AB INITIO CALCULATIONS OF STRUCTURE AND …iopenshell.usc.edu/people/thesis-dolgikh.pdf · the...

AB INITIO CALCULATIONS OF STRUCTURE AND IONIZATION ENERGIES

OF THE FIVE GUANINE TAUTOMERS

by

Stanislav Aleksandrovich Dolgikh

A Dissertation Presented to theFACULTY OF THE GRADUATE SCHOOL

UNIVERSITY OF SOUTHERN CALIFORNIAIn Partial Fulfillment of the

Requirements for the DegreeMASTER OF SCIENCE

(CHEMISTRY)

August 2009

Copyright 2009 Stanislav Aleksandrovich Dolgikh

Acknowledgments

I’d like to express my deep thanks to my graduate adviser Prof. Anna I. Krylov

for mentoring me throughout my research. It was a great pleasure to be in her group.

Not only did we do great science, but also we had lots of fun during our regular group

”get together” events.

Also I’d like to thank my senior colleges, Dr. Ksenia Bravaya and Dr. Arik

Landau, for their guidance throughout the project and useful advice I get from them.

Special thanks go to Vadim Mozhayskiy for his willingness to help and always nice

attitude to everybody and to Dr. Kadir Diri for keeping relaxed and fun atmosphere

in our group.

ii

Abstract

Ionization of guanine might play a key role in radiative and oxidative damage of

DNA following the ionization of latter. Recent VUV photoionization experiment re-

ports accurate ionization energies (IEs), however, the interpretaiton of the spectrum

is challenging due to variety of tautomers present in the experimental beam. In the

present paper we theoretically investigated ionization processes of the five most stable

guanine tautomers. The thermodynamic distribution at the temperature of the ex-

periment has been evaluated, indicating the relative populations in the experimental

beam. The equilibrium geometries of the neutral and cation guanine tautomers have

been calculated and compared. Structural changes upon ionization turned out to be

similar for all the tautomers. Calculated vertical and adiabatic IEs show close agree-

ment with measured experimental data. Molecular orbitals (MOs) of the tautomers

have also been investigated. MO analysis shows the order and character of the lowest

ionized states, demonstrating the importance of correlation in the right description

of the electronic structure.

iii

Contents

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii

List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

Chapter 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Chapter 2. Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.1. Model systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.2. Computational methods . . . . . . . . . . . . . . . . . . . . . . . . . 3

Chapter 3. Results and Discussion . . . . . . . . . . . . . . . . . . . . 5

3.1. Relative stabilities and dipole moments of the tautomers . . . . . . . 5

3.2. Populations in the experimental beam . . . . . . . . . . . . . . . . . 8

3.3. VIEs and the respective MOs of the tautomers . . . . . . . . . . . . 10

3.4. Geometry relaxation and AIEs . . . . . . . . . . . . . . . . . . . . . 17

3.5. Comparison to the experiment . . . . . . . . . . . . . . . . . . . . . 22

Chapter 4. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

Appendix:

Appendix A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

iv

List of Tables

3.1 Relative ground state energies ∆E, (kcal/mol) and dipole moments

µ, (Debye) of the five most stable guanine tautomers . . . . . 6

3.2 Thermochemistry data for the guanine tautomers(ωB97X/6-

31+G(d,p)// ωB97X/6-31+G(d,p)) . . . . . . . . . . . . . . 9

3.3 VIEs, EOM-IP-CCSD/FNO, extrapolation to the cc-pVTZ limit.

(R1) denotes the leading EOM amplitude, Orb denotes the orbital

from which an electron is removed, KT is a Koopmans’ theorem

IE; HOMO is denoted by H, HOMO-1 by H-1 etc. . . . . . . . 16

3.4 First AIE and VIE, EOM-IP-CCSD/FNO, extrapolation to the

cc-pVTZ limit. ∆ R=VIE-AIE . . . . . . . . . . . . . . . . . 18

1.1 Total energies,nuclear repulsion and CCSD, (hartree) using FNO

extrapolation to the cc-pVTZ . . . . . . . . . . . . . . . . . . 29

1.2 Geometry of the neutral 7H-AH-G(RN1) tautomer, RI-MP2/ext-

cc-pVTZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

1.3 Geometry of the cation 7H-AH-G(RN1) tautomer, ωB97/ext-cc-

pVTZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30


cc-pVTZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30


pVTZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

v


cc-pVTZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31


pVTZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

1.8 Geometry of the neutral 7H-1H-AO-G tautomer, RI-MP2/ext-

cc-pVTZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

1.9 Geometry of the cation 7H-1H-AO-G tautomer, ωB97/ext-cc-

pVTZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

1.10 Geometry of the neutral 9H-1H-AO-G tautomer, RI-MP2/ext-

cc-pVTZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

1.11 Geometry of the cation 9H-1H-AO-G tautomer, ωB97/ext-cc-

pVTZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

vi

List of Figures

2.1 Chemical structures of the five most stable guanine tautomers:

1, 7H-1H-AO-G; 2, 9H-1H-AO-G; 3, 9H-AH-G(RN1); 4, 9H-AH-

G(RN7) ; 5, 7H-AH-G(RN1) . . . . . . . . . . . . . . . . . . 4

3.1 Relative energies (EOM-IP-CCSD/cc-pVTZ) and dipole moments

(RI-MP2/ext-cc-pVTZ) of guanine tautomers . . . . . . . . . 7

3.2 Six lowest ionized states with the respective VIEs and the

corresponing MOs of the five most stable guanine tautomers . 12

3.3 Comparison of VIEs and the characters of ionized states computed

by EOM-IP-CCSD and Koopmans’ theorem (HF) methods.

