
responding to different orbitals being singly-occupied. Our best estimates, i.e., EOM-
IP-CCSD/6-311(+)G(d,p), show that stacking and hydrogen-bonding interactions lower
the first ionization energy of the dimer by 0.34 and 0.13 eV, respectively, relative to
uracil. The magnitude of the IE decrease in the stacked dimer is remarkably close to
that in benzene. Thus, the uracil dimers are ionized more easily than the monomer.
Another interesting observation is a relationship between the drop in IE and the degree
of initial hole localization. Since a larger IE drop is a consequence of better orbital over-
lap, the dimer configurations that ionize easier would feature more extensive initial hole
48
Table 3.6: Ten lowest vertical IEs (eV) of the hydrogen-bonded uracil dimer calculatedwith EOM-IP-CCSD/6-311(+)G(d,p) versus the energy-additivity scheme results esti-mated from 6-31(+)G(d).
State IED6−31(+)G(d) ∆IEM
6−311(+)−6−31(+)G(d) IED,estimated6−311(+)G(d,p) IED
6−311(+)G(d,p) Abs. Error
X2Au 9.26 0.10 9.36 9.35 0.01
12Bg 9.37 0.10 9.47 9.47 0.00
12Bu 10.13 0.06 10.19 10.20 0.01
12Ag 10.17 0.06 10.23 10.25 0.02
22Bg 10.62 0.07 10.69 10.69 0.00
22Au 10.65 0.07 10.72 10.72 0.00
22Bu 11.12 0.06 11.18 11.19 0.01
22Ag 11.49 0.06 11.55 11.55 0.00
32Au 12.76 0.07 12.83 12.83 0.00
32Bg 12.87 0.07 12.94 12.95 0.01
delocalization. This might have mechanistic consequences for the ionization-induced
processes in DNA, where different relative nucleobase configurations are present due to
structural fluctuations.
Electronic transitions in the dimers belong to the two different types, namely,
CR (charge resonance) and LE (local excitations). The former are derived from
the transitions between the bonding and anti-bonding DMOs, e.g., see Fig. 1.1 and
Eqns. (1.12),(1.13), and are unique for the ionized dimers. The latter are the transi-
tions between DMOs formed from different FMOs, and resemble the monomer transi-
tions. Another difference between the CR and LE transitions is that the transition dipole
moment of the former increases linearly with the fragment separation, whereas the LE
bands decay [11]. The strong sensitivity of the CR bands to the dimer geometry sug-
gests to employ these transitions as a spectroscopic probe of structure and dynamics in
ionizedπ-stacked and h-bonded systems.
49
Stacked uracil dimer cation
The calculated electronic spectrum of stacked dimer cation at the neutral’s geometry is
shown in Fig. 3.6; the corresponding excitation energies, transition dipoles and oscillator
strengths are provided in Table 3.7 The ground electronic state of the cation is12B (the
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00.00
0.02
0.04
0.06
0.08
0.10
Osc
illat
or S
treng
th
Energy, eV
b
a
b a b
a
b a
b
a
Figure 3.6: Vertical electronic spectrum of the stacked uracil dimer cation at the geom-etry of the neutral. Dashed lines show the transitions with zero oscillator strength. MOshosting the unpaired electron in final electronic state, as well as their symmetries, areshown for each transition. The MO corresponding to the initial (ground) state of thecation is shown in the middle.
respective singly-occupied orbital is shown). All nine arising transitions are allowed by
symmetry: the transitions of theB → A type are perpendicular, whereas theB → B
transitions are parallel with respect to the inter-fragment axis. The four most intense
bands correspond to the final electronic states12A, 32A, 52B and52A, the first one
giving rise to the CR band. Note that the intensity of the LE transitions between the
lone-pair like andπ-like orbitals remains very small.
50
Table 3.7: Oscillator strengths and transition dipole moments for the electronic transi-tions in the ionized stacked uracil dimer calculated with EOM-IP-CCSD/6-31(+)G(d) atthe geometry of the neutral.
Transition ∆E, eV < µ2 >, a.u. f
X2B → 12A 0.523 7.2917 0.0935
X2B → 22B 1.027 0.0028 0.0000
X2B → 22A 1.081 0.1503 0.0039
X2B → 32B 1.349 0.1141 0.0037
X2B → 32A 1.406 0.5170 0.0178
X2B → 42B 1.906 0.0023 0.0001
X2B → 42A 1.952 0.0052 0.0002
X2B → 52A 3.844 0.3530 0.0332
X2B → 52B 3.573 0.9990 0.0874
To estimate the effect of geometry relaxation of the cation on the spectrum, we also
computed the excitation spectrum at the relaxed dimer cation geometry. The correspond-
ing excitation energies, transition dipoles, and oscillator strengths are given in Table 3.8.
As in the benzene dimer cation, the optimized geometry of the uracil dimer cation fea-
tures shorter interfragment distance that facilitates more efficient orbital overlap.
Fig. 3.7 compares the spectra calculated at the neutral geometry and at the opti-
mized geometry of the cation. The intensity pattern is similar to the spectrum at the
neutral geometry: the most intense bands correspond to the final electronic states12A,
32A, 52B and52A. A significant increase (approximately threefold) in intensity of the
CR band is observed; LE band intensity increases for some electronic states (32A ) and
slightly decreases for the others (52B and52A). Overall, the excitation energies uni-
formly increase, with the shift being around 1.1 eV.
51
Table 3.8: Oscillator strengths and transition dipole moments for the electronic transi-tions in the ionized stacked uracil dimer calculated with EOM-IP-CCSD/6-31(+)G(d) atthe equilibrium geometry of the ionized dimer.
Transition ∆E, eV < µ2 >, a.u. f
X2B → 12A 1.60 6.6438 0.2601
X2B → 22B 2.08 0.0006 0.0000
X2B → 22A 2.10 0.0075 0.0003
X2B → 32B 2.48 0.0721 0.0044
X2B → 32A 2.63 0.4591 0.0295
X2B → 42B 3.09 0.0011 0.0000
X2B → 42A 3.09 0.0008 0.0000
X2B → 52A 4.88 0.1995 0.0238
X2B → 52B 4.60 0.7477 0.0842
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.00.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
0.22
0.24
0.26
0.28
Osc
illat
or S
treng
th
Energy, eV
Figure 3.7: Vertical electronic spectra of the stacked uracil dimer cation at two differentgeometries: the geometry of the neutral (bold lines) and the relaxed cation geometry(dashed lines). MOs hosting the unpaired electron in final electronic state are shown foreach transition.
52
Hydrogen-bonded uracil dimer cation
The spectrum of the hydrogen-bonded dimer at the geometry of neutral is presented in
Fig. 3.8. Comparison of this spectrum with the stacked dimer example instantly reveals
an important difference, i.e., smaller number of peaks with non-zero intensity owing to
higher symmetry of hydrogen-bonded complex. The ground electronic state of cation
is X2Au and theAu → Au andAu → Bu transitions are now forbidden by symmetry.
Two transitions derived from the allowed parallel transitions,Au → Ag, are also of zero
intensity in the spectrum. Three transitions of theAu → Bg type are the most intense,
among them theX2Au → 12Bg CR band. The CR band in h-bonded dimer appears
at 0.11 eV, which is 0.4 eV below that of theπ-stacked dimer, however, its oscillator
strength is only slightly smaller (0.076 vs. 0.094). The intensity of the CR transition is
lower than the most intense LE transition, i.e.,X2Au → 32Bg.
3.4 Conclusions
We charactarized the electronic structure of theπ-stacked and hydrogen-bonded uracil
dimer cations by EOM-IP-CCSD. We computed IEs corresponding to the ground and
electronically excited states of the cations and calculated transition dipoles and oscilla-
tor sthengths for the electronic transions between the cation states. The results of the
calculations are rationalized within DMO-LCFMO framework.
Similarly to the benzene dimer, theπ-stacking lowers the first IE by about 0.4 eV
vertically. The magnitude of the IE decrease correlates with the degree of initial hole
localization, as both depend on orbital overlap. Thus, the dimer configurations that
ionzie easier would feature a more delocalized hole.
Ionization changes the bonding from non-covalent to covalent, which induces sig-
nificant geometrical changes, e.g., fragments move closer to each other to maxmize the
53
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00.00
0.02
0.04
0.06
0.08
0.10
0.12
Osc
illat
or S
treng
th
Energy, eV
bu ag
bg
au bu ag au
au
bg
bg
Figure 3.8: Vertical electronic spectrum of the hydrogen-bonded uracil dimer cationat the geometry of the neutral. Dashed lines show the transitions with zero oscillatorstrength. MOs hosting the unpaired electron in final electronic state, as well as theirsymmetries, are shown for each transition. The MO corresponding to the initial (ground)state of the cation is shown in the middle.
orbital overlap. The electronic spectra of the ionized dimers feature strong CR bands
whose position and intensity is very sensitive to the structure: geometrical relaxation
in the π-stacked dimer blue-shifts the CR band by more than 1 eV and results in the
three-fold intensity increase. These properties of the CR transitions may be exploited
in pump-probe experiments targeting the ionization-induced dynamics in systems with
π-stacking interactions, e.g., DNA or RNA strands. The perturbation in the LE bands in
the dimer is also described. The hydrogen-bonded dimer features slightly less intense
CR bands at lower energies.
Benchmark calculations in a variety of basis sets show that 6-311(+)G(d,p) basis
yields sufficiently converged IEs, and that energy-additivity scheme based on dimer
54
calculations in a small 6-31(+)G(d) basis allows efficient and accurate evaluation of the
dimer IEs.
3.5 Reference list
[1] P. Jurecka, J.Sponer, J.Cerny, and P. Hobza, Benchmark database of accurate(MP2 and CCSD(T) compl ete basis set limit) interaction energies of small modelcomplexes, DNA base pairs, and amino acid pairs, Phys. Chem. Chem. Phys.8,1985 (2006).
[2] A.A. Zadorozhnaya and A.I. Krylov, Ionization-induced structural changes inuracil dimers and their spectroscopic signatures, J. Chem. Theory Comput. (2010),In press.
[3] W.J. Hehre, R. Ditchfield, and J.A. Pople, Self-consistent molecular orbital meth-ods. XII. Further extensions of gaussian-type basis sets for use in molecular orbitalstudies of organic molecules, J. Chem. Phys.56, 2257 (1972).
[4] R. Krishnan, J.S. Binkley, R. Seeger, and J.A. Pople, Self-consistent molecularorbital methods. XX. A basis set for correlated wave functions, J. Chem. Phys.72,650 (1980).
[5] T.H. Dunning, Gaussian basis sets for use in correlated molecular calculations. I.The atoms boron through neon and hydrogen, J. Chem. Phys.90, 1007 (1989).
[6] Y. Shao, L.F. Molnar, Y. Jung, J. Kussmann, C. Ochsenfeld, S. Brown, A.T.B.Gilbert, L.V. Slipchenko, S.V. Levchenko, D.P. O’Neil, R.A. Distasio Jr, R.C.Lochan, T. Wang, G.J.O. Beran, N.A. Besley, J.M. Herbert, C.Y. Lin, T. VanVoorhis, S.H. Chien, A. Sodt, R.P. Steele, V.A. Rassolov, P. Maslen, P.P. Koram-bath, R.D. Adamson, B. Austin, J. Baker, E.F.C. Bird, H. Daschel, R.J. Doerksen,A. Drew, B.D. Dunietz, A.D. Dutoi, T.R. Furlani, S.R. Gwaltney, A. Heyden, S.Hirata, C.-P. Hsu, G.S. Kedziora, R.Z. Khalliulin, P. Klunziger, A.M. Lee, W.Z.Liang, I. Lotan, N. Nair, B. Peters, E.I. Proynov, P.A. Pieniazek, Y.M. Rhee, J.Ritchie, E. Rosta, C.D. Sherrill, A.C. Simmonett, J.E. Subotnik, H.L. WoodcockIII, W. Zhang, A.T. Bell, A.K. Chakraborty, D.M. Chipman, F.J. Keil, A. Warshel,W.J. Herhe, H.F. Schaefer III, J. Kong, A.I. Krylov, P.M.W. Gill, M. Head-Gordon,Advances in methods and algorithms in a modern quantum chemistry programpackage, Phys. Chem. Chem. Phys.8, 3172 (2006).
55
[7] D. Dougherty, K. Wittel, J. Meeks, and S. P. McGlynn, Photoelectron spectroscopyof carbonyls. Ureas, uracils, and thymine, J. Am. Chem. Soc.98, 3815 (1976).
[8] S. Urano, X. Yang, and P.R. LeBrenton, UV photoelectron and quantum mechani-cal characterization of DNA and RNA bases: Valence electronic structures of ade-nine, 1,9-dimethylguanine, 1-methylcytosine, thymine and uracil, J. Mol. Struct.214, 315 (1989).
[9] G. Lauer, W. Schafer, and A. Schweig, Functional subunits in the nucleic acidbases uracil and thymine, Tetrahedron Lett.16, 3939 (1975).
[10] D. Roca-Sanjuan, M. Rubio, M. Merchan, and L. Serrano-Andres, Ab initio deter-mination of the ionization potentials of DNA and RNA nucleobases, J. Chem.Phys.125, 084302 (2006).
[11] P.A. Pieniazek, A.I. Krylov, and S.E. Bradforth, Electronic structure of the benzenedimer cation, J. Chem. Phys.127, 044317 (2007).
56
Chapter 4
Ionization-induced structural changes
in uracil dimers and their spectroscopic
signatures
4.1 Overview
Ionization-induced structural changes and properties of the three representative isomers
of the ionized uracil dimer, i.e. the stacked, t-shaped and h-bonded, are characterized by
high-level electronic structure calculations. First we discuss the electronic structure of
the t-shaped isomer (Section 4.3.1). Then, the equilibrium geometries (Section 4.3.2),
energetics (Section 4.3.3), and electronic spectroscopy (section 4.3.4) are considered.
Finally, the benchmark results for density functional theory (DFT) with long-range cor-
rected functionals are presented in the Postscript.
4.2 Computational detais
We used EOM-IP-CCSD in calculations of IEs, electronic spectra, and dissociation ener-
gies of the dimers, whereas for geometry optimizations and frequencies we employed
IP-CISD andωB97X-D. IP-CISD with the 6-31(+)G(d) basis [1] was used to optimize
the SU+2 and HU+
2 (TS) structures. The TU+2 and HU+2 (PT) structures were optimized
with ωB97X-D and the 6-311(+)G(d,p) basis set [2].
57
For both the IP-CISD and DFT-D optimizations, tight convergence criteria were
enforced: the gradient and energy tolerance were set to3 · 10−5 and1.2 · 10−4 respec-
tively; maximum energy change was set to1·10−7. To ensure the accuracy of the DFT-D
optimizations we employed the extra-fine EML(99,590) grid.
We use the best available geometries for calculations of energy differences. The
choice of the geometries is described below. In calculations of vertical properties (i.e.,
at the equilibrium geometries of the neutral dimers) we used the geometries from the
S22 set of Hobza and coworkers [3]. The geometry of the t-shaped isomer was opti-
mized with the DFT-D as described above. To assess possible effect of the BSSE on
the structures, our study of adenine and thymine dimers [4] compared the B3LYP-D/6-
31+G(d,p) optimized structure of the stacked AT dimer versus the one from the S22
set [3]. We found that the interfragment distance differs from the BSSE-corrected RI-
MP2/TZVPP value [3] by only 0.076A. The increase of the basis set from 6-31+G(d,p)
to 6-311++G(2df,2pd) results in 0.004A increase in inter-fragment separation. Thus,
we do not expect significant BSSE effects on our optimized structures.
In monomer calculations, we used the structures of the uracil cation and the neutral
optimized by IP-CISD/6-31(+)G(d) and RI-MP2/cc-pVTZ, respectively, with the stan-
dard convergence thresholds (the gradient and energy tolerance3 · 10−4 and1.2 · 10−3
and maximum energy change1 · 10−6). In all optimizations of the symmetric structures
(i.e., all isomers, except for the TU02, TU+2 , and HU+
2 (PT)) the symmetry was enforced.
For the stacked dimer cation we carried out an additional DFT-D optimization without
theC2 symmetry constraint that showed that the minimum indeed corresponds to the
symmetric structure. In addition, vibrational analysis was also performed.