Ionized states are labeled by the character of the corresponding

MO(π, σ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.4 First two ionized states and the corresponding MOs for the five

guanine tautomers . . . . . . . . . . . . . . . . . . . . . . . . 14

3.5 Third to sixth ionized states and the corresponding MOs of the

five guanine tautomers . . . . . . . . . . . . . . . . . . . . . . 15

3.6 Geometry changes of the 7H-1H-AO-G upon ionization. Bond

lenghts are in A, angles are in degrees. Geometry of the neutral

is computed by RI-MP2/ext-cc-pVTZ, geometry of the cation is

computed by ωB97/ext-cc-pVTZ . . . . . . . . . . . . . . . . 19

3.7 Geometry changes of the 9H-1H-AO-G upon ionization. Bond


vii



3.8 Geometry changes of the 9H-AH-G(RN1) upon ionization. Bond












3.11 PES1,10 compared with the computed AIEs and VIEs of different

tautomers. AIEs are the lines below 8.0 eV, the rest are the

VIEs. AIEs and VIEs corresponding to different tautomers are

marked by different colors and line patterns. The top curve is

the pseudo-PES obtained by Ahmed and co-workers,1 the bottom

curve is PES obtained by LeBreton and co-workers.10 Calculated

AIEs and VIEs were computed by EOM-IP-CCSD/cc-pVTZ . 24

viii

Chapter 1

Introduction

DNA and RNA nucleobases have attracted considerable attention lately.5,9, 12 For-

mation of a cation-radical following ionization is the first step in an oxidative and

radiative damage of DNA. Such processes are relevant to cancerogenesis, mutagene-

sis and aging. Among all the nucleobases constituting DNA and RNA, guanine has

the lowest adiabatic and vertical IEs that makes it the most sucseptible to oxida-

tion. Therefore, guanine is also the most likely candidate to be ionized by ultraviolet

radiation. Thus, an investigation of ionization processes in guanine might help to

understand a mechanism of an oxidative and radiative damage of DNA.

IEs can be obtained from photoelectron spectra (PES).7 A number of experimental

and theoretical studies of guanine have been performed over the last decades.4,7, 8, 10,11,14,15,17

Due to complexity of the problem it is difficult to interpret the experiments in realistic

enviroment, and the investigation of guanine in a gas phase is important prerequisite.

Recently, Ahmed with co-workers17 investigated two different methods of preparing

guanine in the gas phase, laser desorption and thermal vaporization, and recorded

the photoionization effiecency (PIE) spectra. Differentiation of PIE yields a pseudo-

photoelectron spectra (PES)2 that contains information about IEs. Moreover it con-

tains useful information about tautomers present in the beam. In this work, the PES

has been obtained using thermal vaporization.1 The assignment of the peaks in the

recorded spectra and the interpretation of the results requires theoretical calculations.

Adiabatic IEs (AIEs) and vertical IEs (VIEs) for a number of guanine tautomers have

been computed before.4,11,14,15,17 Dolgounitcheva et al. calculated first 13 VIE for 5

lowest guanine tautomers by using electron propagator theory.4 AIE and first VIE

1

for eight lowest energy tautomers computed by DFT at B3LYP level were reported

by Ahmed and co-workers;17 AIE and first VIE were also calculated by Merchan for

only one tautomer, the biologically relevant form, by a variety of methods: HF, MP2,

B3LYP, CCSD, CCSD(T), CASPT2, and the results were compared.14 The first VIE

for several tautomers have also been reported by Marian and Shukla.11,15 Overall,

the IEs values in the literature vary by more than 0.3 eV. The goal of our study

was to compute AIEs and VIEs of tautomers which are likely to be present in the

experiment using high level theory. We also explore how tautomerism affects the

electronic structure of guanine and its IEs. Geometry changes upong ionization were

also examined. In addition, this work presents equilibrium geometries of different

tautomers, their dipole moments and relative energies.

2

Chapter 2

Methods

2.1. Model systems

There are 15 tautomeric forms of guanine, and many of them have multiple con-

formations.11 Here we focus only on the tautomers that are likely to be present in

the experimental beam. 5% population threshold with respect to the most stable

tautomer is used as a criterion for selecting the tautomers for the calculations. Only

the lowest energy tautomers that are within 4.2 kcal/mol in energy satisfy this crite-

rion at the experimental temperature equal 440 ◦C. Several papers have been revised

for selecting the tautomers fitting the specified energetic threshold.11,15,17 According

to them, the following 5 tautomers have been selected for the investigation: 7H-

1H-AO-G , 9H-1H-AO-G , 9H-AH-G(RN1) , 9H-AH-G(RN7) , 7H-AH-G(RN1) (see

Figure 2.1).

2.2. Computational methods

All calculations were performed with the Q-Chem ab initio package.16 The geome-

tries of the neutral molecules of the five most stable guanine tautomers were optimized

with MP2 using resolution-of-identity technique (RI-MP2) with an extended cc-pVTZ

basis set (ext-cc-pVTZ) and the cc-pVTZ auxilary basis set. The ext-cc-pVTZ basis

set was derived by adding s and p diffuse functions for the second row elements and

an s function for hydrogen to the original cc-pVTZ basis.8 The exponents of the

diffuse functions were taken from the 6-311(2+,+)G basis set.8 The geometries of

the cations were optimized using Density Functionlal Theory (DFT) with the ωB97

functional3 and the ext-cc-pVTZ basis set. This functional was chosen because it

3

Figure 2.1: Chemical structures of the five most stable guanine tautomers: 1, 7H-1H-AO-G; 2, 9H-1H-AO-G; 3, 9H-AH-G(RN1); 4, 9H-AH-G(RN7) ; 5, 7H-AH-G(RN1)

had demonstrated an improved performance in geometry optimization for open shell

species and cations in benchmark calculations.3 The ground state energies and VIEs

were computed by EOM-CCSD/cc-pVTZ. To reduce computational cost, frozen nat-

ural orbitals (FNO) approach with an extrapolation to the full virtual space (FVS)

limit has been employed.8 FNO calculations were performed with 99%, 99.15 %,

99.3% and 99.45% recovery of population of the orbitals. Then data for each VIE

and ground state energy were linearly fitted and extrapolated to 100 % recovery of the

population. AIEs were computed by taking the difference between the extrapolated

ground state energies of the cations and the neutrals for each tautomer.

Core electrons in all calculations were frozen. The RI technique has been used in

integral transformations in EOM-CCSD with the cc-pVTZ auxilary basis set.