58
For the accurate energy estimates, single-point calculations were carried out at
the geometries obtained as described above. The IP-CCSD method with the 6-
311(+)G(d,p) basis was employed. For benchmark purposes, we also presentωB97X-
D/6-311(+)G(d,p)/EML(99,590) estimates calculated at the respective DFT-D minima.
The performance of different methods is discussed in the Postscript.
While the BSSE corrections can be substantial for weakly-bound systems when
compact basis sets are employed [3, 5, 6], using augmented triple-zeta bases reduces
the BSSE considerably. Moreover, empirical dispersion correction in DFT-D methods
mitigates the BSSE. For example, the counterpoise correction for binding energy in
the stacked adenine-thymine dimer at the B3LYP-D/6-311+G(2df) is only 1.4 kcal/mol
[4,7].
For the neutral stacked uracil dimer, theωB97X-D and CCSD values ofDe are 10.5
and 11.1 kcal/mol (with the 6-311(+)G(d,p) basis set), in a good agreement with the
CCSD(T)/CBS value of 9.7 kcal/mol [8]. Thus, the BSSE effects are relatively small
at theωB97X-D/6-311(+)G(d,p) level even for the most problematic neutral stacked
dimers. In the ionized systems, which are much stronger bound, the effect of BSSE on
the binding energy should be even smaller. To quantify this, we computed the counter-
poise correction for the stacked uracil dimer cation. The computed BSSE is 1.3 kcal/mol
as estimated at theωB97X-D level with 6-311(+)G(d,p) basis set.
To obtain the standard thermodynamic quantities and the ZPE corrections, we per-
formed the vibrational analysis at theωB97X-D/6-311(+)G(d,p)/EML(99,590) level for
all complexes at the respective reoptimized geometries.
The electronic spectra of the dimer cations were obtained with IP-CCSD/6-
31(+)G(d) at the cation and neutral geometries described above.
59
All open-shell DFT-D calculations employed the spin-unrestricted references. In
these calculations, the spin-contamination of the doublet Kohn-Sham determinant was
low with the typical〈S2〉 values of 0.76 - 0.78.
All electrons were correlated in all the optimizations; in the single-point energy
and spectra calculations the core electrons were frozen unless otherwise stated. The
optimized geometries, corresponding reference energies and frequencies are provided
in the Supplementary Materials of Ref. 101.
Throughout this work, we use the following notations for the isomers: HU2, SU2 and
TU2 refer to the h-bonded, stacked and t-shaped isomers, respectively. For the hydrogen-
bonded cations, we distinguish between the symmetric structure, which is a transition
state (TS), and a proton-transferred one (PT) corresponding to the true minimum.
4.3 Results and discussion
4.3.1 Molecular orbital framework
The character of electronic states and the bonding patterns in ionized non-covalent
dimers depend strongly on the relative orientation of the fragments [4, 9–12]. Orbital
overlap and electrostatic interactions are the most important factors determining the
degree of hole delocalization, changes in bond strength due to ionization, and subse-
quent nuclear dynamics. When the two fragments are equivalent by symmetry, as in
sandwich benzene dimers [9] or stackedC2 nuclear base dimers [4,11], the dimer states
are derived from in-phase (bonding) and out-of-phase (antibonding) combination of the
fragments MOs, and the initial hole is equally delocalized between the two fragments.
The changes in IE due to dimerization depend on the orbital overlap, e.g., larger changes
are observed for the states derived from ionizations ofπ orbitals [4, 9, 11]. Ioniza-
tions from anti-bonding orbitals increase formal inter-fragment bond order, and produce
60
tighter-bound structures, whereas ionizations from the bonding orbitals result in disso-
ciative states.
Orbital picture, changes in vertical IEs and initial hole delocalization are similar in
symmetric hydrogen bonded dimers, however, the ionization-induced dynamics is more
complex and involves proton transfer [4, 13]. The changes in vertical IEs are smaller
for most of the states due to a less favorable overlap. In dimers with non-equivalent
fragments, the MOs (and, consequently, the initial hole) become more localized, how-
ever, changes in IEs and wave functions can also be explained by overlap considerations
within DMO-LCFMO framework [10, 12]. Finally, in non-symmetric h-bonded dimers
electrostatic interactions become more important than orbital overlap. For example, we
observed large changes (0.4-0.7 eV) in IEs and binding energies in some non-symmetric
hydrogen-bonded dimers of thymine and cytosine [4,13]. In these dimers, the hole local-
ized on one of the fragments is stabilized by the dipole moment of the neutral fragment.
The electronic structure of the stacked and symmetric h-bonded uracil dimers at the
respective neutral geometries was discussed in detail in Ref. 11. Below we focus on
the t-shaped isomer. The principal difference between the t-shaped and the stacked or h-
bonded structures is that in the former the two fragments are not equivalent by symmetry,
which affects its electronic structure. The ten lowest ionized states of the t-shaped uracil
dimer and the corresponding MOs are presented in Figure 4.1. As in the stacked and
h-bonded systems, the dimer MOs are formed from the MOs of the fragments, and the
ionized states of the dimer correlate well with the states of the monomer (i.e., no mixing
of the MOs of different character is observed). For example, the two highest-lying MOs
are the linear combinations of theπCC MOs of the fragments. However, the MOs of
the t-shaped dimer are more localized. For example, thelp(O) MO of the dimer is a
localizedlp(O) orbital of one of the fragments. For the four delocalized dimer orbitals
(formed by theπCC and lp(O) + lp(N) fragment orbitals) the distribution of electron
61
Ioni
zatio
n En
ergy
, eV
9.13 9.24
9.839.94
10.1410.28
10.7110.87
12.6712.72
Figure 4.1: The ten lowest ionized states of the t-shaped uracil dimer at the neutralgeometry calculated with the IP-CCSD/6-311(+)G(d,p).
density is also uneven. Owing to a less favorable overlap between the fragment MOs,
the splittings between the pairs of ionized states in the t-shaped dimer is smaller. The
largest splitting of 0.14 eV was observed for the dimer states derived from from the
π-like lp(O) + lp(N) fragment orbitals.
Despite less efficient overlap and smaller splittings between the pairs of states
derived from the same FMOs, the absolute changes in IEs in this isomer are similar
to those in the stacked dimer. For example, the lowest IE of this isomer is 9.13 eV.
This value is red-shifted by 0.35, 0.22 and 0.01 eV relative to the 1st IE of the monomer,
symmetric h-bonded andπ-stacked dimers, respectively. This is similar to large changes
in IEs observed in the non-symmetric h-bonded dimers of thymine and cytosine, where
lowering of IE was due to electrostatic stabilization of the localized hole by the dipole
moment of the “neutral” fragment. The dipole moment of uracil is 4.19 D, which is
comparable to the dipole moment of thymine (4.11 D).
62
4.3.2 Ionization-induced structural changes: Equilibrium geome-
tries of the uracil dimer cations
Ionization induces significant structural changes in the dimers, as can be seen from Fig-
ure 4.2. In the analysis below, we distinguish between the changes in the structures of
the fragments (and compare those to ionization-induced changes in the monomer) and
the inter-fragment relaxation. The definitions of parameters are given in Figure 4.3,
and their values are summarized in Tables 4.1 and 4.2. Only the symmetry-unique
parameters are given. First, let us consider the effect of ionization on intra-fragment
parameters (see Table 4.1) and compare the monomer and the symmetric dimer cations
data. The magnitude of relaxation in the monomer is larger than in the stacked and
h-bonded dimers. For instance, the C5C6 bond increases by 0.043A in the monomer
versus 0.018A and 0.002A in the stacked and h-bonded dimers, respectively. The sign
of the change in the monomer and the symmetric dimers is the same for all the parame-
ters, which is consistent with the DMO-LCFMO picture. The magnitude of the changes
is smaller in the dimers because the hole is delocalized over the two fragments. In the
non-symmetric dimers, the fragments are not equivalent and the orbital picture is more
complicated. The hole is distributed unevenly between the two fragments, such that the
positive charge is localized on one of them. Comparing the data presented in Table 4.1
for the h-bonded proton-transfered and the t-shaped dimer cations with the monomer, we
observe that the structural changes of Fragment 1 of HU+2 (PT), Fragment 2 of TU+2 and
the monomer cation are very similar. For instance, the C5C6 bond increases by 0.057,
0.050 and 0.043A in Fragment 1 of HU+2 (PT), Fragment 2 of TU+2 and the monomer
cation, respectively. Thus, one of the fragments in non-symmetric dimers relaxes simi-
larly to the monomer cation, while the other adjusts accordingly. This is similar to the
t-shaped benzene dimer [10].
63
Tabl
e4.
1:T
heva
lues
ofop
timiz
edst
ruct
ural
para
met
ers
(A
,D
egre
e)of
the
frag
men
tsin
the
stac
ked,
h-bo
nded
,h-
tran
sfer
edh-
bond
edan
dt-
shap
edur
acil
dim
erca
tions
.T
hedi
ffere
nces
(A
,D
egre
e)w
.r.t.
the
equi
libriu
mge
omet
ryof
the
resp
ectiv
ene
utra
lco
mpl
exar
eal
sogi
ven
show
ing
the
ioni
zatio
n-in
duce
dch
ange
sin
geom
etry
.S
eeF
ig.
4.3
for
the
defin
ition
sof
the
para
met
ers.
Par
amet
erS
U+ 2H
U+ 2
(TS
)H
U+ 2
(PT
),F
1H
U+ 2(P
T),
F2
TU+ 2
,F1
TU
+ 2,F
2U
+
C4C
51.
461
+0.
010
1.46
1+
0.01
11.
461
+0.
011
1.45
8+
0.00
81.
431
-0.0
261.
475
+0.
024
1.45
7+
0.01
1
C5C
61.
367
+0.
018
1.35
2+
0.00
21.
407
+0.
057
1.33
7-0
.013
1.35
3+
0.01
11.
392
+0.
050
1.38
6+
0.04
3
C6N
11.
330
-0.0
381.
352
-0.0
171.
310
-0.0
591.
391
+0.
022
1.35
7-0
.012
1.32
4-0
.045
1.31
6-0
.049
N1C
21.
405
+0.
023
1.37
9+
0.01
21.
411
+0.
044
1.33
2-0
.035
1.38
9-0
.002
1.42
9+
0.04
41.
433
+0.
053
C2N
31.
368
-0.0
141.
349
-0.0
221.
363
-0.0
081.
331
-0.0
401.
401
+0.
023
1.37
7-0
.003
1.35
7-0
.017
N3C
41.
384
-0.0
171.
399
-0.0
081.
400
-0.0
071.
438
+0.
031
1.36
5-0
.032
1.38
4-0
.007
1.38
7-0
.010
C4O
21.
198
-0.0
241.
190
-0.0
281.
204
-0.0
141.
194
-0.0
241.
257
+0.
041
1.20
6-0
.014
1.19
5-0
.020
C2O
11.
182
-0.0
341.
208
-0.0
231.
216
-0.0
151.
287
+0.
056
1.19
5-0
.012
1.19
0-0
.017
1.17
8-0
.034
C4C
5C
611
9.3
-0.5
119.
5-0
.111
9.4
-0.2
120.
4+
0.7
118.
4-1
.111
9.5
+0.
3119
.7-0
.1
C5C
6N
112
1.0
-0.9
121.
1-1
.512
3.1
+0.
612
1.8
-0.7
121.
9+
0.2
120.
1-1
.811
9.4
-2.6
C6N
1C
212
4.3
+0.
812
3.4
+0.
912
0.1
-2.4
121.
0-1
.512
3.7
+0.
212
4.9
+1.
4125
.5+
2.0
N1C
2N
311
3.8
+0.
811
5.4
+1.
111
8.2
+3.
911
8.8
+4.
511
2.9
-0.6
113.
5+
0.41
13.6
+0.
8
C2N
3C
412
6.9
-1.2
126.
3-1
.812
5.5
-2.6
125.
5-2
.612
6.2
-1.1
127.
0-0
.412
6.2
-2.4
N3C
4C
511
4.7
+1.
311
4.3
+1.
411
3.7
+0.
811
2.5
-0.4
116.
9+
2.5
114.
7+
0.21
15.7
+2.
4
Σ(a
ngle
)71
9.9
+0.
3–
––
720.
0+
0.0
719.
7+
0.1
720.
0+
0.0
64
Figure 4.2: The geometries of the cations versus the respective neutrals for the threeuracil dimer isomers .
SU20
C2C2
SU2+
TU2+ TU2
0
C1 C1
Cs
HU2+
C2h
HU20
C2h
65
Figure 4.3: The definitions of the intra- and inter-fragment geometric parameters foruracil dimer isomers.
N12
3
4
5
6
1
C2
N3
C4C5
C6
O1
O2
H2
H1
O2N1
C5C6
F2F1O2H1
O1H1
F2H2O2
O2C5 O2C6
F1
The ionization-induced changes in the inter-fragment parameters (given in Table 4.2)
and the MOs (shown in Fig. 4.4) are consistent with the DMO-LCFMO predictions —
the fragments adjust their relative orientation to maximize the overlap between their
HOMOs (πCC). The change in the MOs is illustrated in Figure 4.4 depicting HOMOs
at the neutral and the cation geometries. In the stacked dimer, the twoπCC FMOs give
rise to the efficient overlap lending a partial covalent character to the ionized dimer.
In the t-shaped dimer, the changes in HOMO are different. Upon relaxation, the hole
becomes more localized on the lower fragment, and the only contribution to the overlap
66
Tabl
e4.
2:T
heva
lues
ofin
ter-
frag
men
tstr
uctu
ralp
aram
eter
s(
A,D
egre
e)of
the
stac
ked,
h-bo
nded
,h-t
rans
fere
dh-
bond
edan
dt-
shap
edur
acil
dim
erca
tions
.T
hedi
ffere
nces
(A
,Deg
ree)
w.r.
t.th
eeq
uilib
rium
geom
etry
ofth
ere
spec
tive
neut
ralc
ompl
exes
are
give
nin
pare
nthe
sis.
See
Fig
.4.3
for
the
defin
ition
sof
the
para
met
ers.
SU
+ 2H
U+ 2
(TS
)H
U+ 2
(PT
)T
U+ 2
C5C
63.
299
(-0.
451)
O1H
11.
828
(+0.
053)
O1H
11.
749
(-0.
026)
H2O
22.
000
(+0.
072)
O2N
13.
116
(-0.
175)
O2H
11.
828
(+0.
053)
O2H
11.
018
(-0.
757)
O2C
52.
178
(-1.
099)
O2C
62.
701
(-0.
950)
α18
.4(+
5.6)
––
–
d3.
51(+
0.34
)–
––
67
Figure 4.4: Two highest occupied MOs of the three isomers of the uracil dimer at theneutral and cation geometry.
SU20 SU2
+
HU20
HU2+ (TS)
HU2+(HT)
TU20 TU2
+
68
is due to the the oxygen lone pair of the top fragment pointing towards theπCC MO of
the lower one.
The magnitude of the relaxation is quantified by Table 4.3, which presents the dif-
ferences in the total energies between the relaxed and vertical structures of the dimer
cations calculated by EOM-IP-CCSD/6-311(+)G(d,p). For the t-shaped, stacked and
h-bonded isomers,∆ECCSD is -12.71, -6.48 kcal/mol, and -0.64 kcal/mol respectively.
Such a large relaxation effect in the t-shaped cation is somewhat surprising, as from
Figure 4.4 the FMOs overlap more efficiently in the stacked dimer. The reason is the
electrostatic interaction of the lone pair on oxygen of Fragment 1 and the hole on the
Fragment 2, which stabilizes the t-shaped structure [4]. The inter-fragment parame-
Table 4.3: Total (Etot, hartree) and dissociation (De, kcal/mol) energies of the fourisomers of the uracil dimer in the neutral and ionized states computed by CCSD/IP-CCSD with 6-311(+)G(d,p). Relevant total energies of the uracil monomer are alsogiven. The relaxation energies (∆E, kcal/mol) defined as the difference in total energiesof the cation at the neutral and relaxed cation geometries are also shown. For HU+
2 (PT)dissociation energies corresponding to the U0 + U+ / (U - H)0 + UH+ channels are given.
Complex ECCSDtot DCCSD
e ∆ECCSD
U0 -413.882 346 – –
U+ -413.542 383 – -5.41
UH+ -414.209 422 – –
(U-H)0 -413.212 558 – –
SU02 -827.782 419 11.1 –
SU+2 -827.456 874 20.2 -6.48
HU02 -827.793 226 17.9 –
HU+2 (TS)a -827.450 565 16.2 -0.64
HU+2 (PT)b -827.475 648 32.0/33.7 –
TU02 -827.779 232 9.1 –
TU+2 -827.463 991 24.6 -12.71
a Transition state.b Proton-transferred structure, UH+(U–H)˙.
69
ters presented in Table 4.2 are consistent with the MO changes. In the stacked dimer
cation, the fragments slide with respect to each other, so the overlap of FMOs centered
on C5, C6, N1 and O2 atoms increases (see Figure 4.4). The C5C6 and O2N1 distances
decrease by 0.451 and 0.175A, respectively. Surprisingly, the distance between the
centers-of-masses of the fragments increases by 0.34A in the cation with respect to the
neutral. This illustrates that the average geometric parameters in polyatomic systems
can be misleading.
In the t-shaped cation, the fragments move to minimize the distance between the lone
pair on O2 of the top fragment and theπCC MO of the bottom one. The characteristic
parameters in this case are the O2C5 and O2C6 distances, which decrease by 1.099 and
0.950A, respectively.
In the symmetric h-bonded dimer, the structural changes and, consequently, relax-
ation energy are small. As one can see from Figure 4.4, there is also no significant
changes in MOs upon relaxation due to unfavorable orbital overlap. Moreover, this
symmetric structure is a transition state, as shown by the vibrational analysis discussed
later. Much larger stabilization is achieved by a proton transfer, which lowers the total
energy by 15.7 kcal/mol making the proton-transfered h-bonded isomer the lowest-
energy structure on the cation’s PES.
4.3.3 Binding energies of the neutral and ionized uracil dimers:
Potential and free energy calculations
Potential energy profile
Figures 4.5 and 4.6 present the relative ordering and binding energies of the neutral and
ionized uracil dimers calculated by IP-CCSD andωB97X-D with the 6-311(+)G(d,p)
basis. In the neutral, the symmetric h-bonded uracil dimer is the minimum energy
70
HU20
SU20
TU20
C1
C2h
C2
-De, kcal/mol
De = 17.9 / 19.4
De = 11.1 / 10.5
De = 9.1 / 8.3
Figure 4.5: The binding energies (kcal/mol) of the three isomers of neutral uracil dimercalculated at two levels of theory: IP-CCSD/6-311(+)G(d,p) (bold) andωB97X-D/6-311(+)G(d,p) (italic).
isomer, with the stacked and t-shaped dimers lying 6.8 and 8.8 kcal/mol higher in
energy. Excluding the proton-transferred dimer, the lowest-energy cation structure is the
t-shaped one. The energy spacing between the t-shaped and the stacked and h-bonded
cations is 4.4 and 8.4 kcal/mol, respectively. Upon the proton transfer the total energy
of the h-bonded cation is lowered by 15.8 kcal/mol, so that it lies 7.4 kcal/mol below
than the t-shaped cation.
The calculated binding energies for the h-bonded, stacked and t-shaped neutral
dimers are 17.9, 11.1 and 9.1 kcal/mol, respectively. The DFT-D and CCSD values
are within 1 kcal/mol from each other. TheDe for the stacked and h-bonded isomer are
also in good agreement with the recent CCSD(T)/CBS values of 20.4 and 9.7 kcal/mol
from Ref. 8.
Note that the interaction of the fragments in the neutral uracil dimers is much
stronger than in the benzene dimers, where the typical interaction energies lie in range
71
TU2+
C1
SU2+
C2 HU2+(TS)
C2h
HU2+(PT)
Cs
-De, kcal/mol
De = 24.6 / 27.0
De = 20.2 / 24.2
De = 16.2 / 20.2
De = 32.0 / 31.2De′ = 33.7 / 38.2
Figure 4.6: The binding energies (kcal/mol) of the three isomers of uracil dimer cationcalculated at two levels of theory: IP-CCSD/6-311(+)G(d,p) (bold) andωB97X-D/6-311(+)G(d,p) (italic). For the proton-transfered h-bonded uracil dimer cation, the bind-ing energies corresponding to the two dissociation limits are presented.
of 1.5-3.0 kcal/mol for all isomers [14, 15]. The binding energies increase upon ion-
ization, in agreement with the DMO-LCFMO predictions. In the t-shaped, stacked and
symmetric h-bonded cations the fragments are bound by 24.6, 20.2 and 16.2 kcal/mol,
respectively. For comparison, in the benzene dimer cation the binding energies are 20
and 12 kcal/mol for the sandwich and t-shaped isomers, respectively [9, 10]. However,
the strongest interaction is observed in the proton-transfered h-bonded cation, where the
binding energy corresponding to the U0+U+ dissociation channel is 32.0 kcal/mol (this
channel lies 1.8 kcal/mol below an alternative (U-H)0+UH+ channel).
In conclusion, when the uracil dimer is ionized the interaction between the fragments
increases almost two-fold for the stacked and h-bonded isomers and more than two-fold
for the t-shaped isomer. Such a strong increase in interaction in the t-shaped structure
is very different from the benzene dimer cation and can be explained by electrostatic
72
interactions rather than orbital overlap considerations. The h-bonded isomer is stabilized
by the proton transfer.
Free energy profile
It has been argued that the entropy contribution to the stability can be important in the
nucleobase dimer systems favoring stacked isomers over h-bonded ones [16]. Thus, we
performed the vibrational analysis usingωB97X-D. Moreover, we wanted to quantify
the zero point energy (ZPE) corrections to the dissociation energies. The calculated
dissociation energies and the standard thermodynamic quantities for the dissociation of
the neutral and the ionized dimers are given in Table 4.4.
Table 4.4: The dissociation energies (kcal/mol) and standard thermodynamic quantitiesof the neutral and the cation uracil dimers calculated at theωB97X-D/6-311(+)G(d,p)level. For the proton-transfered cation the values corresponding to the two differentdissociation limits are given.
Reaction De D0 ∆H0, kcal/mol ∆S0, cal/mol×K ∆G0, kcal/mol
SU02 → U0 + U0 10.5 9.8 8.4 31.5 -1.0
SU+2 → U0 + U+ 24.4 22.7 20.9 40.4 8.8
HU02 → U0 + U0 19.4 18.2 16.8 38.1 5.4
HU+2 (TS)→ U0 + U+ 20.2 21.8 23.2 40.5 11.1
HU+2 (TS)→ HU+
2 (PT) 11.0 13.1 -8.8 2.7 -9.6
HU+2 (PT)→ U0 + U+ 31.2 30.6 -0.7 37.7 18.7
HU+2 (PT)→ (U −H)0 + UH+ 38.2 37.0 -1.3 38.6 24.2
TU02 → U0 + U0 8.3 7.6 6.2 29.6 -2.6
TU+2 → U0 + U+ 27.0 25.1 23.0 38.8 11.4
Among the neutral uracil dimers, only the h-bonded isomer is predicted to be stable
under the standard conditions (∆G0 = 5.4 kcal/mol). Standard Gibbs free energies,
∆G0, of the stacked and t-shaped are -1.0 and -2.6 kcal/mol, respectively. The data in
Table 4.4 shows that the entropy contribution is similar for all three isomers:∆S0 of
dissociation is 31.5, 38.1 and 29.6 cal/mol×K for the stacked, h-bonded and t-shaped
73
isomers, respectively. However, more appropriate treatment including anharmonicities
may discriminate between the isomers more. The enthalpy contribution is different: for
the h-bonded uracil dimer the enthalpy of dissociation is 16.8 kcal/mol, whereas the
corresponding values for the stacked and t-shaped isomers are 8.4 and 6.2 kcal/mol,
respectively.
Unlike neutrals, all of the dimer cation isomers are stable under the standard con-
ditions. The most stable isomer is the proton-transfered h-bonded cation with∆G0 of
18.7 kcal/mol. In order of the decreasing stability, the proton-transferred dimer is fol-
lowed by the t-shaped, symmetric h-bonded (TS) and the stacked isomers. Again, the
∆S0 values are very close for all of the isomers being 40.4, 40.5, 37.7 and 38.8 for
SU+2 , HU+
2 (TS), HU+2 (PT) and TU+
2 , respectively, whereas the∆H0 contributions are
different.
Thus, we conclude that the enthalpy determines the relative stability of the neutral
and ionized uracil dimers to a high degree, while the entropy contribution has a less
pronounced effect.
Lastly, the ZPE corrections lower the dissociation energy estimates by 0.6–1.9
kcal/mol for all the neutral and ionized dimers, except for the symmetric h-bonded
dimer. In the symmetric h-bonded dimer, the ZPE correction has the opposite sign
and increases the dissociation energy by 1.6 kcal/mol, which is because this structure is
a transition state with one imaginary frequency.
4.3.4 The electronic spectra of the uracil dimer cations
This section presents the calculated electronic spectra of the uracil dimer cations.
The spectra of the stacked and h-bonded isomers at the geometry of the neutral were
74
described in a detail in the previous work [11], therefore, we focus on the effect of geom-
etry relaxation on the spectroscopic properties. For the h-bonded dimer, we present the
spectra of both the symmetric (TS) and the proton-transfered structures.
Figures 4.7-4.9 present the electronic spectra of the stacked, h-bonded and t-shaped
uracil dimers, respectively, calculated by IP-CCSD/6-31(+)G(d) at the neutral and the
cation geometries. Figures 4.7-4.9 also show the character of the electronic states cor-
responding to the three most intense transitions in each spectra. The transition energies,
transition dipole moments and oscillator strengths are provided in Tables 4.5– 4.8.
The spectrum of the stacked dimer at the neutral geometry is dominated by the three
intense lines at 0.5, 3.5 and 3.8 eV (see Fig. 4.7). The first peak is the CR band, which
is unique to the dimer, while the others are the local excitations (LE) between the states
of cation with the variousπ-orbitals singly occupied. Upon geometric relaxation, the
spectrum shifts to the higher energies by approximately 0.8 eV, so the lines appear at
1.2, 4.4, and 4.6 eV. The intensity of the charge resonance band increases more than
two-fold upon relaxation. The h-bonded dimer cation spectra at the geometry of the
neutral (see Fig. 4.8) features two intense lines at 0.1 and 3.6 eV and a small peak at
1.3 eV. As in the stacked cation, these lines are the CR band and two local excitations
(LE) corresponding to the transition between theπ-orbitals of cation (see Fig. 4.8). The
CR band is less intense than in the stacked cation and the most intense transition is the
LE at 3.6 eV. The spectrum at the transition state structure exhibits only minor differ-
ences, i.e, 0.1 eV blue shifts in peak positions with the intensities remaining the same.
However, the spectrum and the character of states changes dramatically upon proton
transfer. A new band appears at 2.5 eV. The localized character of the states andCs
symmetry make the proton-transfered h-bonded cation spectrum very similar to that of
the uracil cation. In the t-shaped cation spectra at the neutral geometry, the CR and
75
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.00.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
0.22
0.24
Osc
illat
or S
treng
th
Energy, eV
Ener
gy, e
V
SU20 SU2
+En
ergy
, eV
ΔE = 0.524
ΔE = 3.573
ΔE = 3.844
ΔE = 1.248
ΔE = 4.390
ΔE = 4.622
Figure 4.7: The electronic spectra (top panel) of the stacked uracil dimer cation atthe neutral (solid black) and the cation (dashed blue) geometries calculated with IP-CCSD/6-31(+)G(d) and the electronic states corresponding to the three most intensetransitions (bottom panel).
the two intense LE transitions appear at 0.1, 3.5 and 3.6 eV (see Fig. 4.9). The spec-
trum is very similar to that of the h-bonded isomer at the neutral geometry. As in the
stacked and h-bonded cations, the transitions between theπ-like orbitals are the most
76
Table 4.5: The excitation energies (∆E, eV), transition dipole moments (< µ2 >, a.u.)and oscillator strengths (f ) of the stacked dimer cation at the geometry of the neutraland cation, IP-CCSD/6-31(+)G(d).
neutral cation
Transition ∆E < µ2 > f ∆E < µ2 > f
X2B → 12A 0.524 7.2918 0.0935 1.248 7.4212 0.2269
X2B → 22B 1.023 0.0028 0.0000 1.799 0.0010 0.0000
X2B → 22A 1.081 0.1503 0.0040 1.809 0.0197 0.0009
X2B → 32B 1.349 0.1141 0.0038 2.190 0.0709 0.0038
X2B → 32A 1.406 0.5171 0.0178 2.362 0.4090 0.0237
X2B → 42B 1.906 0.0024 0.0001 2.798 0.0010 0.0000
X2B → 42A 1.952 0.0053 0.0003 2.800 0.0016 0.0001
X2B → 52B 3.573 0.3531 0.0333 4.390 0.7613 0.0819
X2B → 52A 3.844 0.9990 0.0875 4.622 0.2323 0.0263
intense. However, the character of the states is different — the states are more local-
ized. Upon relaxation, the spectrum changes completely, as does the character of the
states. The maximum intensity increases 2.5 times, new intense lines appear in the
1.7-3.0 eV and 4.5-5.0 eV regions. The orbital picture is now much more complex —
the DMOs become combinations of several FMOs. Thus, the electronic transitions can
no longer be described as CR or LE excitations. The most intense bands correspond
to the transitions between the cation states with theπCC orbital and thelp(O) orbital
singly occupied and are of charge-transfer character. To summarize, the three isomers
have distinctly different spectra, which can be used to distinguish between them exper-
imentally. Moreover, significant changes upon relaxation may be exploited to monitor
ionization-induced dynamics in a pump-probe experiment. Immediately upon the ion-
ization, the isomers will exhibit the intense lines in the three regions: 0.0-0.7 eV, 1-1.5
eV and 3.0-4.0 eV. While the spectra of the h-bonded and t-shaped dimers at the neu-
tral geometry are similar, the stacked cation can be distinguished by the two peaks of
77
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.50.00
0.02
0.04
0.06
0.08
0.10
0.12
Osc
illat
or S
treng
th
Energy, eV
HU20 HU2
+(TS) HU2+(HT)
Ener
gy, e
V
Ener
gy, e
V
Ener
gy, e
V ΔE = 0.113
ΔE = 1.358
ΔE = 3.615
ΔE = 0.121
ΔE = 1.632
ΔE = 3.835
ΔE = 2.475
ΔE = 3.650
ΔE = 3.984
Figure 4.8: The electronic spectra (top panel) of the h-bonded uracil dimer cation at theneutral (solid black), symmetric transition state (dashed blue) and the proton-transferredcation (dash-dotted pink) geometries calculated with IP-CCSD/6-31(+)G(d) and theelectronic states corresponding to the three most intense transitions (bottom panel).
moderate intensity in the 0.5-0.7 eV 3.5-4.0 eV regions. Upon the relaxation, the most
intense CR band of the stacked isomer shifts to 1.2 eV and acquires additional intensity.
The relaxation of the t-shaped cation manifests itself by significant growth of intensity
78
Table 4.6: The excitation energies (∆E, eV), transition dipole moments (< µ2 >, a.u.)and oscillator strengths (f ) of the symmetric h-bonded dimer cation at the geometry ofthe neutral and cation, IP-CCSD/6-31(+)G(d).
neutral cation
Transition ∆E < µ2 > f ∆E < µ2 > f
X2Au → 12Bg 0.113 27.4607 0.0763 0.121 28.7406 0.0849
X2Au → 12Bu 0.871 0.0000 0.0000 1.064 0.0000 0.0000
X2Au → 12Ag 0.915 0.0003 0.0000 1.123 0.0003 0.0000
X2Au → 22Bg 1.358 0.2527 0.0084 1.632 0.3048 0.0122
X2Au → 22Au 1.391 0.0000 0.0000 1.683 0.0000 0.0000
X2Au → 22Bu 1.867 0.0000 0.0000 1.954 0.0000 0.0000
X2Au → 22Ag 2.232 0.0000 0.0000 2.381 0.0000 0.0000
X2Au → 32Au 3.501 0.0000 0.0000 3.740 0.0000 0.0000
X2Au → 32Bg 3.615 1.3026 0.1154 3.835 1.2053 0.1133
in the 2.5-3.0 eV region. The hydrogen-bonded complex is more difficult to distinguish
because of the overlap of its spectral lines with the stacked and t-shaped spectra. Still,
the signature of proton transfer is the 0.3-0.4 eV blue shift of the intense transition in
the 3.5-4.0 eV region.