4

Chapter 3

Results and Discussion

3.1. Relative stabilities and dipole moments of the tau-

tomers

Table 3.1 and Figure 3.1 present relative energies and dipole moments of the

tautomers. Subject to small differencies, RI-MP2 and CCSD methods agree with

each other on the energetic ordering of the tautomers. Both methods predict that

the 7H-1H-AO-G tautomer is the most stable one. The next three tautomers 9H-

1H-AO-G , 9H-AH-G(RN1) and 9H-AH-G(RN7) have been found to be higher by

∼ 1.4 kcal/mol according to the CCSD calculations. These three tautomers should

be considered degenerate because the computed energy differencies are too small and

the present level of accuracy does not allow for distinguishing between them. The

7H-AH-G(RN1) tautomer turned out to be 4.8 kcal/mol higher than the most stable

7H-1H-AO-G form; that makes it the highest in energy among all the tautomers

studied here.

The 9H-1H-AO-G tautomer has the largest dipole moment and as seen from Fig-

ure 3.1, the 7H-1H-AO-G has the smallest dipole moment. Having the largest dipole

moment the 9H-1H-AO-G tautomer is expected to have the strongest interaction with

polar molecules of water in biological environment. Given this interaction, along with

already small energy gap between the 9H-1H-AO-G and 7H-1H-AO-G tautomers, the

9H-1H-AO-G form becomes the most stable and dominant in biological systems15

and is often reffered to as biologically relevant form. Similar effect may play a role

5

Table 3.1: Relative ground state energies ∆E, (kcal/mol) and dipole moments µ,(Debye) of the five most stable guanine tautomers

∆E

Tautomers RI-MP2/ext-cc-pVTZCCSD/cc-pVTZ

extrapolatedµ,

RI-MP2/ext-cc-pVTZ7H-1H-AO-G 0 0 1.869H-1H-AO-G 0.6 1.4 6.30

9H-AH-G(RN1) 0.5 1.3 3.029H-AH-G(RN7) 0.7 1.4 3.817H-AH-G(RN1) 3.4 4.8 4.22

when dimers are formed, and the dipole moments might be determening factors in

the relative stabilities of the guanine dimers as well.

The structure of a tautomer obviously affects the magnitude and orientation of

a dipole moment. For example, a transition from an enol- to a keto- form usually

leads to an increase of the dipole moment, and upon a transition from both the 9H-

AH-G(RN7) and 9H-AH-G(RN1) guanine tautomers to the 9H-1H-AO-G form we

observe ∼ 2.5 and ∼ 3.3D dipole moment change respectievly. However, the position

of hydrogen attached to N in the imidazole ring of guanine has much greater influence

on the dipole moment. Not only does it affect the magnitude of the dipole moment

but it even changes its orientation. This is indicated by the fact that the orientation of

dipole moments in the 9H-1H-AO-G , 9H-AH-G(RN1) and 9H-AH-G(RN7) tautomers

of guanine with H attached to the N9 atom is almost opposite to that in 7H-1H-AO-

G and 7H-AH-G(RN1) forms in which H is attached to the N7 nitrogen in imidazole

ring.

6

Figure 3.1: Relative energies (EOM-IP-CCSD/cc-pVTZ) and dipole moments (RI-MP2/ext-cc-pVTZ) of guanine tautomers

7

3.2. Populations in the experimental beam

Calculated relative energies (see Table 3.1) suggest that guanine should be present

as a mixture of tautomers in the gas phase. However, comparison of electronic en-

ergies does not give a full picture on relative populations under thermal equilib-

rium conditions. Since relative populations are determined by Gibbs free energy,

one should take into account enthalpy and entropy contributions. We estimated

those, as well as the free energy differences between the five tautomers, using Rigid

Rotator-Harmonic Oscillator-Ideal Gas (RR-HO-IG) approximation at the standard

conditions (T=298.15 ◦K, p=1 atm). The free energy difference between tautomers

(∆G0), which is the free energy for the tautomerization reaction can be expressed as

follows:

∆G0 = ∆H0 − T ·∆S0

where ∆H0 (∆S0) is tautomerization reaction enthalpy (entropy), including vibra-

tional, translational and rotational contributions. ∆H0 also accounts for the elec-

tronic energy difference between the tautomers. We have calculated the relative

Gibbs free energy at 298.15 ◦K for all the tautomers and the results are presented

in Table 3.2. We found out that enthalpy and entropy for all five tautomers are

rather similar and the relative ordering drawn from the comparison of pure electronic

energies has not changed. The thermal distribution of tautomers in the molecular

beam at 298.15◦K and at temperature of the experiment equal 713.15 ◦K has also

been computed (see Table 3.2). First four low-energy tautomers are expected to

have similar populations (of the same order). Since having significantly higher Gibbs

free energy, the fifth tautomer (7H-AH-G(RN1) ) is expected to be present only as

a small fraction. Thus, the 7H-AH-G(RN1) tautomer is not likely to be observed in

the experiment.

Although our estimates provide some insight about relative populations at the

thermal conditions, however it is not clear if the populations in the beam can be

8

Table 3.2: Thermochemistry data for the guanine tautomers(ωB97X/6-31+G(d,p)//ωB97X/6-31+G(d,p))

7H-1H-AO-G 9H-1H-AO-G 9H-AH-G(RN1) 9H-AH-G(RN7) 7H-AH-G(RN1)H298◦K Enthalpy, 80.6 80.5 80.5 80.5 80.4

kcal/molS298◦K Entropy, 88.534 88.565 87.670 87.766 88.000

cal/(mol·K)∆E, kcal/mol 0 1.4 1.3 1.4 4.8

∆G298◦K , kcal/mol 0 1.3 1.5 1.5 4.8Population 1 0.11 0.08 0.08 � 0.01(298.15 ◦K)Population 1 0.40 0.35 0.35 0.03

(Texp = 713.15 ◦K)

treated using Boltzmann distribution as several non-equilibrium steps may be in-

volved (fast heating followed by cooling down applied to the sample). For example,

the lowest barrier to an intramolecular H-shift was estimated to be no less than

35 kcal/mol.4 Therefore, tautomerization is not allowed at the conditions of the gas

phase experiment and thermodynamic equilibrium can not be reached. Consequently,

the actual distribution in the molecular beam might be different from the calculated

one. Most likely, the real distribution is defined by the initial populations in the

probe from which guanine is evaporated.

9

3.3. VIEs and the respective MOs of the tautomers

To model PES provided by Ahmed and co-workers,17 we calculated VIEs of the five

tautomers. The results for the first seven ionization levels are presented in Table 3.3

and visualized in Figure 3.4, Figure 3.2, Figure 3.5. The leading EOM amplitude

(R1) corresponding to the orbital from which an electron is removed are also given in

the table. HOMO is denoted as H, the next lower energy orbital HOMO-1 is denoted

H-1 etc. For comparison, Koopmans’ theorem (KT ) IEs are also provided.

The first VIE is almost the same for all the tautomers and equal ∼ 8.1 eV except

for the 7H-1H-AO-G which has VIE 0.1 eV higher. However, this trend does not hold

for higher ionization levels. Although most ionized states are of single determinant

character, some states are mixed, as observed for the 2nd and 3rd ionizations of the

9H-1H-AO-G , the 4th, 5th and 6th ionizations of the 9H-AH-G(RN1) and 4th and 5th

ionizations of the 9H-AH-G(RN7)

Electronic states of the ionization levels have also been investigated. Six HOMOs

for all the tautomers have been calculated and are represented on Figure 3.2. Gener-

ally, all the tautomers, except 9H-1H-AO-G and 9H-AH-G(RN7) forms that are dis-

cussed later on, have the following order of the orbitals being ionized: π1, σ1, π2, σ2, π3

and π4. The orbitals computed at both EOM-CCSD and HF levels are compared on

Figure 3.3 for 7H-1H-AO-G and 9H-AH-G(RN1) forms. Not only does HF level give

estimations of the ionization energies that are off by ∼ 2 eV comparing to EOM-

CCSD for higher level ionizations, but it even messes up the order of the orbitals

ionized. Also, the order of the ionized orbitals given by HF is different for keto- and

enol- forms of guanine. As one can see from Figure 3.3 σ2 and π4 orbitals at HF level

are interchanged in 7H-1H-AO-G tautomer comparing to 9H-AH-G(RN1) ; at the

same time in EOM-CCSD calculations the order of the orbitals is the same for both

keto- and enol-tautomers. That means the correction given by EOM-CCSD to the

HF ionization energy is different for different orbitals. Indeed, as we found out, the

π1 level is corrected by 0.1-0.2 eV, π2 level is corrected by 0.6-0.9 eV, π3 and π4 are

10

corrected by 1-1.3 eV and both σ1 and σ2 ionization levels are corrected by 1.7-2 eV

with EOM-CCSD method. That explains why the σ2 orbital in 9H-AH-G(RN1) tau-

tomer that is higher in energy than π4 at HF level appears in the right place before

π3 and π4 orbitals at EOM-CCSD level as well as it does in 7H-1H-AO-G tautomer.

Orbitals corresponding to first two ionization levels are shown in Figure 3.4. First

ionized state is derived from the π1 orbital (HOMO) which has the same character for

all the tautomers. The orbital corresponding to the second ionized state is denoted σ1

and is HOMO-2 which, in keto-tautomers, has some electron density on oxygen, the

most electronegative atom in guanine. It might be the reason why second ionization

energy is higher for keto-tautomers (see Figure 3.4). The MOs for higher ionization

states are compiled in Figure 3.5. As it mentioned above, the third ionized state has

π character and presented by π2 orbital for all the tautomers except 9H-1H-AO-G . In

the 9H-1H-AO-G tautomer the states dominated by π2 and σ2 orbitals change their

relative order. The third state is a mix of σ2 (HOMO-4), which is dominant, and

HOMO-2 in 9H-1H-AO-G tautomer. That might lead to alternating the energy of

the states. As a consequence of alternating the energy the interchange of the order of

the states could arise. In 9H-AH-G(RN7) the states dominated by σ2 and π3 orbitals

are also interchanged that again might be explained by the mixed character of those

states.

11

8.06 eV

9.53 eV9.68 eV

10.55 eV10.67 eV

11.08 eV

9H-AH-G(RN1) 9H-AH-G(RN7)

8.08 eV

9.48 eV

9.69 eV

10.63 eV10.73 eV

11.20 eV

7H-AH-G(RN1)

8.07 eV

9.41 eV9.56 eV

10.42 eV

10.64 eV

11.18 eV

VIE

, eV

8.19 eV

9.83 eV

9.97 eV

10.28 eV

10.60 eV

11.02 eV

7H-1H-AO-G

8.05 eV

9.76 eV

10.20 eV

10.04 eV

10.50 eV

11.18 eV9H-1H-AO-G

VIE

, eV

Figure 3.2: Six lowest ionized states with the respective VIEs and the corresponingMOs of the five most stable guanine tautomers

12

8.19 eV

9.83 eV9.97 eV

10.28 eV10.60 eV

11.42 eV

8.06 eV

9.53 eV9.68 eV

10.55 eV10.67 eV11.08 eV

σ1

8.35 eV

10.61 eV

11.67 eV11.95 eV12.25 eV12.60 eV

8.14 eV

10.50 eV

11.24 eV

11.92 eV12.05 eV12.46 eV

π1

π2

π3

π4

σ2

σ1

π1

π2

π3π4

σ2

π1

σ1

π2

σ2

π3

π4

π1

σ1

π2

σ2

π3π4

VIE

,eV

7H-1H-AO-G 9H-AH-G(RN1)

EOM-CCSD EOM-CCSDHF HF

Figure 3.3: Comparison of VIEs and the characters of ionized states computed byEOM-IP-CCSD and Koopmans’ theorem (HF) methods. Ionized states are labeledby the character of the corresponding MO(π, σ)

13

7H-1H-AO-G9H-AH-G(RN1) 9H-AH-G(RN7)7H-AH-G(RN1) 9H-1H-AO-G

π1

σ1

VIE

, eV

Figure 3.4: First two ionized states and the corresponding MOs for the five guaninetautomers

14

7H-1H-AO-G9H-AH-G(RN1) 9H-AH-G(RN7)7H-AH-G(RN1) 9H-1H-AO-G

π2

π3

π4

σ2

π4

π3

π2

σ2

VIE

, eV

Figure 3.5: Third to sixth ionized states and the corresponding MOs of the fiveguanine tautomers

15

Table 3.3: VIEs, EOM-IP-CCSD/FNO, extrapolation to the cc-pVTZ limit. (R1)denotes the leading EOM amplitude, Orb denotes the orbital from which an electronis removed, KT is a Koopmans’ theorem IE; HOMO is denoted by H, HOMO-1 byH-1 etc.