4.4 Conclusions
We characterized the electronic structure of the three representative isomers of the ion-
ized uracil dimers: h-bonded, stacked, and t-shaped. The interactions between the frag-
ments lower vertical IEs by 0.13-0.35 eV, the largest drop in IE being observed for the
stacked and t-shaped isomers. Interestingly, the character of the ionized states and the
origin of the IE change is different in these two isomers. In the stacked dimer, the hole
is delocalized between the two fragments, and orbital overlap determines the change in
79
Table 4.7: The excitation energies (∆E, eV), transition dipole moments (< µ2 >,a.u.) and oscillator strengths (f ) of the h-bonded dimer cation at the optimized proton-transferred geometry, IP-CCSD/6-31(+)G(d).
Transition ∆E < µ2 > f
X2A′′ → 12A′ 1.702 0.0004 0.0000
X2A′′ → 22A′′ 2.475 0.7690 0.0466
X2A′′ → 22A′ 2.782 0.0040 0.0003
X2A′′ → 32A′ 3.325 0.0024 0.0002
X2A′′ → 32A′′ 3.650 0.0605 0.0054
X2A′′ → 42A′′ 3.984 1.1704 0.1142
X2A′′ → 42A′ 4.493 0.0001 0.0000
X2A′′ → 52A′′ 5.343 0.0162 0.0021
X2A′′ → 52A′ 6.082 0.0039 0.0006
IE. In the t-shaped isomer, the hole is localized, and the change in IE is due to elec-
trostatic interactions between the “ionized” and the “spectator” fragment. The change
in IE for the symmetric h-bonded dimer is small, because neither overlap nor electro-
static interactions can stabilize the hole, however, larger changes are expected for the
non-symmetric h-bonded dimers [4].
The geometric relaxation is also different for the three isomers. The stacked isomer
relaxes to tighter structure with more efficient overlap between the FMOs, and the hole
remains delocalized between the fragments. The h-bonded isomer undergoes proton
transfer forming lowest-energy structure on the cation’s surface in which the charge and
the unpaired electron are localized on different moieties. Finally, the t-shaped dimer
relaxes to the structure with the localized hole. The respective binding energies of the
cation isomers are 20.2, 32.0 and 24.6 kcal/mol.
Finally, we characterized the electronic spectra of the cations at the neutral and the
relaxed geometries. At the neutral geometry, the h-bonded and stacked isomers feature
intense CR bands at 0.1 and 0.5 eV, respectively. The CR band in the t-shaped isomer is
80
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.00.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
0.11
0.12
0.13
Osc
illat
or S
treng
th
Energy, eV
TU20 TU2
+
Ener
gy, e
V
ΔE = 0.108
ΔE = 3.561
Ener
gy, e
V
ΔE = 3.613
ΔE = 2.622
ΔE = 2.945
ΔE = 4.757
Figure 4.9: The electronic spectra (top panel) of the t-shaped uracil dimer cation atthe neutral (solid black) and the cation (dashed blue) geometries calculated with IP-CCSD/6-31(+)G(d) and the electronic states corresponding to the three most intensetransitions (bottom panel).
less intense, and appears at the same energy as in the h-bonded dimer (0.1 eV). For all
three isomers, the spectra change dramatically upon relaxation. In the stacked isomer,
the intense CR band shifts to higher energies (i.e., from 0.5 to 1.3 eV) and becomes even
81
Table 4.8: The excitation energies (∆E, eV), transition dipole moments (< µ2 >, a.u.)and oscillator strengths (f ) of the t-shaped dimer cation at the geometry of the neutraland cation, IP-CCSD/6-31(+)G(d).
neutral cation
Transition ∆E, eV < µ2 >, a.u. f ∆E, eV < µ2 >, a.u. f
X2A1 → 22A1 0.108 18.4996 0.0488 1.866 0.5715 0.0261
X2A1 → 32A1 0.725 0.1761 0.0031 2.384 0.7506 0.0438
X2A1 → 42A1 0.841 0.0436 0.0009 2.622 1.8376 0.1180
X2A1 → 52A1 1.031 0.1376 0.0035 2.750 0.0428 0.0029
X2A1 → 62A1 1.176 0.5961 0.0172 2.945 1.1927 0.0861
X2A1 → 72A1 1.609 0.0095 0.0004 3.324 0.0042 0.0003
X2A1 → 82A1 1.776 0.0261 0.0011 3.584 0.3711 0.0326
X2A1 → 92A1 3.561 0.6475 0.0565 4.757 0.6759 0.0788
X2A1 → 102A1 3.613 0.6276 0.0555 5.539 0.0295 0.0040
more intense. In the h-bonded isomer, the CR bands (present at the neutral geometry at
0.1 eV) disappears upon proton transfer, and the spectrum becomes very similar to that
of the monomer. In the t-shaped isomer, new intense lines corresponding to the charge-
transfer transitions develop at 2.5-3.0 eV. Thus, the spectra evolution in these isomers is
rather different, which may be exploited for their experimental determination.
Postscript: Performance ofωB97X-D for the structures and energet-
ics of non-covalent neutral and ionized dimers
Self-interaction corrected functionals provide more reliable (although not fully satis-
factory) description of the ionized non-covalent dimers than the standard non-corrected
82
functionals. To investigate the performance of theωB97X-D functional [17] as an inex-
pensive alternative to more reliable wave function methods, we benchmarked this func-
tional using the stacked uracil isomer. We compared the intra and inter-fragment struc-
tural parameters of theωB97X-D/6-311(+)G(d,p) optimized geometries of the neutral
and cation to the best available geometries. For the neutral system, the geometry from
the S22 set of Hobza and coworkers was used as a benchmark [3]. For the cation, we
used the IP-CISD/6-31(+)G(d) optimized geometry for comparison. The average abso-
lute errors and the standard deviations for the bond lengths and angles in the DFT-D
optimized geometries were calculated. In the neutral, the average absolute error and the
standard deviation for bond lengths were 0.004 and 0.003A, respectively; the average
absolute error and standard deviation for angles were 0.247 and 0.182 Degree. In the
cation, the corresponding values were 0.010 and 0.005A, 0.377 and 0.233 Degree. As
of the inter-fragment parameters, in the neutral the DFT-D parameters (C5C6 and O2N1)
differ by less than 0.05A from the geometry from the S22 set, while in the cation the
DFT-D overestimated them by 0.15A comparing to the IP-CISD/6-31(+)G(d) value.
Given the tendency of IP-CISD to overestimate the inter-fragment distances in weakly
bound systems by 0.2-0.3A (as compared to more accurate IP-CCSD [18]), the DFT-D
geometry of the cation may be more accurate than the IP-CISD one. We conclude that
theωB97X-D structures are reasonably accurate, which validates the use of this method
for geometry optimizations of our system.
To assess the performance of theωB97X-D functional for the energetics, we com-
puted the dissociation energies for all isomers of the neutral and cation dimers and com-
pared them to the IP-CCSD/6-311(+)G(d,p) values. The results are summarized in Fig-
ures 4 and 5.ωB97X-D predicts the correct relative ordering of the neutral and cation
isomers. Quantitatively, the DFT-D errors in dissociation energies with respect to the IP-
CCSD values are in 1-2 kcal/mol range for the neutral dimers and in 1-5 kcal/mol range
83
for the cations. The errors inDe are non-systematic. Therefore, DFT-D withωB97X-D
functional provides a correct qualitative picture for energetics; the quantitative predic-
tions are of moderate accuracy, so a more reliable approach should be employed.
4.5 Reference list
[1] W.J. Hehre, R. Ditchfield, and J.A. Pople, Self-consistent molecular orbital meth-ods. XII. Further extensions of gaussian-type basis sets for use in molecular orbitalstudies of organic molecules, J. Chem. Phys.56, 2257 (1972).
[2] R. Krishnan, J.S. Binkley, R. Seeger, and J.A. Pople, Self-consistent molecularorbital methods. XX. A basis set for correlated wave functions, J. Chem. Phys.72,650 (1980).
[3] P. Jurecka, J.Sponer, J.Cerny, and P. Hobza, Benchmark database of accurate(MP2 and CCSD(T) compl ete basis set limit) interaction energies of small modelcomplexes, DNA base pairs, and amino acid pairs, Phys. Chem. Chem. Phys.8,1985 (2006).
[4] K.B. Bravaya, O. Kostko, M. Ahmed, and A.I. Krylov, The effect ofπ-stacking,h-bonding, and electrostatic interactions on the ionization energies of nucleic acidbases: Adenine-adenine, thymine-thymine and adenine-thymine dimers, Phys.Chem. Chem. Phys. (2010), in press, DOI:10.1039/b919930f.
[5] D. Roca-Sanjuan, M. Merchan, and L. Serrano-Andres, Modelling hole-transferin DNA: Low-lying excited states of oxidized cytosine homodimer and cytosine-adenine heterodimer, Chem. Phys.349, 188 (2008).
[6] G. Olaso-Gonzales, D. Roca-Sanjuan, L. Serrano-Andres, and M. Merchan,Toward understanding of DNA fluorescence: The singlet excimer of cytosine, J.Chem. Phys.125, 231002 (2006).
[7] K. Bravaya, Private communication.
[8] M. Pitonak, K.E. Riley, P. Neogrady, and P. Hobza, Highly accurate CCSD(T) andDFT-SAPT stabilization energies of H-bonded and stacked structures of the uracildimer, Comp. Phys. Comm.9, 1636 (2008).
[9] P.A. Pieniazek, A.I. Krylov, and S.E. Bradforth, Electronic structure of the benzenedimer cation, J. Chem. Phys.127, 044317 (2007).
84
[10] P.A. Pieniazek, S.E. Bradforth, and A.I. Krylov, Charge localization and Jahn-Teller distortions in the benzene dimer cation, J. Chem. Phys.129, 074104 (2008).
[11] A.A. Golubeva and A.I. Krylov, The effect ofπ-stacking and H-bonding on ion-ization energies of a nucleobase: Uracil dimer cation, Phys. Chem. Chem. Phys.11, 1303 (2009).
[12] P.A. Pieniazek, J. VandeVondele, P. Jungwirth, A.I. Krylov, and S.E. Bradforth,Electronic structure of the water dimer cation, J. Phys. Chem. A112, 6159 (2008).
[13] O. Kostko, K.B. Bravaya, A.I. Krylov, and M. Ahmed, Ionization of cytosinemonomer and dimer studied by VUV photoionization and electronic structure cal-culations, Phys. Chem. Chem. Phys. (2010), In press, DOI: 10.1039/B921498D.
[14] M.O. Sinnokrot and C.D. Sherrill, Highly accurate coupled cluster potential energycurves for the benzene dimer: Sandwich, t-shaped, and parallel-displaced config-urations, J. Phys. Chem. A108, 10200 (2004).
[15] M.O. Sinnokrot and C.D. Sherrill, High-accuracy quantum mechanical studies ofpi-pi interactions in benzene dimers, J. Phys. Chem. A110, 10656 (2006).
[16] M. Kratochvil, O. Engkvist, J. Sponer, P. Jungwirth, and P. Hobza, Uracil dimer:Potential energy and free energy surfaces. Ab initio beyond Hartree-Fock andempirical potential studies, J. Phys. Chem. A102, 6921 (1998).
[17] J.-D. Chai and M. Head-Gordon, Long-range corrected hybrid density functionalswith damped atom-atom dispersion interactions, Phys. Chem. Chem. Phys.10,6615 (2008).
[18] A.A. Golubeva, P.A. Pieniazek, and A.I. Krylov, A new electronic structuremethod for doublet states: Configuration interaction in the space of ionized 1hand 2h1p determinants, J. Chem. Phys.130, 124113 (2009).
85
Chapter 5
Ionized states of dimethylated uracil
dimers
5.1 Overview
Electronic structure, equillibrium geometries and properties of 1,3-dimethyluracil and
its dimer are characterized by electronic structure calculations. Section 5.3.1 discusses
the structures and binding energies of several low-lying neutral isomers. We investigate
the effect of methylation on the ionized states of the monomer and the dimers, and
quantify the changes in IEs due toπ-stacking interactions (Section 5.3.2). The structural
relaxation in the ionized systems and the binding energies of the cations are discussed
in Section 5.3.3, as well as the electronic spectra of the monomer and the lowest-energy
dimer isomer.
5.2 Computational details
In this study, we employed a variety ofab initio techniques. The structures were
obtained as follows. For the monomer, we employed the RI-MP2/cc-pVTZ and IP-
CISD/6-31(+)G(d) methods [1, 2] in the neutral and the cation optimizations, respec-
tively. Different starting geometries were used in optimizations including theCs andC1
conformers with different angles of rotation of the CH3 groups. We found that both the
86
neutral and the ionized 1,3-dimethyluracil haveCs structures in which only the hydro-
gens of the CH3 groups lie out of plane.
By considering the two main factors contributing to the stability of the stacked
dimers, i.e., electrostatic interactions and steric repulsion, five starting geometries were
generated for the optimization, which employed a DFT-D method with theωB97X-D
functional [3], the 6-311(+,+)G(2d,2p) basis set [4], and the EML(75,302) grid. The
basis set and grid combination was chosen based on the numerical tests, which showed
that calculations with smaller bases, e.g., 6-311(+,+)G(d,p), and smaller grids fail to
reproduce the degeneracy of enantiomeric structures. Tight convergence criteria were
enforced in all optimizations, with the gradient and energy tolerance set to3 · 10−5 and
1.2 · 10−4, respectively, and the maximum energy change1 · 10−7. For the only sym-
metric isomer we carried out additional optimization without the symmetry constraint,
which proved that the minimum-energy structure is indeedCi symmetric.
The same level of theory was used in the dimer cation optimizations. We used the
neutral structures as the starting geometries. All cation optimizations employed the
spin-unrestricted references. The spin-contamination of the doublet Kohn-Sham deter-
minant was low with the typical〈S2〉 values within the 0.76 - 0.77 range. Just like in
the neutrals, theCi symmetry of the only symmetric isomer was tested by additional
optimizations without theCi constraint.
The dissociation and ionization energies and the electronic spectra of the cations
were then calculated with the IP-CCSD method and a moderate 6-31(+)G(d) basis set. In
the monomer calculations, we also employed a larger 6-311(+)G(d,p) basis to investigate
the basis set effect on ionization energies. Core electrons were frozen in the single-point
IP-CCSD energy and spectra calculations.
Optimized geometries, relevant total energies, and harmonic frequencies are given in
the Supporting Materials of Ref. 102. The data on the non-methylated uracil monomer
87
and dimer to which we frequently refer in this work are from Refs. 9,17. All calculations
were performed using theQ-CHEM electronic structure program [5].
5.3 Results and Discussion
5.3.1 Potential energy surface of the neutral dimers: Structures and
energetics
Nucleobase dimers form numerous isomers [6–8], which can be described as the
stacked, t-shaped and h-bonded structures. Three representative isomers from each man-
ifold have been characterized in our recent study of the uracil dimer [9]. The h-bonded
structure corresponds to the global energy minimum in non-methylated species.
Methylation at nitrogens reduces polarity of the molecule, eliminates hydrogens that
can participate in h-bonding, and introduces bulky groups. These factors destabilize
the t-shaped and h-bonded structures of the 1,3-dimethyluracil dimers. The molecular
dynamics study by Hobza and coworkers [10] showed that the potential energy sur-
face (PES) of the 1,3-dimethyluracil dimers is dominated by the stacked structures, the
t-shaped isomers lying 5-6 kcal/mol higher in energy and h-bonded isomers being unsta-
ble. Our calculations usingωB97X-D/6-311(+)G(d,p) found an h-bonded-like structure
(which is better described as a van der Waals dimer) about 10 kcal/mol above the stacked
manifold. Thus, we focus on the stacked isomers of the 1,3-dimethyluracil dimer.