7H-1H-AO-G 9H-1H-AO-G 9H-AH-G(RN1) 9H-AH-G(RN7) 7H-AH-G(RN1)VIE KT VIE KT VIE KT VIE KT VIE KT

(R1) Orb (R1) Orb (R1) Orb (R1) Orb (R1) Orb8.19 8.35 8.05 8.11 8.06 8.14 8.08 8.19 8.07 8.30

(0.96) H (0.96) H (-0.96) H (-0.96) H (0.96) H9.83 11.67 9.76 11.65 9.53 11.24 9.48 11.21 9.41 11.13

(0.93) H-2 (0.90) H-2 (0.95) H-2 (0.96) H-2 (0.95) H-2(0.31) H-4

9.97 10.61 10.04 11.97 9.68 10.50 9.69 10.53 9.56 10.12(0.94) H-1 (0.89) H-4 (0.95) H-1 (-0.95) H-1 (0.95) H-1

(0.31) H-210.28 12.25 10.20 11.13 10.55 12.46 10.63 11.89 10.42 12.38

(0.92) H-4 (0.94) H-1 (-0.89) H-5 (-0.73) H-3 (-0.92) H-5(0.33) H-3 (-0.59) H-5

10.60 11.95 10.50 11.70 10.67 11.92 10.73 12.60 10.64 11.86(-0.91) H-3 (0.89) H-3 (0.75) H-3 (-0.75) H-5 (0.93) H-3

(-0.29) H-5 (-0.48) H-4 (0.53) H-311.02 13.09 11.30 12.49 11.08 12.05 11.20 12.19 11.18 12.25

(0.93) H-6 (0.87) H-5 (0.82) H-4 (-0.90) H-4 (0.92) H-4(0.27) H-6 (0.48) H-3

11.42 12.60 11.48 13.50 11.77 13.85 11.81 13.91 11.49 13.52(0.90) H-5 (-0.91) H-6 (0.95) H-6 (0.95) H-6 (0.94) H-6

16

3.4. Geometry relaxation and AIEs

Table 3.4 presents lowest AIEs and compares them with the first VIEs of the

tautomers. The relaxation energies (∆R)are provided as well. The lowest AIE found

the for 9H-1H-AO-G form, although all AIEs are very close and equal ∼ 7.7 eV.

Relaxation energies are also similar for all the tautomers and are about 0.4 eV. Below

we analyze geometry changes upon an ionization. Since equilibrium geometries for

the cations and the neutrals were computed by different methods (RI-MP2 for the

neutrals and DFT with the ωB97 functional for the cations) the observed geometry

differences could be due to different performance of the methods and not to ionization.

Thus, to ensure that the change comes from ionization and not from the methods,

we compare the performance of different methods applied to the same molecule. The

equilibrium geometries for the neutral 7H-1H-AO-G form computed by both methods

were compared. The differences in bond lengths computed by the two methods are

0.000-0.005 A for most of the bonds and do not exceed 0.014 A. Therefore, the changes

larger than 0.02 A can be safely assigned as due to ionization. Figure 3.6, Figure 3.7,

Figure 3.8, Figure 3.9 and Figure 3.10 show the geometries of the neutrals and the

cations and the changes upon the ionization for the 7H-1H-AO-G , 9H-1H-AO-G , 9H-

AH-G(RN1) , 9H-AH-G(RN7) and 7H-AH-G(RN1) tatuomers of guanine respectievly.

The geometry changes are almost the same for all the tautomers. The C(2)-N(3) and

C(4)-C(5) bonds get longer, as expected from the character of the HOMO, which

is the same for all the tautomers. The C(5)-C(6) bond length elongates, however

it is not directly related to the character of the HOMO, and is due to the further

redistribution of the density. Due to electron density in HOMO between the N(7)

and C(8) atoms, an increase in the bond lenght was also expected between those

atoms. However, it was observed only for the 7H- tautomeric forms (7H-1H-AO-

G and 7H-AH-G(RN1) ). Shortening of the amino-N-C(2) and O-C(6)bonds was

also observed in all 5 tautomers. A participation of a lone pair of amino-N in the

delocalization of the positive charge formed in the π-system makes the N-C(2) bond

17

Table 3.4: First AIE and VIE, EOM-IP-CCSD/FNO, extrapolation to the cc-pVTZlimit. ∆ R=VIE-AIE

7H-1H-AO-G 9H-1H-AO-G 9H-AH-G(RN1) 9H-AH-G(RN7) 7H-AH-G(RN1)AIE, eV 7.78 7.67 7.71 7.77 7.72VIE, eV 8.19 8.05 8.06 8.08 8.07∆R, eV 0.41 0.38 0.35 0.31 0.35

acquire some double bond character that explains its shortening. The same effect

(except that now it is a lone pair of oxygen participating in the delocalization) is

responsible for shortening of the O-C(6) bonds in the enol forms. In the keto forms,

the origin of the effect is more complicated. In the neutrals, the keto C(6)=0 double

bond is conjugated with a lone pair of the adjacent N(2) atom that makes N(2)-

C(6) bond be partially double and the C(6)=O double bond to partially loose its

double character. In the cation the lone pair of the N(2) atom participates in the

delocalization of the positive charge in the purine ring and its conjugation with the

C(6)=O double bond is no longer possible. As a concequence, the C(6)=O bond has

now fully double character, which explains the observed contraction relative to the

neutral. For all 5 tautomers, we found that the amino group that is pyramidal in the

neutrals becomes planar in the cations.

It should be noted that the observed changes are consistent with the relaxation

energies. The fact that the geometry changes for each bond in all 5 tautomers are

of the same sign and, moreover, of the same magnitude, agrees well with similar

VIE-AIE relaxation.

18

Figure 3.6: Geometry changes of the 7H-1H-AO-G upon ionization. Bond lenghts arein A, angles are in degrees. Geometry of the neutral is computed by RI-MP2/ext-cc-pVTZ, geometry of the cation is computed by ωB97/ext-cc-pVTZ

Figure 3.7: Geometry changes of the 9H-1H-AO-G upon ionization. Bond lenghts arein A, angles are in degrees. Geometry of the neutral is computed by RI-MP2/ext-cc-pVTZ, geometry of the cation is computed by ωB97/ext-cc-pVTZ

19

Figure 3.8: Geometry changes of the 9H-AH-G(RN1) upon ionization. Bond lenghtsare in A, angles are in degrees. Geometry of the neutral is computed by RI-MP2/ext-cc-pVTZ, geometry of the cation is computed by ωB97/ext-cc-pVTZ


20


21

3.5. Comparison to the experiment

Figure 3.11 compares the experimental PES1 with the computed AIEs and VIEs.