The five optimized structures of the neutral stacked 1,3-dimethyluracil are shown
in Figure 5.1; the corresponding binding and relative energies calculated withωB97X-
D/6-311(+,+)G(2d,2p) and CCSD/6-31(+)G(d) are summarized in Tables 5.1 and 5.2,
respectively. The lowest-energy structure of the dimethylated uracil dimer is non-
symmetric isomer 1, which is similar to the minimum-energy stacked uracil structure
88
Isomer 1 (0)
De=13.8 / 15.9
Isomer 2 (+1.2)
De=12.6
CiC1
De=12.4
Isomer 3 (+1.5)
De=11.7
Isomer 4 (+2.2)
C1
C1
De=10.9
Isomer 5 (+2.9)C1
Figure 5.1: Five isomers of the stacked neutral 1,3-dimethyluracil dimer and their bind-ing energies (kcal/mol). The energy spacings (kcal/mol) between the lowest-energystructure and other isomers are given in the parenthesis. All values were obtained withωB97X-D/6-311(+,+)G(2d,2p) except for theDe value of isomer 1 shown in bold, whichis the IP-CCSD/6-31(+)G(d) estimate.
from the S22 set by Hobza and coworkers [11]. This isomer is followed by isomers 2
(Ci), 3 (C1), 4 (C1) and 5 (C1) lying 1.2, 1.5, 2.2, and 2.9 kcal/mol higher in energy,
respectively. The energy gaps between the isomers are very small: the five isomers lie
in just 2.9 kcal/mol range, and some of them are nearly degenerate, i.e., separated by
0.3 kcal/mol. These energy differences are of the order of kT(298.18 K) = 0.6 kcal/mol,
which suggests significant populations of all these isomers at the standard conditions.
The denseπ-stacked manifold and structural motifs are similar to stacked thymine
dimers [12], where five isomers lie within 2.2 kcal/mol. Interestingly, no low-energy
stacked isomers were identified for dimers of another pyrimidine, cytosine dimer [13].
The binding energies of the neutral stacked 1,3-dimethyluracil dimers lie in the range
of 10.9-13.8 kcal/mol, as computed by DFT-D. For the lowest-energy isomer we also
89
Table 5.1: The total (hartree) and dissociation energies (kcal/mol) of the neutraland ionized 1,3-dimethyluracil monomer and dimers calculated at theωB97X-D/6-311(+,+)G(2d,2p) level of theory.
Complex EtotDFT−D DDFT−D
e
mU0 -493.431022 –
mU+ -493.111429 –
S(mU)02, isomer 1 -986.884084 13.8
S(mU)02, isomer 2 -986.882142 12.6
S(mU)02, isomer 3 -986.881741 12.4
S(mU)02, isomer 4 -986.880611 11.7
S(mU)02, isomer 5 -986.879409 10.9
S(mU)+2 , isomer 1 -986.587029 28.0
S(mU)+2 , isomer 2 -986.570893 17.9
S(mU)+2 , isomer 3 -986.578185 22.4
S(mU)+2 , isomer 4 -986.576570 21.4
T(mU)+2 , isomer 5 -986.572944 19.1
computed the CCSD/6-31(+)G(d) value. The resulting binding energy of 15.9 kcal/mol
is in a good agreement with 13.8 kcal/mol computed withωB97X-D/6-311(+)G(d,p).
Based on our results for uracil [9], using larger basis set in CCSD calculations lowers
the CCSD binding energy and improves the agreement between the methods.
The binding energy of the lowest energy isomer (13.8 kcal/mol) is larger than that
of the stacked non-methylated uracil dimer for whichDe = 10.5 kcal/mol (these are
DFT-D values, but the similar trend is observed for the CCSD/6-31(+)G(d) binding
energies, which are 15.9 and 12.2 kcal/mol). For comparison, the binding energy of the
lowest stacked thymine and adenine homodimers are 12.5 kcal/mol and 10.6 kcal/mol,
respectively [12].
An increase in binding energy upon methylation is somewhat surprising, as methy-
lated uracil is less polar than uracil (the RI-MP2/cc-pVTZ dipole moments are 4.19 D
versus 4.02 D) and, therefore, one may expect weaker electrostatic interaction between
90
Table 5.2: The total (hartree) and dissociation energies (kcal/mol) of the neutral andionized 1,3-dimethyluracil and its dimer (lowest energy isomer) calculated at the IP-CCSD/6-31(+)G(d) level of theory. For the monomer and the dimer cations, the relax-ation energy (∆ECCSD
relax , kcal/mol) is provided.a The uracil and uracil dimer IP-CCSD/6-31(+)G(d) resultsb are included for comparison.
Complex EtotCCSD DCCSD
e ∆ECCSDrelax
mU0 -492.032033 – –
mU+ -491.715681 – -3.8
S(mU)02, isomer 1 -984.089466 15.9 –
S(mU)+2 , isomer 1 -983.798612 31.9 -11.2
U0 -413.683919 – –
U+ -413.345482 – -4.1
SU02 -827.387312 12.2 –
SU+2 -827.069011 24.9 -8.7
a The difference between the total energies of the cation at the vertical and the relaxedgeometries.
b For these estimates, we employed same structures as in Ref. 9 For the stacked uracildimer cation, the DFT-D/ωB97X-D/6-311(+)G(d,p) optimized geometry was used.
the fragments in the 1,3-dimethyluracil dimer. However, this difference appears to be
too small, and local electrostatic interactions play a more important role. The anal-
ysis of the structures reveals that the (NCH2)Hδ+· · ·Oδ−(C) distance in the stacked
1,3-dimethyluracil dimer is shorter than the (N)Hδ+· · ·Oδ−(C) distance in the stacked
uracil dimer, which results in stronger electrostatic interaction between the fragments
in the former complex. A tighter structure of the methylated dimer is also counterin-
tuitive because of the presence of the bulky methyl groups. The observed increase in
binding energy upon substitution is consistent with the results of Sherrill and cowork-
ers [14, 15], who demonstrated that the electrostatic considerations alone are not suffi-
cient to explain the changes in binding inπ-stacked systems upon substitution and that
differential changes in dispersion interactions play an important role.
91
5.3.2 The effect of methylation on the ionized states of the monomer
and the dimers
1,3-dimethyluracil
Figure 5.2 presents the five highest occupied MOs of 1,3-dimethyluracil and uracil and
the corresponding VIEs calculated at the IP-CCSD/6-311(+)G(d,p) level. The shapes
of the MOs are similar in the two molecules, except for theσCH electronic density on
the CH3 groups of 1,3-dimethyluracil. Another minor difference can be seen in the
lp(N) + πCC + πCO orbital, which is more localized in dimethylated uracil.
The order of the ionized states in methylated uracil is the same as in uracil. The
HOMO is theπ-like MO centered at the C–C double bond, and the corresponding IE
is 8.87 eV. This state is followed by ionization from the two lone pair and twoπ-like
orbitals with VIEs of 9.74 (lp(O1)), 9.77 (lp(O) + lp(N)), 10.66 (lp(O2)) and 12.16 eV
(lp(N) + πCC + πCO).
However, the values of IEs and the spacings between the ionized states are different.
Methylation lowers the first IE by 0.6 eV relative to uracil. Similar effect is observed
for other states: the VIEs of12A′, 12A′′, 22A′ and22A′′ states decrease by 0.37, 0.74,
0.43 and 0.86 eV, respectively. Note that for the oxygen lone-pair states, the magnitude
of the effect is smaller than for the states derived from ionization fromπ-like orbitals.
The largest shifts are observed for the states with large contributions from lone pairs of
nitrogens, which are primary substitution sites. As a result, the12A′ and12A′′ states that
are separated by 0.4 eV in uracil become almost degenerate in 1,3-dimethyluracil. The
IEs are lowered due to electron-donating CH3 groups increasing electron density in the
ring (destabilization of the respective MOs) and due to a larger size of the methylated
species contributing to hole stabilization. The effect is larger in the states derived from
ionization from delocalizedπ orbitals, in which the CH3 group donates the electron
92
8.87
9.77
9.74
10.66
12.16
πCC / a´´
lp(N)+lp(O) / a´´
lp(O1) / a´
lp(O2) / a´
lp(N)+πCC+ πCO / a´´
Ioni
zatio
n En
ergy
, eV
9.48
10.51
10.11
11.09
13.02
πCC / a´´
lp(N)+lp(O) / a´´
lp(O1) / a´
lp(O2 ) / a´
lp(N)+πCC+ πCO / a´´
Ioni
zatio
n En
ergy
, eV
Figure 5.2: The five lowest ionized states and the molecular orbitals of dimethyluracil(top) and uracil (bottom) calculated by IP-CCSD/6-311(+)G(d,p).
density to theπ system via thelp(N) component, whereas the in-planelp(O) orbitals
are affected less.
93
Table 5.3: The five lowest ionized states and the corresponding IEs (eV) of the 1,3-dimethyluracil at the vertical geometry calculated by IP-CCSD with the 6-31(+)G(d)and 6-311(+)G(d,p) bases. The IE shifts (eV) with respect to the uracil values are givenin parenthesis.
Basis X2A′′ 12A′ 12A′′ 22A′ 22A′′
6-31(+)G(d) 8.77 (-0.61) 9.67 (-0.38) 9.69 (-0.75) 10.58 (-0.45) 12.07 (-0.88)
6-311(+)G(d,p) 8.87 (-0.61) 9.74 (-0.37) 9.77 (-0.74) 10.66 (-0.43) 12.16 (-0.86)
Dimethyluracil dimers
Similarly to otherπ-stacked dimers [9, 12, 16, 17], the electronic structure and ionized
states of the 1,3-dimethyluracil dimer can be described within the DMO-LCFMO frame-
work [16]. The molecular orbitals of the dimer (DMOs) shown in Figure 5.3 are the in-
and out-of-phase combinations of the FMOs. Figure 5.3 also presents the correspond-
ing IEs. Because of the lower symmetry, some of the electronic states of the methylated
uracil dimer are localized on individual fragments. The first IE of the 1,3-dimethyluracil
dimer corresponds to ionization from theπCC(F1) − πCC(F2) DMO. Stacking inter-
action lowers it by 0.37 eV relative to the monomer, i.e, 8.40 eV versus 8.77 eV as
calculated at the IP-CCSD/6-31(+)G(d) level. Thus, the magnitude of the effect is com-
parable to that in the non-methylated stacked uracil dimer and the stacked thymine dimer
(both have 0.35 eV decrease in IE), whereas the shift in adenine dimer is smaller (0.2
eV) [12].
The order of the ionized states in the 1,3-dimethyluracil dimer is different from the
uracil dimer. In the latter (as well as in the stacked thymine dimer, see Ref. 12), the
states corresponding to the in- and out-of-phase FMO combinations appear pair by pair
in the same order as the respective monomer states. In the methylated uracil dimer,
the states arising from ionization fromlp(O1) FMOs lie in between the pair of states
corresponding to thelp(O) + lp(N) FMOs.
94
Ioni
zatio
n En
ergy
, eV
9.42 9.669.69
9.85
10.51 10.46
11.8811.67
8.40
8.81
Figure 5.3: The ten lowest ionized states and the corresponding MOs of the lowest-energy isomer of the neutral stacked 1,3-dimethyluracil computed with IP-CCSD/6-31(+)G(d).
The largest splittings between the pairs of states are observed for the states derived
from theπ-like FMOs owing to their larger overlap. Compare, for example, the 0.41,
0.43 and 0.21 eV splittings for the states derived from ionization from theπ-like orbitals
to the 0.06 and 0.03 eV splittings for the lone-pair states. Overall, the magnitude
of the splittings in methylated and non-methylated dimers is similar, except for the
lp(O) + lp(N) pair of states (0.43 eV vs. 0.06 eV in the 1,3-dimethyluracil and uracil
dimers, respectively). Due to large weight oflp(N), these MOs are most affected by the
electron-donating CH3 groups. The increased electron density in theπ-system results in
larger overlap and, consequently, larger splittings. This large splitting is responsible for
different state ordering. So far, this is the first example of that type — in all other model
95
systems we have studied (benzene, water, uracil, and adenine dimers) the stacking inter-
actions did not change the relative order of the ionized states, even though the splittings
in different pairs of states were quite different.
5.3.3 Ionization-induced changes in the monomer and the dimers:
Structures and properties
Ionization induces considerable structural changes. For the lowest ionized state, relax-
ation pattern is consistent with the MO character. In the uracil monomer, double CC
bond elongates inducing the changes in an entire bond-alternation pattern [9]. In the
dimer, these changes are accompanied by the rings re-orienting to increase the over-
lap between the respective FMOs [9]. Methylated species show very similar behavior.
Below we discuss changes in binding energies and relative order of the isomers and
characterize spectroscopic signatures of the structural relaxation.
Binding energies of the dimer cations
Figure 5.4 presents five relaxed structures of the 1,3-dimethyluracil dimer cations. The
total and dissociation energies of the dimer cations estimated byωB97X-D are given
in Table 5.1; and the CCSD/6-31(+)G(d) estimates for the lowest-energy isomer are
provided in Table 5.2. Similarly to the neutral dimers, the global minimum corresponds
to isomer 1 (C1). However, in all other aspects the PES of the dimer cation differs
drastically from that of the neutral.
The order of the isomers and the energy gaps between them change upon ionization.
Following isomer 1, isomers 3, 4, 5 and 2 lie 5.6, 6.6, 8.8 and 10.1 kcal/mol higher in
energy. In contrast to the neutral, the five minima on the cation PES are well-separated
in energy. For example, the two lowest-energy structures are more than 5 kcal/mol
apart, whereas all five neutral isomers lie within 2.9 kcal/mol interval. Thus, we expect
96
Isomer 1 (0)
De= 28.0 / 31.9
Isomer 2 (+10.1)
De= 17.9
CiC1
De= 22.4
Isomer 3 (+5.6)
De= 21.4
Isomer 4 (+6.6)
C1
C1
De=19.1
Isomer 5 (+8.8)
C1
Figure 5.4: Five low-lying isomers of the 1,3-dimethyluracil dimer cation and the disso-ciation energies (kcal/mol). The energy spacings (kcal/mol) between the lowest-energystructure and other isomers are given in the parenthesis. All values were obtained withωB97X-D/6-311(+,+)G(2d,2p) except for theDe value of isomer 1 (shown in bold),which is the IP-CCSD/6-31(+)G(d) estimate.
dominant population of the lowest-energy structure (isomer 1) of the cation under the
standard conditions. Another difference is the appearance of the t-shaped dimer cation
(isomer 5) among low-lying structures. It is 8.8 kcal/mol above the isomer 1 (but 1.5
kcal/mol below one of the stacked structures).
The dissociation energies of 1,3-dimethyluracil cations fall within the 17.9-28.0
kcal/mol range, as computed with DFT-D. Therefore, the fragments in ionized dimers
are bound 1.4 to 2.0 times stronger than in the neutral dimers with the largest and the
smallest increases observed for isomers 1 and 2, respectively. The magnitude of the
increase is similar to that observed in the uracil dimers. Note that, similarly to the neu-
tral dimers, the interaction between the fragments is stronger in the methylated dimers
than in the non-methylated analogues. The best estimate of the binding energy for the
97
lowest-energy cation structure (isomer 1) is 31.9 kcal/mol (at IP-CCSD/6-31(+)G(d)
level), which is 7.0 kcal/mol larger than that of the stacked uracil dimer (24.9 kcal/mol
at IP-CCSD/6-31(+)G(d) level). The binding energy of the ionized stacked thymine
dimer is similar to that of uracil, i.e., 19.8 kcal/mol. The increase of binding energy
upon methylation can be explained by the increased electron density in theπ-system
resulting in larger overlap, and is consistent with a slightly larger change of IE due to
dimerization. Another contribution into the binding energy comes from the geometric
relaxation, which is larger in the methylated dimer relative to the non-methylated species
(11.2 versus 8.7 kcal/mol). The corresponding relaxation energies in both monomers are
about 3-4 kcal/mol (see Table 5.2). Larger geometric relaxation in the methylated dimer
is similar to the results for the stacked thymine and adenine homodimers [12], where the
difference between VIE and AIE was 15.0 kcal/mol and 11.3 kcal/mol for TT and AA,
respectively, and the corresponding monomer values were 5-6 kcal/mol.
Equilibrium geometries of the cations
The ionization-induced changes in geometry and the electronic structure of isomers 1-5
of the 1,3-dimethyluracil dimer are illustrated in Figures 5.5- 5.9. In each picture, the
neutral and the cation geometries and the two highest MOs of the dimer are shown. The
analysis of these five cases reveals two distinct trends. In isomers 1,2 and 4 (Group 1),
the relaxation results in the increased FMO overlap and, consequently, the delocalized
DMOs at the cation geometry. Isomers 3 and 5 (Group 2) exhibit a different pattern:
the DMOs are localized on one of the fragments at the cation geometry and no signifi-
cant FMO overlap develops upon the relaxation. In both structureslp(O) of one of the
fragments moves toward the hole centered onπCC MO of the other fragment. Thus,
Group 2 cations are stabilized by the favorable electrostatic interaction of the localized
hole and the negative charge onlp(O). This motif, which is similar to the t-shaped
98
uracil dimer [9], demonstrates that electrostatic interactions can be competitive with
the hole delocalization effects even in the stacked systems. Therefore, two factors
(mU)20
isomer 1(mU)2
+
isomer 1
De=28.0 / 31.9 De=13.8 / 15.9
(mU)20
isomer 1(mU)2
+
isomer 1
Figure 5.5: The ionization-induced changes in geometry, binding energies (kcal/mol)and the MOs of isomer 1 of the stacked 1,3-dimethyluracil dimer. TheωB97X-D/6-311(+,+)G(2d,2p) optimized structures, dissociation energies and the HF/6-31(+)G(d)MOs are presented.
are responsible for the stabilization of the ionized 1,3-dimethyluracil dimer cations: the
DMO-LCFMO mechanism in which the stabilization of the ionized state is proportional
to the FMO overlap [16], and the electrostatic mechanism [9,12,13]. The magnitude of
99
(mU)20
isomer 2(mU)2
+
isomer 2
De=17.9De=12.6
(mU)20
isomer 2(mU)2
+
isomer 2
Figure 5.6: The ionization-induced changes in geometry, binding energies (kcal/mol)and the MOs of isomer 2 of the stacked 1,3-dimethyluracil dimer. TheωB97X-D/6-311(+,+)G(2d,2p) optimized structures, dissociation energies and the HF/6-31(+)G(d)MOs are presented.
relaxation is comparable for the two mechanisms, e.g., in Group 1 the binding energy
increases 1.4 to 2.0 times relative to the neutrals, and for Group 2 the increase is 1.7
to 1.8 fold. However, one may expect that the DMO-LCFMO stabilization is more
sensitive to relative orientation of the fragments than electrostatic interactions and that
the constrained environments (e.g., DNA) may discriminate between the two effects,
100
(mU)20
isomer 3(mU)2
+
isomer 3
De=22.4De=12.4
(mU)20
isomer 3(mU)2
+
isomer 3
Figure 5.7: The ionization-induced changes in geometry, binding energies (kcal/mol)and the MOs of isomer 3 of the stacked 1,3-dimethyluracil dimer. TheωB97X-D/6-311(+,+)G(2d,2p) optimized structures, dissociation energies and the HF/6-31(+)G(d)MOs are presented.
although it is clear how strong perturbation by the backbone can affect relative strengths
of these interactions.
Let us now compare the absolute values of the binding energies for isomers 1-5.
For the Group 1 isomers stabilized via DMO-LCFMO mechanism, the strongest and the
101
(mU)20
isomer 4(mU)2
+
isomer 4
De=21.4De=11.7
(mU)20
isomer 4(mU)2
+
isomer 4
Figure 5.8: The ionization-induced changes in geometry, binding energies (kcal/mol)and the MOs of isomer 4 of the stacked 1,3-dimethyluracil dimer. TheωB97X-D/6-311(+,+)G(2d,2p) optimized structures, dissociation energies and the HF/6-31(+)G(d)MOs are presented.
weakest inter-fragment interaction is observed in isomer 1 (28.0 kcal/mol) and symmet-
ric isomer 2 (17.9 kcal/mol), respectively. The difference between these two cases is
apparent from Figures 5.5 and 5.6. In isomer 1, the DMOs look more like a bonding
orbital, whereas isomer 2 fails to develop significant FMO overlap. Isomer 4 (see Fig-
ure 5.8) lies in between these two limiting cases with the moderate overlap and binding
102
(mU)20
isomer 5
De=19.1De=10.9
(mU)2+
isomer 5
(mU)20
isomer 5(mU)2
+
isomer 5
Figure 5.9: The changes in geometry, binding energies (kcal/mol) and the MOs ofisomer 5 of the stacked 1,3-dimethyluracil dimer at ionization. TheωB97X-D/6-311(+,+)G(2d,2p) optimized structures, dissociation energies and the HF/6-31(+)G(d)MOs are presented.
energy of 21.4 kcal/mol. In Group 2, the values of binding energies are less diverse,
which is consistent with the electrostatic stabilization mechanism. In isomers 3 and 5
the fragments are bound by 22.4 and 19.1 kcal/mol, respectively
103
Electronic spectra of the cations
1,3-dimethyluracil The electronic spectra of the methylated uracil and uracil cations
at the vertical and relaxed geometries calculated by IP-CCSD/6-31(+)(d) are shown in
Figure 5.10. Table 5.4 provides the values of transition energies, dipole moments and
oscillator strengths. Owing to the similarity in their structures and MOs, the spectra of
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.50.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14O
scill
ator
Stre
ngth
Energy, eV
πCC / a´´
lp(N)+lp(O) / a´´
lp(N)+πCC+ πCO / a´´
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.50.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Osc
illat
or S
treng
th
Energy, eV
πCC / a´´
lp(N)+lp(O) / a´´
lp(N)+πCC+ πCO / a´´
Figure 5.10: The electronic spectra of 1,3-dimethyluracil (left) and uracil (right) atthe vertical (solid black) and the relaxed (dashed blue) geometries calculated by IP-CCSD/6-31(+)G(d).
104
Table 5.4: The electronic spectrum of the 1,3-dimethyluracil cation at the vertical andrelaxed geometries calculated at the IP-CCSD/6-31(+)G(d) level.
neutral cation
Transition ∆E, eV < µ2 >, a.u. f ∆E, eV < µ2 >, a.u. f
X2A′′ → 12A′ 0.899 0.0004 0.0000 1.269 0.0004 0.0000
X2A′′ → 12A′′ 0.917 0.5222 0.0117 1.557 0.3996 0.0152
X2A′′ → 22A′ 1.809 0.0000 0.0000 2.399 0.0000 0.0000
X2A′′ → 22A′′ 3.297 1.6952 0.1369 3.822 1.4258 0.1335
methylated and non-methylated uracil cation are very similar (see Figure 5.10). In both
cases, the two bright transitions correspond to the transitions between the states of the
cations with theπ-orbitals singly-occupied. The methylated uracil spectrum is slightly
blue-shifted. The effect of the geometry relaxation on the spectra is larger in the uracil
cation than in the 1,3-dimethyluracil cation with the line shifts of +0.7-0.8 eV for the
former and +0.5-0.6 eV for the latter. This can be explained by the electron-donating
properties of the CH3 groups which reduce the effect of ionization on the structure.
1,3-dimethyluracil dimer cation Table 5.5 presents IEs of isomer 1 computed at the
vertical and relaxed geometries. The respective MOs are shown in Figure 5.3. Due
to low symmetry and large size of the methylated dimer we only computed the exci-
tation energies, as calculations of the oscillator strengths for the electronic transitions
in the cation are more computationally expensive than just energy calculations. How-
ever, the intensities of the peaks can be estimated based on the intensities in the uracil
dimer cation [9, 17] and DMO-LCFMO analysis (see Ref. 16 for the DMO-LCFMO
nomenclature), as explained below. These results are visualized in Figure 5.11. In
105
Table 5.5: The ionization energies (eV) and the DMO charactera corresponding to theten lowest ionized states of the stacked 1,3-dimethyluracil dimer at the vertical geometry(isomer 1) calculated at the IP-CCSD/6-31(+)G(d) level.
neutral cation
State DMO IE DMO Eex
X2A1 ψ−(πCC) 8.40 (-0.63) ψ−(πCC) 0.00
12A1 ψ+(πCC) 8.81 (-0.75) ψ+(πCC) 1.48
22A1 ψ−(lp(O) + lp(N)) 9.42 (-0.96) ψ−(lp(O) + lp(N)) 1.99
32A1 lp(O1), F1 9.66 (-0.40) ψ−(lp(O1) 2.15
42A1 lp(O1), F2 9.69 (-0.43) ψ+(lp(O1) 2.18
52A1 ψ+(lp(O) + lp(N)) 9.85 (-0.59) ψ+(lp(O) + lp(N)) 2.44
62A1 lp(O2), F1 10.46 (-0.48) ψ−(lp(O1) 3.07
72A1 lp(O2), F2 10.51 (-0.48) ψ+(lp(O1) 3.09
82A1 ψ−(lp(N) + πCC + πCO) 11.67 (-0.94) ψ−(lp(N) + πCC + πCO) 4.25
92A1 ψ+(lp(N)+πCC+πCO) 11.88 (-1.00) ψ+(lp(N) + πCC + πCO) 4.37a In the DMO-LCFMO notations [16], theψ+(ν) andψ−(ν) represent the bonding and
antibonding combinations of the MOs of fragments 1 and 2 (νF1 andνF2).b The shifts of IEs (eV) of the dimethylated uracil dimer relative to the non-methylatedanalogue are given in parenthesis. For the relaxed cation, the excitation energies (eV)
calculated at IP-CCSD/6-31(+)G(d) level are presented.
the stacked uracil dimer cation, theψ−(π) → ψ+(π) andψ−(π) → ψ−(π) transi-
tions (i.e. the transitions between the electronic states derived from the ionization from
the DMOs composed out ofπ-like FMOs) are intense, whereas theψ−(π) → ψ+(lp)
andψ−(π) → ψ−(lp) transitions are weak. Analogously to the stacked uracil dimer,
in the methylated dimer cation spectrum at the vertical geometry, we expect at least
three intense peaks: at 0.41, 1.45 and 3.27 eV. The former peak is the CR band, and
the latter two are the local excitations (LE) involving otherπ-like DMOs, i.e. the
106
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.50.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
0.22
0.24
Osc
illat
or s
treng
th
Energy, eV
12A1
52A1
X2A1
82A1
Figure 5.11: The three most intense transitions in the electronic spectrum of the lowestisomer of stacked 1,3-dimethyluracil cation at vertical (solid black) and cation (dashedblue) geometries. The DMOs corresponding to the ground state (framed) and excitedstates (regular) are shown. The positions of the peaks were calculated at IP-CCSD/6-31(+)G(d) level, while the intensities are from the non-methylated dimer calculations.
ψ+(lp(O)+lp(N) andψ−(lp(N)+πCC +πCO). The transition dipole moment is related
to sνF1νF2, the overlap of the FMOs on fragments 1 and 2, by the following equation:
I(ψ−(ν) → ψ+(ν)) ∝ RAB√1− sνF1νF2
, (5.1)
whereRAB is the inter-fragment distance.
Upon the geometry relaxation, the states of the dimer become more delocalized, as
can be seen in Fig. 5.5 showing the two highest-occupied DMOs at the neutral and
cation geometries. The states derived from thelp(O1) andlp(O2) FMOs are no longer
localized on one of the fragments, as they were at the vertical geometry (not shown).
Thus, we expect the following changes in the spectrum. The increasing overlap between
107
theψ+(πCC) andψ−(πCC) DMOs leads to the growth of the intensity of CR band, which
shifts to 1.48 eV upon the relaxation. Based on the similarity of the methylated and non-
methylated systems, we expect the intensity of the CR band to (at least) double at the
relaxed geometry. The position of the LE band that appears at 1.45 eV at the vertical
geometry shifts to 2.44 eV; however, as follows from the FMO overlaps and splittings
no considerable increase of intensity is expected. Finally, the LE transition at 3.27 eV
in the vertical spectrum shifts by +1.0 eV and its intensity decreases upon relaxation.
5.4 Conclusions
The structures, binding energies, properties of several isomers of the neutral and ionized
1,3-dimethylated uracil dimers are characterized usingab initio methods. The methyla-
tion suppresses the formation of hydrogen-bonded and t-shaped neutral structures, how-
ever, theπ-stacked manifold is rather dense. Five lowest isomers of the stacked dimer
lie within the 2.9 kcal/mol range, which suggests that all of the isomers will be present
at the standard conditions. The binding energies of the neutral dimers are in the range
of 10.9-13.8 kcal/mol (DFT-D). Surprisingly, in sterically-constrained and less polar
methylated species the fragments are bound stronger than in the non-methylated analogs
(the corresponding DFT-D estimate for the stacked uracil dimer is 10.5 kcal/mol).
The MOs of the uracil are only slightly perturbed by the CH3 group; however, the
effect is significant for the values of IEs. The methylation lowers the first IE of the 1,3-
dimethyluracil by 0.6 eV as compared to uracil; the higher-lying states also exhibit red
shifts of a varying magnitude (0.37-0.86 eV). This IE lowering is due to the electron-
donating CH3 groups, which increase the electron density in the ring and stabilize the
ionized state. The effect is bigger in the states derived from ionization from the delocal-
izedπ orbitals, in which the electron density is efficiently donated to theπ-system via
108
the lp(N) component. The magnitude of the effect correlates with the weight oflp(N)
in the leading MO, which is not surprising as nitrogens are the primary substitution sites.
Similarly to uracil dimer, the electronic structure of the methylated uracil dimer is
well described by DMO-LCFMO. The stacking interactions lower the first IE by 0.37
eV in the methylated dimers, which is very similar to 0.35 eV lowering in the non-
methylated system (and the stacked dimer of thymine). Another important finding is the
0.6 eV lowering of the IE in the methylated dimer due to the methylation: the effect
is the same as in the monomer. It implies that the effect of substitutions can be incor-
porated into the qualitative DMO-LCFMO picture as a constant shifts of the dimer and
monomer levels, whereas the splittings between the in-phase and out-of-phase DMOs
are surprisingly insensitive to the substitution, except for the states derived from orbitals
with large weights oflp(N). These states exhibit much larger splittings than in non-
methylated species (i.e., 0.43 versus 0.06 eV), which ultimately results in changes in the
states ordering. This is different from other model systems that we have studied (ben-
zene, water, uracil, and adenine dimers) where the stacking interactions do not change
the relative order of the ionized states, even though the splittings in different pairs of
states are quite different.
Ionization changes the bonding pattern inducing considerable changes in structures
and binding energies. The energy separation between the isomers increases, so one
can expect dominant population of the lowest isomer at the standard conditions. The
binding energies increase 1.4-2.0 fold upon ionization and lie in 17.9-28.0 kcal/mol
range (DFT-D); for the lowest-energy dimer cation structure, the IP-CCSD value ofDe
is 31.9 kcal/mol. This binding energy is larger than that in the non-methylated uracil and
thymine dimers. Similarly to the neutrals, the methylation increases the inter-fragment
interaction in the dimer.
109
The relaxation of the cation structures is governed by two distinct mechanisms: the
hole delocalization (and the FMO overlap) and the electrostatic stabilization (interaction
of thelp(O) with the localized hole).
Finally, we presented electronic spectra of the ionized species. Significant changes
in the spectra upon relaxation can be exploited to monitor the ionization-induced dynam-
ics in dimethylated uracils. At the vertical geometry, there are three intense transitions:
at 0.41, 1.45 and 3.27 eV, the CR band at 0.41 eV and LE at 1.45 eV being the most
intense. Upon relaxation, these bands are blue-shifted, and their intensities change to
1.48 (CR), 2.44 (LE) and 4.25(LE) eV. The CR band at 1.48 eV is expected be the most
intense and can be used to monitor the relaxed stacked dimer cation formation.
5.5 Reference list
[1] W.J. Hehre, R. Ditchfield, and J.A. Pople, Self-consistent molecular orbital meth-ods. XII. Further extensions of gaussian-type basis sets for use in molecular orbitalstudies of organic molecules, J. Chem. Phys.56, 2257 (1972).
[2] T.H. Dunning, Gaussian basis sets for use in correlated molecular calculations. I.The atoms boron through neon and hydrogen, J. Chem. Phys.90, 1007 (1989).
[3] J.-D. Chai and M. Head-Gordon, Long-range corrected hybrid density functionalswith damped atom-atom dispersion interactions, Phys. Chem. Chem. Phys.10,6615 (2008).