We see very nice agreement between the onset of the PESs with the lowest AIE corre-

sponding to the 9H-1H-AO-G . The VIEs of the tautomers present in the experiment

should coincide with the peaks of the obtained PES. Thus, only those tautomers that

have VIE coinciding with the peak maxima are present in the experimental beam.

The first computed VIEs (8.05-8.19 eV) do not match the first experimental peak

(8.3-8.4 eV). Several reasons might explain the discrepancy. First, we assumed that

the maxima of the peaks correspond to the VIEs based on the Franck-Condon ap-

proximation.

The intensity Iκµ of a transition between two vibronic states dependens on the

electric transition dipole moment Rκµ.13 In the adiabatic approximation, Rκµ can be

expressed as13

Rκµ ≈ 〈χk,κ(Q)|Mk,m(Q) |χm,µ(Q)〉

where,〈χk,κ(Q)| and |χm,µ(Q)〉 denote the final (k, κ) and the initial (m, µ) vibra-

tional states respectievly and Mk,m(Q) denotes the electronic transition dipole mo-

ment; Q stands for the nuclear coordinates. The Condon approximation neglects the

dependence of the electronic transition dipole moment Mk,m on nuclear coordinates

and intensities of vibronic transitions are simply evaluated as the overlap integral

(Franck-Condon factor) between the vibrational states.13 If a final electronic state

is strongly coupled with another state, the electronic transition dipole moment may

become strongly dependent on nuclear coordinates. Should the electronic transition

dipole moment depend on nuclear coordinates such that it is larger for higher vi-

bronic states, it will cause the maximum intensity transition to appear at a higher

energy. Therefore, experimentally observed maxima might have higher energy than

ones predicted by Franck-Condon approximation. That might be the reason why

the computed VIEs are below the observed peak in the experiment. For example,

22

in the simulation of the photodetachment spectrum for 1-pyrazolide Franck-Condon

approximation fails, because the ground and first excited states in 1-pyrazolyl, the

product of the detachment, are nearly degenerate and, thus, are strongly interacting.6

The second reason for the discrepancy might be due to computational and exper-

imental errors. Taking into account the accuracy of EOM-IP-CCSD being about 0.1

eV, some errors could arise from the experiment allows for diverging of the calculated

and experimental results by 0.1-0.2 eV. The difference that we observe between the

calculations and the experiment is of this magnitude. Therefore, with present level

of accuracy we can not conclude that calculated VIEs do not match the experimental

peaks.

Much better agreement is observed for higher ionization levels. Higher VIEs of all

the tautomers agree well with the experimental PES. That might mean that all the

tautomers were present in the experimental beam. However, comparing the calculated

VIEs with the recorded PES does not really allow us to sort out the tautomers present

in the experiment from those that were not. First, the interpretation is complicated

because many VIEs of different tautomers coincide and a peak in the spectrum could

be due to either of those tautomers. Another problem is that the width of the bands

in the spectrum is too broad therefore many tautomers might fit there. In addition,

Franck-Condon progression and photoionization cross-sections were not taken into

account; that makes it hard to confirm that some of the tautomers were in the beam

and to rule out others.

23

7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.50

5

10

15

20

25

30

Photon energy, eV

7H-1H-AO-G

9H-AH-G(RN1)

9H-AH-G(RN7)

7H-AH-G(RN1)

9H-1H-AO-GIn

tens

ity, a

.u.

Figure 3.11: PES1,10 compared with the computed AIEs and VIEs of different tau-tomers. AIEs are the lines below 8.0 eV, the rest are the VIEs. AIEs and VIEscorresponding to different tautomers are marked by different colors and line patterns.The top curve is the pseudo-PES obtained by Ahmed and co-workers,1 the bottomcurve is PES obtained by LeBreton and co-workers.10 Calculated AIEs and VIEswere computed by EOM-IP-CCSD/cc-pVTZ

24

Chapter 4

Conclusions

We present theoretical study of ionized states of the five most stable guanine

tautomers.

It is shown that tautomerization has small effect on the IEs and character of

ionized states. There is a general trend in the order of ionized states for all five

tautomers: the corresponding molecular orbitals for the six ionized states are of π1,

σ1, π2, σ2, π3, π4 character. The two exceptions are interchanged fourth and fifth

ionized states for the 9H-AH-G(RN7) and third and fourth states of the 9H-1H-AO-

G tautomer, which can be explained by the strong mixing, i.e. multiconfigurational

character of the wavefunctions.

Comparison of EOM-IP-CCSD VIEs with Koopmans’ theorem estimations shows

that the latter provides qualitatively wrong description of these systems, giving the

wrong order of the ionized states.

In addition, electron correlation reduces the IEs by 1 to 2 eV.

Tautomerization also does not have strong effect on the geometry changes upon

ionization. That is in agreement with the fact that the relaxation energies for different

tautomers are also very close (0.3-0.4 eV). The main geometry changes are skeleton

deformations and changes in the NH2 group dihedral angles from slightly pyramidal

for the neutral guanine to the planar structure for ionized molecule.

Comparison of the computed AIEs and VIEs with the experimental differentiated

PIE spectrum is in agreement with significant population of all of the considered

guanine tautomers. AIEs agree well with the experimental onset of 7.75±0.05 eV. VIE

for the first ionized state of guanine tautomers is notably red-shifted in comparison to

25

the maximum of the first band in the experimental spectrum. This can be explained

by assumption of strong electronic coupling of the two lowest ionized states of the

guanine.

26

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[3] J.D. Chai and M. Head-Gordon, Systematic optimization of long-range correctedhybrid density functionals, J. Chem. Phys. 128 (2008), no. 8, 084106.

[4] O. Dolgounitcheva, V.G. Zakrzewski, and J.V. Ortiz, Electron Propagator Theoryof Guanine and Its Cations: Tautomerism and Photoelectron Spectra, J. Am.Chem. Soc. 122 (2000), no. 49, 12304–12309.

[5] P.T. Henderson, D. Jones, G. Hampikian, Y. Kan, and G.B. Schuster, Long-distance charge transport in duplex DNA: The phonon-assisted polaron-like hop-ping mechanism, Proc. Nat. Acad. Sci. 96 (1999), no. 15, 8353–8358.

[6] T. Ichino, A.J. Gianola, W.C. Linebrger, and J.F. Stanton, Nonadiabatic effectsin the photoelectron spectrum of the pyrazolide-d(3) anion: Three-state interac-tions in the pyrazolyl-d(3) radical, J. Chem. Phys. 125 (2006), 084312–084334.

[7] N.S. Kim, Q. Zhu, and P.R. LeBreton, Aqueous Ionization and Electron-DonatingProperties of Dinucleotides: Sequence-Specific Electronic Effects on DNA Alky-lation, J. Am. Chem. Soc. 121 (1999), no. 49, 11516–11530.

[8] A. Landau, K. Khistyaev, S. Dolgikh, and A. I. Krylov, Frozen Natural Or-bitals for Ionized States within Equation-of-Motion Coupled Cluster Formalism,Department of Chemistry, University of Southern California, Los Angeles, CA90089-0482.

[9] F.D. Lewis, R.L. Letsinger, and M.R. Wasielewski, Dynamics of photoinducedcharge transfer and hole transport in synthetic DNA hairpins, Acc. Chem. Res.34 (2001), 159–170.

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[10] J. Lin, C. Yu, S. Peng, I. Akiyama, K Li, Li Kao Lee, and P. R. LeBreton,Ultraviolet photoelectron studies of the ground-state electronic structure and gas-phase tautomerism of hypoxanthine and guanine, J. Phys. Chem. 84 (1980),no. 9, 1006–1012.

[11] C.M. Marian, The Guanine Tautomer Puzzle: Quantum Chemical Investigationof Ground and Excited States, J. Phys. Chem. A 111 (2007), no. 8, 1545–1553.

[12] M.E. Nacuteunez, D.B. Hall, and J.K. Barton, Long-range oxidative damage toDNA: Effects of distance and sequence, Chem. and Biol. 6 (1999), no. 2, 85–97.

[13] I. Pugliesi and K. Muller-Dethlefs, The Use of Multidimensional Franck-CondonSimulations to Assess Model Chemistries: A Case Study on Phenol, J. Phys.Chem. 110 (2006), 4657–4667.

[14] D. Roca-Sanjuan, M. Rubio, M. Merchan, and L. Serrano-Andres, Ab initio de-termination of the ionization potentials of DNA and RNA nucleobases, J. Chem.Phys. 125 (2006), no. 8, 084302.

[15] M.K. Shukla and J. Leszczynski, Spectral origins and ionization potentials of gua-nine tautomers: Theoretical elucidation of experimental findings, Chem. Phys.Lett. 429 (2006), no. 1-3, 261–265.

[16] 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. Ko-rambath, 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.Woodcock III, 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 quan-tum chemistry program package, Phys. Chem. Chem. Phys. 8 (2006), 3172–3191.

[17] J. Zhou, O. Kostko, C. Nicolas, X. Tang, L. Belau, M.S. de Vries, and M. Ahmed,Experimental Observation of Guanine Tautomers with VUV Photoionization, J.Phys. Chem. A 113 (2009), no. 17, 4829–4832.

28

Appendix A

Table 1.1: Total energies,nuclear repulsion and CCSD, (hartree) using FNO extrap-olation to the cc-pVTZ

7H-1H-AO-G 9H-1H-AO-G 9H-AH-G(RN1) 9H-AH-G(RN7) 7H-AH-G(RN1)ENR 596.447783 595.794784 596.733549 597.532427 596.623189

ECCSD -541.587200 -541.585000 -541.585100 -541.584900 -541.579600

Table 1.2: Geometry of the neutral 7H-AH-G(RN1) tautomer, RI-MP2/ext-cc-pVTZ

I Atom X Y Z1 N 1.518916 0.818678 -0.0006552 C 0.295319 1.294259 -0.0010813 O 0.091808 2.628034 0.0086624 H 0.973941 3.029048 0.0040475 C 1.677780 -0.535766 -0.0044156 N 0.727722 -1.460041 0.0049247 C -0.516820 -0.955006 0.0006528 N 2.984654 -0.963405 -0.0745749 H 3.668206 -0.307025 0.26123210 H 3.122520 -1.920660 0.20316411 N -1.695461 -1.667554 0.00840312 C -2.635563 -0.744787 0.00320513 H -3.694802 -0.941474 0.00484114 N -2.151125 0.536741 -0.00550015 H -2.687345 1.387922 -0.01198916 C -0.789037 0.420798 -0.008156

29

Table 1.3: Geometry of the cation 7H-AH-G(RN1) tautomer, ωB97/ext-cc-pVTZ

I Atom X Y Z1 N 1.549564 0.816847 0.0002302 C 0.353318 1.319931 0.0000023 O 0.130174 2.614693 0.0002484 H 0.971159 3.098094 0.0007165 C 1.672403 -0.544476 -0.0001116 N 2.899185 -1.021178 -0.0000617 H 3.687867 -0.392152 0.0001428 H 3.039679 -2.020954 -0.0000699 N 0.673686 -1.480129 -0.00004710 C -0.525382 -0.972247 -0.00030811 N -1.733947 -1.648041 0.00049912 C -2.628976 -0.720451 0.00028513 H -3.700087 -0.877757 0.00061514 N -2.102791 0.577497 -0.00037715 H -2.628186 1.439687 -0.00097116 C -0.773314 0.437335 -0.000555


I Atom X Y Z1 N 1.531861 0.781016 -0.0012062 C 0.319426 1.305975 -0.0004963 O 0.195260 2.639325 0.0070754 H 1.100744 2.984439 0.0020085 C 1.657146 -0.568124 -0.0043146 N 0.676397 -1.469755 0.0040827 C -0.525615 -0.888762 0.0004688 N -1.753672 -1.495700 0.0060769 H -1.920670 -2.488295 0.00477510 C -2.692352 -0.493045 0.00102811 H -3.747849 -0.708110 0.00200812 N -2.170590 0.717668 -0.00408513 N 2.946557 -1.038966 -0.07208214 H 3.652773 -0.394592 0.23916015 H 3.063917 -1.995542 0.21556616 C -0.812748 0.481900 -0.004954