[4] R. Krishnan, J.S. Binkley, R. Seeger, and J.A. Pople, Self-consistent molecularorbital methods. XX. A basis set for correlated wave functions, J. Chem. Phys.72,650 (1980).
[5] Y. Shao, L.F. Molnar, Y. Jung, J. Kussmann, C. Ochsenfeld, S. Brown, A.T.B.Gilbert, L.V. Slipchenko, S.V. Levchenko, D.P. O’Neil, R.A. Distasio Jr, R.C.Lochan, T. Wang, G.J.O. Beran, N.A. Besley, J.M. Herbert, C.Y. Lin, T. VanVoorhis, S.H. Chien, A. Sodt, R.P. Steele, V.A. Rassolov, P. Maslen, P.P. Koram-bath, R.D. Adamson, B. Austin, J. Baker, E.F.C. Bird, H. Daschel, R.J. Doerksen,A. Drew, B.D. Dunietz, A.D. Dutoi, T.R. Furlani, S.R. Gwaltney, A. Heyden, S.
110
Hirata, C.-P. Hsu, G.S. Kedziora, R.Z. Khalliulin, P. Klunziger, A.M. Lee, W.Z.Liang, I. Lotan, N. Nair, B. Peters, E.I. Proynov, P.A. Pieniazek, Y.M. Rhee, J.Ritchie, E. Rosta, C.D. Sherrill, A.C. Simmonett, J.E. Subotnik, H.L. WoodcockIII, W. Zhang, A.T. Bell, A.K. Chakraborty, D.M. Chipman, F.J. Keil, A. Warshel,W.J. Herhe, H.F. Schaefer III, J. Kong, A.I. Krylov, P.M.W. Gill, M. Head-Gordon,Advances in methods and algorithms in a modern quantum chemistry programpackage, Phys. Chem. Chem. Phys.8, 3172 (2006).
[6] K. M uller-Dethlefs and P. Hobza, Noncovalent interactions: A challenge for exper-iment and theory, Chem. Rev.100, 143 (2000).
[7] J. Sponer, J. Leszczynski, and P. Hobza, Electronic properties, hydrogen bonding,stacking, and cation binding of DNA and RNA bases, Biopolymers61, 3 (2002).
[8] H. Saigusa, Excited-state dynamics of isolated nucleic acid bases and their clusters,Photochem. Photobiol.7, 197 (2006).
[9] A.A. Zadorozhnaya and A.I. Krylov, Ionization-induced structural changes inuracil dimers and their spectroscopic signatures, J. Chem. Theory Comput. (2010),In press.
[10] M. Kratochvıl, O. Engkvist, J. Vacek, P. Jungwirth, and P. Hobza, Methylateduracil dimers: Potential energy and free energy surfaces, Phys. Chem. Chem.Phys.2, 2419 (2000).
[11] P. Jurecka, J.Sponer, J.Cerny, and P. Hobza, Benchmark database of accurate(MP2 and CCSD(T) compl ete basis set limit) interaction energies of small modelcomplexes, DNA base pairs, and amino acid pairs, Phys. Chem. Chem. Phys.8,1985 (2006).
[12] K.B. Bravaya, O. Kostko, M. Ahmed, and A.I. Krylov, The effect ofπ-stacking,h-bonding, and electrostatic interactions on the ionization energies of nucleic acidbases: Adenine-adenine, thymine-thymine and adenine-thymine dimers, Phys.Chem. Chem. Phys. (2010), in press, DOI:10.1039/b919930f.
[13] O. Kostko, K.B. Bravaya, A.I. Krylov, and M. Ahmed, Ionization of cytosinemonomer and dimer studied by VUV photoionization and electronic structure cal-culations, Phys. Chem. Chem. Phys. (2010), In press, DOI: 10.1039/B921498D.
[14] M.O. Sinnokrot and C.D. Sherrill, Unexpected substituent effecst in face-to-faceπ-stacking interactions, J. Phys. Chem. A107, 8377 (2003).
[15] M.O. Sinnokrot and C.D. Sherrill, Substituent effects inπ− π interactions: Sand-wich and t-shaped configurations, J. Am. Chem. Soc.126, 7690 (2004).
111
[16] P.A. Pieniazek, A.I. Krylov, and S.E. Bradforth, Electronic structure of the benzenedimer cation, J. Chem. Phys.127, 044317 (2007).
[17] A.A. Golubeva and A.I. Krylov, The effect ofπ-stacking and H-bonding on ion-ization energies of a nucleobase: Uracil dimer cation, Phys. Chem. Chem. Phys.11, 1303 (2009).
112
Chapter 6
Ionized non-covalent dimers: Outlook
and future research directions
6.1 Overview
The non-covalent ionized clusters pose a challenge to theory; at the same time, this very
complexity makes them an exicting and rewarding research topic. Closely-lying elec-
tronic states result in multi-configurational wave functions and rich electronic structure
with large number of states and multiple conical intersections. Weak dispersion inter-
actions and large number of degrees of freedom together make the geometry search dif-
fucult, but produce potential energy surfaces with a variety of distinct structures, both
minima and transition states. In this chapter, two of the numerous possible research
directions will be explored.
6.2 Conical intersections in ionized non-covalent
dimers: Benzene dimer cation revisited
It has been shown that the radiationless decay through the conical intersections between
the electronic states of the nucleobase dimers contributes to the DNA’s intrinsic stabil-
ity [1], pariticipates in the DNA charge transfer process [2–4] and can be responsible
for some mutations [4] (see Ref. 52 for the most recent review). For instance, based on
the calculations Merchan and coworkers [2,3] proposed the cooperative micro-hopping
113
mechanism of the hole transfer in DNA. According to this mechanism, the hole migra-
tion is a series of transitions between the intersecting electronic states of the nucleobase
dimers facilitated by the thermal fluctuations of the flexible DNA chain.
In connection with the CI theme, we revisited the familiar benzene dimer [5]. This
system was a subject of extensive theoretical [5–9] and experimental [10–14] investiga-
tion for several decades. However, not all of the questions have been answered yet.
In the previous study of the benzene dimer cation [5], the excited states and proper-
ties of the three isomers of the Bz+2 (thex-dispaced (XD) sandwich,y-displaced (YD)
sandwich and t-shaped) were investigated using EOM-IP-CCSD. The minimum corre-
sponds to the displaced isomers, which are nearly-degenerate, and the t-shaped cation
was estimated to lie 6 kcal/mol higher in energy. The calculated electronic spectrum of
the cation agrees well with the gas-phase [10–13] and condensed phase [14,15] experi-
ments: the position of the CR band at 1.35 eV was predicted with a remarkable 0.02 eV
accuracy. However, the theory underestimated the intensity of the secondary CR peak
at 1.07 eV in the experimental spectrum by more than two orders of magnitude, and the
reason for this was unclear. Based on the experimental observations [13], this feature
was assigned as one of the two CR transitions corresponding to the single isomer of
Bz+2 .
Motivated by discussion with Prof. Bally from the University of Fribourg, we con-
sidered three alternative benzene dimer cation structures: the two strongly-displaced
sandwich isomers (XSD and YSD, which are displaced along thex- andy-axis, respec-
tively) and the fused structure (FD) that were proposed in Ref. 82. The ground-state
geometries of XSD, YSD and FD were optimized at IP-CISD/6-31(+)G(d) level; the
XD, YD and TS structures were obtained previously [5] employing the IP-CCSD opti-
mization with the 6-31(+)G(d) basis. The optimized ground state geometries of the
six isomers of Bz+2 and the estimated energy gaps are presented in Fig. 6.1. Table 6.1
114
YDXD
XSDTS
FD
0.23/ 0.20 6.37 / 5.89 7.42 / 7.79
33.28 / 27.29
E, kcal/mol
YSD
4.43 / 3.80
Figure 6.1: The six optimized geometries of the benzene dimer cation and the cor-responding energy gaps calculated at the IP-CCSD(dT)/6-31(+)G(d) (italic) and IP-CCSD/6-311(+,+)G(d,p) (bold) levels of theory.
provides the ground state total energies calculated at three different levels of theory.
Table 6.2 summarizes the characteristic geometric parameters, which are explained in
Figure 6.2, for the six isomers. As follows from Table 6.2, the displacement cordi-
nate values for the XSD and YSD structure are more than 2A larger relative to the
moderately-displaced XD and YD structures. Surprisingly, the separation coordinate
and the distance between the centers of mass of the fragments are 0.2-0.4A smaller
for the XSD and YSD isomers relative to the XD and YD isomers, respectively. As
IP-CISD tends to overestimate the intermolecular separations relative to IP-CCSD by
0.2-0.3A the actual difference for moderately and strongly-displaced structures may be
even more pronounced. In the fused structure FD, the two covalent bonds are formed,
which can be seen from the smallh anddCOM values.
115
Table 6.1: The ground state total energies (in hartree) of the six isomers of Bz+2 calcu-
lated at three levels of theory: IP-CCSD/6-31(+)G(d), IP-CCSD(dT)/6-31(+)G(d) andIP-CCSD/6-311(+,+)G(d,p)+FNO(99.25%)
Isomer Ground StateEtotCCSD/6−31(+)G(d) Etot
CCSD(dT )/6−31(+)G(d) EtotCCSD/6−311(+,+)G(d,p)
XD X2Bg -462.717304 -462.910464 -462.727685
YD X2Bg -462.717660 -462.910781 -462.728058
TS X2B2 -462.705866 -462.898372 -462.716231
XSD X2Bu -462.707551 -462.901399 -462.717910
YSD X2Bu -462.710547 -462.904717 -462.720998
FD X2Au -462.664903 -462.867298 -462.675027
dCOM
Δ
h
Figure 6.2: The definitions of structural parameters for the benzene dimer cation. Thedistance between the centers of mass of the fragmentsdCOM , separationh and slidingcoordinates∆ are shown.
In accord with the previous study [5], the two lowest structures of Bz+2 are the nearly-
degenerate XD and YD sandwich isomers, which lie more than 7 kcal/mol below the TS
structure (see Fig. 6.1). Not surprisingly, the fused FD structure lies much higher in
energy, so we omit it from further consideration. However, the two strongly-displaced
116
Table 6.2: The characteristic geometric parameters of the six ground-state structures ofthe benzene dimer cation. The distances between the centers of mass of the fragmentsdCOM (in A), separationh (in A) and sliding coordinate∆ (in A) values are presented.
Isomer dCOM h ∆
XD 3.27 3.09 1.07
YD 3.29 3.10 1.10
TS 4.57 – –
XSD 3.01 2.91 3.16
YSD 2.81 2.77 3.22
FD 1.64 1.49 3.15
structures - XSD and YSD - were found to lie in between the sandwich and t-shaped
structures, the lowest one less than 4 kcal/mol apart from the XD and YD isomers. It
is unclear whether the XSD and YSD are the minima or transition states. Note that the
discussed energy differences are estimated at IP-CCSD/6-311(+)G(d,p) level. Our tests
showed that the effect of triple contributions is almost neglegible and changes the energy
differences by only 0.01-0.03 kcal/mol for four low-lying isomers and 0.17 kcal/mol for
FD structure. At the same time, increasing the basis set to 6-311(+)G(d,p) at IP-CCSD
level results in 0.02, 0.66, 0.45, 0.39 and 5.82 kcal/mol changes in energy differences
for XD, YSD, XSD, TS and FD isomers, respectively. Therefore, we expect the IP-
CCSD/6-311(+)G(d,p) estimates to be of better quality than IP-CCSD(dT)/6-31(+)G(d).
This finding shows that the PES of the benzene dimer cation (as well as other ionized
non-covalent dimers) is shallow and rugged. What consequences does it have for the
electronic structure?
Consider Figure 6.3, which depicts the evolution of the four lowest electronic states
of Bz+2 along thex- (top panel) andy- (bottom panel) displacement coordinates. The
corresponding singly-occupied MOs of the cation and the calculated enegy spacings (the
ground state of the XD and YD structures are chosen as the zero-level) are presented.
117
0.27 eV
0.51eV
1.28 eV
1.40 eV
0.86 eV
1.23 eV
1.25 eV
Bg
Bu
Ag
AuAu
Ag
Bg
Bu
Displacement along x axis
E, eV
0 eV
XD XSD
CI?
ΔE
E, eV
0.19 eV
1.07 eV
1.28 eV
1.43 eV
0.91 eV
1.25 eV
1.29 eV
Bg
Bu
Ag
Au
Au
Ag
Bg
Bu
Displacement along y axis
0 eV
ΔE
CI?
YD YSD
Figure 6.3: The evolution of the four lowest electronic states of the benzene dimer cationalong thex- (top panel) andy- (bottom panel) displecement coordinates calculated withIP-CCSD/6-31(+)G(d). Two moderately (XD, YD) and two strongly-displaced (XSD,YSD) fully-optimized ground-state structures were employed. The blue arrows depictthe CR transitions at four geometries and the dashed lines interconnect the related elec-tronic states.
118
The dashed lines connect the related electronic states in moderately and strongly-
displaced sandwich isomers; the blue arrows mark the CR transitions. As it appears,
the electronic states change the order along thex- andy- displacement coordinate. For
instance, in the XSD structure the states, when ordered by the increasing energy, appear
asX2Bu, 12Bg, 12Ag and12Au as opposed to theX2Bg, 12Ag, 12Bu and12Au order
in the XD isomer. This points to the presense of the conical intersections between the
surfaces, for example, the12Bg and12Bu states of thex-displaced structures; moreover,
the intersection point is likely to be located along thex-coordinate. Interestingly, the
optimization of the geometry of the excited12Bg state of XSD converges to the ground
state XD geometry. Analogously, in they-displaced structures, the CI point between
theX2Bg and12Bu states may exist along they-axis. In theC2h group theBg → Bu
transitions are allowed by symmetry, so the interconversion between the ground states of
moderately (XD, YD) and the corresponding strongly-displaced (XSD, YSD) structures
can occur.
These findings suggest an alternative explanation of the origin of the broad peak
at 1.07 eV observed in the gas-phase experiment. As the authors point out [13], the
two-photon ionization leads to a large excess of energy in the experimental system.
The estimate of the lowest IE of the benzene dimer is significantly lower than the 12
eV available to the system and is in the range of 8.59-8.79 eV for all the isomers [5].
Some of the energy dissipates in the evaporative cooling process, but it is still likely
that the hot ionized dimers are produced in this experiment. If the height of the barrier
for theX2Bg → X2Bu interconversion through the CI is significantly smaller than the
energy excess, the strongly-displaced structures will be populated at the experimental
conditions along with XD and YD. Therefore, four CR bands will be observed in the
spectrum — at 0.96, 1.10, 1.40 and 1.43 eV (see Fig. 6.3 and Tables 6.4 and 6.3) —
consistently with the experimental findings. The relative intensity of the two arising
119
Tabl
e6.
3:T
hesi
xlo
wes
tsym
met
ry-a
llow
edtr
ansi
tions
inth
eel
ectr
onic
spec
trum
ofth
ebe
nzen
edi
mer
catio
nat
the
XD
and
XS
Dop
timiz
edge
omet
ries.
Cal
cula
ted
with
IP-C
CS
D/6
-31(
+)G
(d).
XD
XS
D
Tra
nsiti
on∆E
,eV
<µ
2>
,a.u
.f
Tra
nsiti
on∆E
,eV
<µ
2>
,a.u
.f
X2B
g→
12B
u1.
280.
0036
0.00
01X
2B
u→
12B
g0.
590.
0055
0.00
00
X2B
g→
12A
u1.
406.
3050
0.21
68X
2B
u→
12A
g0.
9611
.152
20.
2619
X2B
g→
22B
u3.
320.
6052
0.04
93X
2B
u→
22A
g3.
560.
0001
0.00
00
X2B
g→
22A
u3.
740.
0040
0.00
04X
2B
u→
22B
g3.
640.
0000
0.00
00
X2B
g→
32B
u3.
800.
0057
0.00
05X
2B
u→
32A
g4.
280.
4044
0.04
24
X2B
g→
32A
u5.
960.
0003
0.00
00X
2B
u→
32B
g6.
040.
0001
0.00
00
120
Tabl
e6.
4:T
hesi
xlo
wes
tsym
met
ry-a
llow
edtr
ansi
tions
inth
eel
ectr
onic
spec
trum
ofth
ebe
nzen
edi
mer
catio
nat
the
YD
and
YS
Dop
timiz
edge
omet
ries.