30


I Atom X Y Z1 N 1.561295 0.778713 0.0000232 C 0.380613 1.330458 0.0000073 O 0.224611 2.624951 0.0001154 H 1.090407 3.062913 0.0002185 C 1.651889 -0.580075 -0.0002066 N 2.865579 -1.088857 0.0000467 H 3.666658 -0.476349 0.0002608 H 2.987290 -2.089932 0.0001589 N 0.624421 -1.491466 -0.00011210 C -0.537650 -0.917071 -0.00015111 N -1.792149 -1.477577 0.00037612 H -2.007285 -2.463473 0.00038113 C -2.677335 -0.449663 -0.00016414 H -3.747875 -0.608117 0.00001715 N -2.102873 0.753609 -0.00010216 C -0.797515 0.492085 -0.000082


I Atom X Y Z1 N 1.517664 0.856428 0.0007802 C 0.285370 1.316455 0.0009193 O 0.117972 2.648705 -0.0079894 H -0.836888 2.811289 -0.0068415 C 1.697092 -0.488057 0.0038436 N 0.762593 -1.443820 -0.0050607 C -0.465187 -0.922822 -0.0005508 N 3.004835 -0.896864 0.0689509 H 3.176357 -1.846546 -0.21224610 H 3.682782 -0.211365 -0.21546411 N -1.676660 -1.568087 -0.00592412 H -1.816284 -2.565116 -0.00583313 C -2.648451 -0.598325 -0.00135914 H -3.696312 -0.847069 -0.00286015 N -2.161551 0.629595 0.00562316 C -0.799090 0.430817 0.006575

31


I Atom X Y Z1 N 1.545450 0.842258 -0.0001952 C 0.346296 1.344354 0.0000323 O 0.195633 2.643048 0.0000274 H -0.741731 2.889233 0.0001165 C 1.685723 -0.510807 -0.0001146 N 2.918392 -0.969191 0.0001967 H 3.084585 -1.963861 0.0002488 H 3.690277 -0.319226 0.0002819 N 0.697127 -1.472763 -0.00025010 C -0.486082 -0.945663 -0.00008011 N -1.727193 -1.541676 0.00003512 H -1.916179 -2.532990 0.00070113 C -2.642533 -0.542131 -0.00003414 H -3.707754 -0.731859 -0.00008615 N -2.100729 0.676529 -0.00003116 C -0.787669 0.448951 0.000236

Table 1.8: Geometry of the neutral 7H-1H-AO-G tautomer, RI-MP2/ext-cc-pVTZ

I Atom X Y Z1 N 1.447853 0.824546 -0.0079212 H 2.230466 1.458301 -0.0980193 C 1.679714 -0.533639 -0.0014404 N 0.751976 -1.442024 0.0105145 C -0.517477 -0.931864 -0.0000666 N -1.669603 -1.670247 -0.0058307 C -2.639410 -0.770098 -0.0012508 H -3.692851 -0.992343 -0.0046899 N -2.174985 0.514192 0.00815210 H -2.714681 1.364728 0.01334411 C -0.815364 0.428471 0.01109812 N 3.013493 -0.897546 -0.07823713 H 3.642158 -0.356827 0.49590214 H 3.122911 -1.890348 0.06705815 C 0.187565 1.443675 0.00342416 O 0.057587 2.661846 -0.003867

32

Table 1.9: Geometry of the cation 7H-1H-AO-G tautomer, ωB97/ext-cc-pVTZ

I Atom X Y Z1 N 1.494553 0.828061 -0.0003522 H 2.284195 1.461502 -0.0009603 C 1.691344 -0.518899 -0.0000424 N 2.923243 -0.992743 0.0004865 H 3.742602 -0.407102 0.0005676 H 3.038012 -1.995541 0.0003847 N 0.692933 -1.431527 -0.0002818 C -0.522519 -0.940276 -0.0000629 N -1.699086 -1.656853 -0.00042410 C -2.631330 -0.760343 -0.00007711 H -3.694555 -0.963404 -0.00005512 N -2.152247 0.550705 0.00051213 H -2.698920 1.400954 0.00071714 C -0.820804 0.457503 0.00047515 C 0.230443 1.460129 -0.00003316 O 0.103762 2.653924 -0.000226

Table 1.10: Geometry of the neutral 9H-1H-AO-G tautomer, RI-MP2/ext-cc-pVTZ

I Atom X Y Z1 N 1.463405 0.782873 -0.0066852 H 2.261874 1.398712 -0.0822523 C 1.662334 -0.568686 -0.0017904 N 0.696716 -1.446303 0.0097185 C -0.525560 -0.850751 -0.0004726 N -1.726943 -1.500635 -0.0030117 H -1.852165 -2.499746 -0.0086428 C -2.702859 -0.536774 -0.0000289 H -3.749923 -0.787552 -0.00220510 N -2.212811 0.688594 0.00755111 C -0.852280 0.502354 0.00709212 N 2.973445 -0.990384 -0.07574813 H 3.644854 -0.436151 0.43136514 H 3.061000 -1.978500 0.10401715 C 0.213579 1.467930 0.00259716 O 0.188301 2.684972 -0.001181

33

Table 1.11: Geometry of the cation 9H-1H-AO-G tautomer, ωB97/ext-cc-pVTZ

I Atom X Y Z1 N 0.000000 0.000000 0.0000002 H 0.000000 0.000000 1.0165103 C 1.173464 0.000000 -0.6846084 N 2.321370 0.001461 -0.0239735 H 2.383438 0.003696 0.9850576 H 3.177875 0.002356 -0.5647957 N 1.255819 -0.000711 -2.0429728 C 0.091165 -0.001517 -2.6422749 N -0.164709 -0.002917 -3.98803510 H 0.527545 -0.003517 -4.72858111 C -1.522659 -0.002446 -4.13125612 H -2.003157 -0.002730 -5.10464213 N -2.179543 -0.001769 -2.96793414 C -1.218883 -0.001413 -2.04538215 C -1.309981 -0.002133 -0.57935416 O -2.290974 -0.003894 0.113716

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