Cal
cula
ted
with
IP-C
CS
D/6
-31(
+)G
(d).
YD
YS
D
Tra
nsiti
on∆E
,eV
<µ
2>
,a.u
.f
Tra
nsiti
on∆E
,eV
<µ
2>
,a.u
.f
X2B
g→
12B
u1.
280.
0029
0.00
01X
2B
u→
12B
g0.
730.
0115
0.00
02
X2B
g→
12A
u1.
436.
2174
0.21
84X
2B
u→
12A
g1.
1010
.615
70.
2871
X2B
g→
22B
u3.
340.
6055
0.04
95X
2B
u→
22B
g3.
580.
0000
0.00
00
X2B
g→
32B
u3.
760.
0069
0.00
06X
2B
u→
22A
g3.
700.
0024
0.00
02
X2B
g→
22A
u3.
820.
0034
0.00
03X
2B
u→
32A
g4.
390.
3794
0.04
09
X2B
g→
32A
u5.
960.
0005
0.00
01X
2B
u→
32B
g6.
090.
0002
0.00
00
121
features in 1.4-1.5 eV and 0.9-1.1 eV spectral regions will be determined by the ratio
of moderately- and strongly-displaced structures at experimental conditions rather than
the calculated intensities of the elementary transitions (which are similar for all CR
bands). The 0.14 eV spacing between the two lowest CR transitions even explains the
broadening of the experimental band at 1.07 eV.
Quite a few questions remain unanswered. Where is the PES crossing point located
and how large is the interconversion barrier? Are the XSD and YSD true minima or
transition states? What is the effect of the entropic contribution on the barriers and
energy gaps? The last point is particularly important when interpreting the results of
finite-temperature experiments, like the one discussed above. The DFT-D vibrational
analysis with theωB97X-D functional can address the latter two questions (for the
ground states). However, one should be careful as the harmonic approximation used
in frequency calculations is likely to be of limited accuracy. As of the former, using the
minimum-energy crossing point search procedure implemented in Q-Chem for EOM-
CC family of methods [16], we can locate the PES crossing point and estimate the barrier
of interconversion.
6.3 The effect of substituents in ionized non-covalent
dimers: Electronic structure and properties
The electronic structure and properties of the chemically-modified nucleobase dimers
is another promising research direction, which is attractive from both the fundamental
and the applied viewpoints. It was shown that the conductivity of the DNA decreases
sufficiently with the increase of the A-T base pair’s content [17–19]. This imposes the
restrictions on the sequence and composition of the DNA molecules that may be suc-
cessful candidates for molecular electronics applications. Another issue is the oxidative
122
degradation of guanine in the chain that is associated with the charge transport [20]. To
overcome these difficulties, synthetic analogs of the DNA can be used in the device con-
struction. In these analogs the target properties can be modified by the introduction of
substituents, like alkyl, halogen groups, additional aromatic rings or heteroatoms in the
”native” nucleobase structures. The latter approach was successfully used by Majima
and coworkers [21]. In their experimental study, the 7-Deazaadenine (Z) (i.e. adenine
with one of the N heteroatoms replaced by the C atom) was introduced in the DNA
sequence instead of the adenine. This increased the efficiency of the charge transport
more than two-fold relative to the original sequence. This effect was explained by the
smaller gap between the HOMOs of the ZT and GC base pairs as compared to AT and
GC. Okamoto and coworkers [20] used another approach, i.e. they extended the nucle-
obase aromatic system. The Benzodeazaadenine was incorporated in the DNA instead
of the native adenine nucleobase. The modified DNA samples exhibited a remarkably
high hole transport ability. The authors indicated that the orderedπ-stacking array, low
oxidation potentials of the nucleobases and suppressed oxidative degradation are the
three essential factors for the successfull design of the synthetic DNA nanowire.
To facilitate the search of promising synthetic DNA analogs, a systematic approach
is needed. A qualitative theory, which would be able to predict the effect of chemical
modifications on the electronic structure, ionization energies and states of the nucle-
obase and nucleobase clusters, would be of great value. We have already investigated the
effect of methylation on the ionized states and electronic structure of the monomer and
dimers of one of the nucleobases. The results showed that the qualitative trends for IEs
of the modified nucleobase can be predicted by classifying the introduced perturbation
as stabilizing or destabilizing for the corresponding ionized state. The simple analysis
of the molecular orbitals of the original nucleobase in conjuction with the qualitative
123
organic chemistry considerations (i.e. inductive and resonance effects, electron-donor
and electron-acceptor groups) can provide an insight.
An interesting question is whether or not the effect of substitutions can be extrap-
olated from the monomer to the dimer system. For instance, in the 1,3-dimethylated
uracils, the effect of methylation on the lowest IE of the dimer was comparable to that in
the monomer: -0.61 and -0.63 eV shifts in the first IE, respectively. For other states, the
methylation-related shifts were also similar (see Table 5.5), unless there was an exces-
sive electron density overlap in the methylated dimer attributed to the CH3 groups, e.g.
as for the22A1 and52A1 states, where theσCH MO component of one of the fragments
overlapped with thelp(O) component of the other. The DMO-LCFMO splittings of
states were also similar in the methylated and non-methylated dimers (0.37 vs. 0.35 eV,
respectively), again excluding the22A1 and52A1 states. Thus, for most states the DMO-
LCFMO overlap and the effect of substituents on the IEs are additive, so the electronic
structure of the substituted dimer cation can be extrapolated from the prototype dimer
using the substituted monomer results. In terms of the qualitative DMO-LCFMO frame-
work, the levels of modified dimers are just shifted up or down by constants equal to the
state shifts observed in the substituted monomer. Such extrapolation schemes can be
useful for approximate estimates when the full calculation is too expensive. It should be
noted, however, that the CH3 groups represent a relatively small perturbation, such that
the shapes of MOs and structures are similar for the methylated- and non-methylated
systems. It is likely that the introduction of strong electron-acceptors, like NO2 and
halogens, or bulk aromatic rings will significantly perturb the structure, MOs and the
states, so that such simplified considerations will be of limited value.
Back to the DNA nanowire design, according to the micro-hopping mechnanism pro-
posed by Merchan and coworkers [2], the hole transfer along the single DNA strand is a
series of hole hops betwen the pairs of adjacentπ-stacked nucleobases, which involves
124
the transitions through the conical intersections. How can we control the efficiency
of such process? First, the low-lying ionized states of the adjacent nucleobase dimers
should be nearly-degenerate. Second, there should exist a low-energy CI between the
PES of the two dimer systems (i.e. the CI on the tetramer surface along the separation
coordinate of the dimers).
Consider Table 6.5 presenting some of the available theoretical estimates of the first
VIE of the DNA and RNA nucleobases and stacked nucleobase dimers. The first VIEs
Table 6.5: Theoretical estimates of the lowest VIE (in eV) of the nucleobase monomersandπ-stacked dimers.
Monomers Stacked dimers
VIE, eV VIE, eV
A 8.37a, 8.37b A2 8.18b
T 9.07a, 9.13b AT2 8.28b
C 8.73a T2 8.78b
G 8.09a U2 9.21c
U 9.42a, 9.55ca Empirically corrected (IPEA=0.25) CASPT2/ANO-L 431/21 from Ref. 22.
b The EOM-IP-CCSD/cc-pVTZ from Ref. 23. For dimers, the extrapolation was used.c The EOM-IP-CCSD/cc-pVTZ from Ref. 24. For dimers, the extrapolation was used.
of the DNA bases lie in the 8.1 - 9.1 eV range, with guanine and adenine ionizing at
lower energies than thymine and cytosine [22, 23]. In RNA, thymine is replaced with
uracil that extends this range to 9.55 eV [24]. The stacked dimer data is incomplete,
and includes three homodimer (U2, T2, A2) and one heterodimer (AT) structure (i.e 4
structures out of 15 possible) [23, 24]. For effective CT, we need to tighten the lowest
VIE range. From the DMO-LCFMO considerations, it follows that homodimers com-
posed from the hard-to-ionize thymine and uracil should affect the CT in DNA and RNA
the most (because for the heterodimers, like AT or TC, VIEs are expected to be lower).
The synthetic RNAs with dimethylated uracils could be one of the possible solutions.
125
However, in such case the double-helix structure of RNA could be perturbed, as the AU
hydrogen-bonding interactions will be suppressed. In the DNA, thymine could also be
methylated at one of the nitrogens to decrease its VIE. Alternatively, another approach
can be exploited, in which the VIEs of the lower-ionizing bases - guanine and adenine
- are altered by the introduction of the electron-acceptors like halogen groups (or NO2).
Therefore, the ionized methylated thymine dimer and halogen-substituted adenine could
be an intriguing target for future studies.
Of course, the above discussion only applies to the single-strand DNA charge trans-
port. In the DNA and RNA double-helices the charge-trapping by the proton-transfer
and other mechanisms affectinging CT need to be considered. Therefore, it would be of
interest to investigate the effect of substituents on the symmetric and proton-transfered
H-bonded structures and the barriers of the proton transfer.
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Appendix A
EOM-IP optimized geometries of Bz+2
X-displaced isomer (XD)
Comment: Ground electronic state (X2Bg) optimized with IP-CCSD/6-31(+)G(d) under
C2h symmetry constraint,ENN=647.863144.Atom x y zC 1.577051 -0.344668 -1.391098H 1.596237 -0.355418 -2.480441C 2.242307 0.695416 -0.691513H 2.753735 1.478322 -1.248242C 2.242307 0.695416 0.691513H 2.753735 1.478322 1.248242C 1.577051 -0.344668 1.391098H 1.596237 -0.355418 2.480441C 0.955447 -1.401972 0.694504H 0.500928 -2.220563 1.249090C 0.955447 -1.401972 -0.694504H 0.500928 -2.220563 -1.249090C -2.242307 -0.695416 0.691513H -2.753735 -1.478322 1.248242C -1.577051 0.344668 1.391098H -1.596237 0.355418 2.480441C -0.955447 1.401972 0.694504H -0.500928 2.220563 1.249090C -0.955447 1.401972 -0.694504H -0.500928 2.220563 -1.249090C -1.577051 0.344668 -1.391098H -1.596237 0.355418 -2.480441C -2.242307 -0.695416 -0.691513H -2.753735 -1.478322 -1.248242
139
Y-displaced isomer (YD)
Comment: Ground electronic state (X2Bg) optimized with IP-CCSD/6-31(+)G(d) under
C2h symmetry constraint,ENN=648.359009.Atom x y zC -2.375370 -0.802427 0.000000H -3.000807 -1.692604 0.000000C -1.970007 -0.221982 1.202903H -2.275235 -0.658658 2.152860C -1.180373 0.964775 1.203183H -0.923839 1.432362 2.152829C -0.826193 1.574414 0.000000H -0.257481 2.501418 0.000000C -1.180373 0.964775 -1.203183H -0.923839 1.432362 -2.152829C -1.970007 -0.221982 -1.202903H -2.275235 -0.658658 -2.152860C 1.970007 0.221982 -1.202903H 2.275235 0.658658 -2.152860C 2.375370 0.802427 0.000000H 3.000807 1.692604 0.000000C 1.970007 0.221982 1.202903H 2.275235 0.658658 2.152860C 1.180373 -0.964775 1.203183H 0.923839 -1.432362 2.152829C 0.826193 -1.574414 0.000000H 0.257481 -2.501418 0.000000C 1.180373 -0.964775 -1.203183H 0.923839 -1.432362 -2.152829
140
T-shaped isomer (TS)
Comment: Ground electronic state (X2B2) optimized with IP-CCSD/6-31(+)G(d) under
C2v symmetry constraint,ENN=600.842133.Atom x y zC 0.000000 -1.399973 -2.278360H 0.000000 -2.488962 -2.299023C -1.217379 -0.699252 -2.285733H -2.158362 -1.246985 -2.316611C 1.217379 -0.699252 -2.285733H 2.158362 -1.246985 -2.316611C -1.217379 0.699252 -2.285733H -2.158362 1.246985 -2.316611C 1.217379 0.699252 -2.285733H 2.158362 1.246985 -2.316611C 0.000000 1.399973 -2.278360H 0.000000 2.488962 -2.299023C 0.000000 0.000000 0.907763C 1.244445 0.000000 1.609353H 2.172257 0.000000 1.041906H 0.000000 0.000000 -0.174517C 1.244368 0.000000 2.986650H 2.173847 0.000000 3.551289C 0.000000 0.000000 3.681626H 0.000000 0.000000 4.770875C -1.244368 0.000000 2.986650H -2.173847 0.000000 3.551289C -1.244445 0.000000 1.609353H -2.172257 0.000000 1.041906
141
Strongly x-displaced isomer (XSD)
Comment: Ground electronic state (X2Bu), optimized with IP-CISD/6-31(+)G(d) under
C2h symmetry constraint,ENN=614.903162.Atom x y zC 1.150552 0.969722 0.707571H 0.419080 1.555055 1.234935C 2.136379 0.279022 1.407161H 2.149267 0.295308 2.481720C 3.108690 -0.404995 0.705527H 3.883640 -0.932554 1.232270C 3.108690 -0.404995 -0.705527H 3.883640 -0.932554 -1.232270C 2.136379 0.279022 -1.407161H 2.149267 0.295308 -2.481720C 1.150552 0.969722 -0.707571H 0.419080 1.555055 -1.234935C -1.150552 -0.969722 -0.707571H -0.419080 -1.555055 -1.234935C -2.136379 -0.279022 -1.407161H -2.149267 -0.295308 -2.481720C -3.108690 0.404995 -0.705527H -3.883640 0.932554 -1.232270C -3.108690 0.404995 0.705527H -3.883640 0.932554 1.232270C -2.136379 -0.279022 1.407161H -2.149267 -0.295308 2.481720C -1.150552 -0.969722 0.707571H -0.419080 -1.555055 1.234935
142
Strongly y-displaced isomer (YSD)
Comment: Ground electronic state (X2Bu) optimized with IP-CISD/6-31(+)G(d) under
C2h symmetry constraint,ENN=617.531975.Atom x y zC -0.948544 1.036858 0.000000H -0.094961 1.691125 0.000000C -1.541681 0.660690 1.221958H -1.103733 0.987375 2.147873C -2.691245 -0.097191 1.218022H -3.158457 -0.383562 2.142498C -3.265501 -0.478245 0.000000H -4.169692 -1.060908 0.000000C -2.691245 -0.097191 -1.218022H -3.158457 -0.383562 -2.142498C -1.541681 0.660690 -1.221958H -1.103733 0.987375 -2.147873C 0.948544 -1.036858 0.000000H 0.094961 -1.691125 0.000000C 1.541681 -0.660690 1.221958H 1.103733 -0.987375 2.147873C 2.691245 0.097191 1.218022H 3.158457 0.383562 2.142498C 3.265501 0.478245 0.000000H 4.169692 1.060908 0.000000C 2.691245 0.097191 -1.218022H 3.158457 0.383562 -2.142498C 1.541681 -0.660690 -1.221958H 1.103733 -0.987375 -2.147873
143
Fused isomer (FD)
Comment: Ground electronic state (X2Au), optimized with IP-CISD/6-31(+)G(d) under
C2h symmetry constraint,ENN=656.211616.Atom x y zC -0.561504 0.600372 0.764805H -0.141109 1.492488 1.205667C -1.817295 0.192585 1.428685H -1.835554 0.189867 2.505310C -2.900883 -0.171726 0.725565H -3.807561 -0.444572 1.235457C -2.900883 -0.171726 -0.725566H -3.807561 -0.444572 -1.235457C -1.817295 0.192585 -1.428685H -1.835554 0.189867 -2.505310C -0.561504 0.600372 -0.764805H -0.141109 1.492488 -1.205667C 0.561504 -0.600372 0.764805H 0.141109 -1.492488 1.205667C 1.817295 -0.192585 1.428685H 1.835554 -0.189867 2.505310C 2.900883 0.171726 0.725565H 3.807561 0.444572 1.235457C 2.900883 0.171726 -0.725566H 3.807561 0.444572 -1.235457C 1.817295 -0.192585 -1.428685H 1.835554 -0.189867 -2.505310C 0.561504 -0.600372 -0.764805H 0.141109 -1.492488 -1.205667
144
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