T H E O R E T I C A L I N V E S T I G A T I O N O F T H R E E - C E N T E R E D H Y D R O G E N

B O N D S IN D N A— D F T A N D N B O STUDIES

by

SZE Chun Ngai (施駿毅）

A Thesis Submitted in Partial Fulfilment

of the Requirements for the Degree of

Master of Philosophy

in

Chemistry

©The Chinese University of Hong Kong

January 2003

The Chinese University of Hong Kong holds the copyright of this thesis. Any person(s) intending to

use a part or whole of the materials in the thesis in a proposed publication must seek copyright release

from the Dean of the Graduate School.

i

阔 ^ fi n lit M 0 u ,1； 11 :— .‘• 广

卜 f

M A S T E R OF P H I L O S O P H Y (2002) The Chinese University of Hong Kong

(Chemistry)

TITLE: T H E O R E T I C A L INVESTIGATION OF T H R E E - C E N T E R H Y D R O G E N

B O N D S IN D N A—D F T A N D N B O STUDIES

A U T H O R : Chun Ngai Sze, B. Sc.

SUPERVISOR: Prof. Steve C. F. Au-Yeung

N U M B E R OF PAGES: xii, 81

Thesis Committee:

Prof. Steve C. F. Au-Yeung (Chairman)

Prof. D. T. W. Chan

Prof. Z. F. Liu

Prof. Y. D. W u (External Examiner)

ii

A B S T R A C T

Hydrogen bonding interaction plays an important role in the stability of D N A

double helix. Besides the simple hydrogen bonds (H-bonds), three-centered H-bonds

in D N A were often characterized by x-ray crystallography and other experimental

methods. This thesis focuses on the computational studies of H-bonds using Density

Functional Theory (DFT) and Natural Bond Orbital (NBO) methods.

The dimer units CC，CA, AA, A C and C G of a D N A duplex d(CCAACGTTGG)2

were extracted for the exploration of the possibility of three-centered hydrogen

bonding. Geometry optimization performed by DFT method resembles the positions

of three-centered hydrogen atoms in major grooves successfully. From the theoretical

calculations, chemical shift changes between dimer and monomer, as well as scalar

coupling constants can provide supportive information for identifying three-centered

H-bonds. The presence of trans-hydxogQn bond scalar coupling constant is the most

concrete evidence among the calculated N M R parameters.

From the N B O analysis, the locations of the three-centered H-bonds in different

dimer molecules are identified by — a*AH interaction. Based on the calculated

N B O results, we are unable to confirm the presence of the suggested three-center

H-bonds of the reference D N A proposed by x-ray crystallography study. However, we

are able to identify one three-center H-bonds not detected by x-ray analysis of the

iii

same D N A sequence. The strengths of charge transfer of intermolecular H-bonds of

D N A dimers are always proportional to their H-bond numbers, except the E(2) energy

of the C C dimer is smaller than that of the C G dimer. The most important factor for

their difference is the H-bond distance between the base pairs.

iv

摘要

氫鍵作用在雙螺旋脫氧核糖核酸的穩定性中扮演著非常重要的角色。除了

一般氫鍵外，脫氧核糖核酸的三中心氫鍵也可被X-射線晶體譜及其他實驗方法

顯示出來。本論文旨在透過密度函數理論(DFT)以及自然鍵軌道(NBO)方法對此

類三中心氧鍵進行硏究。 •

本論文首先從雙螺旋脫氧核糖核酸d(CCAACGTTGG)2中取出CC、CA、AA、

AC及CG雙聚物單位，繼而尋出三中心氫鍵之存在。使用DFT方法的結構優

化，成功地重現三中心氫鍵於主溝之位置。透過理論計算，雙聚物與單聚物間

化學位移之變化及偶合常數提供分別出三中心氫鍵之有力的資料。而在各NMR

的參數中，過氣鍵偶合常數之出現是最明顯的證據。

不同雙聚物分子之三中心氫鍵的位置亦可通過如—a*AH作用被自然鍵軌

道(NBO)分析出來。雖然根據NBO的計算結果，我們未能確定從核酸範本中被

X-射線晶體譜所測定的三中心氫鍵，但是我們能於同一脫氧核糖核酸序列中找

出一三中心氧鍵。除了 CC雙聚物的E⑵能較CG雙聚物的E⑵能爲少外，分子

間氫鍵的電荷傳遞之強度與其氬鍵之數目是成正比的。核酸驗對間之氫鍵距離

是此例外之主因。

V

A C K N O W L E D G E M E N T S

I would like to thank m y research supervisor, Prof. Steve C. F. Au-Yeung for the

advice and support he has provided me throughout m y stay at C U H K . Through the

discussions and explorations with him, I have leamt a lot from him. Also, he had

granted me a great deal of freedom throughout m y M. Phil, study.

I wish to thank Dr. W. L. A. Kurtz Chiu for his many useful comments and

discussions on this work. His expertise in chemistry and computational sciences

improved m y research skills.

In addition, I would also like to thank Ms. Carol Y. Y. Au, Ms. Kyna K. Y. Tang,

Dr. Leo Y. C. Li and Mr. Herman W. H. Ip for their supports, encouragement and the

joys they brought me. I would also like to express m y appreciation to all the other

people who have made my time here enjoyable.

I would also like to thank the support from the Information Technology Services

Centre of C U H K on the use of the SGI Origin 2000 servers.

Last but not least, I would like to thank m y family and friends I met in the

secondary school, who has been a great source of strength all through this work.

vi

T A B L E O F C O N T E N T S

PAGE

A B S T R A C T iii

A C K N O W L E D G E M E N T S vii

C H A P T E R ONE: I N T R O D U C T I O N A N D B A C K G R O U N D 1

1.1 Introduction 1

1.2 Definitions of Hydrogen Bonds (H-bonds) 1

1.3 Experimental Evidences of Hydrogen Bonding 3

1A Three-Centered H-bonds 5

1.5 Scope of the Thesis 6

C H A P T E R T W O : T H E O R Y A N D C O M P U T A T I O N A L DETAILS 8

2.1 Introduction 8

2.2 Theory 9

2.2.1 Density Functional Theory (DFT) 9

2.2.2 Chemical Shifts 10

2.2.3 Spin-Spin Coupling Constants 11

2.2.4 Natural Bond Orbital (NBO) Analysis 13

2.3 Methodology 16

2.3.1 Geometry Optimization 16

2.3.2 Nuclear Magnetic Resonance (NMR) 21 Properties

2.3.3 N B O Analysis 22

2.4 Geometry Optimization 23

2.5 Summary 29

C H A P T E R THREE: RESULTS A N D DISCUSSION 30

3.1 Introduction 30

vii

T A B L E O F C O N T E N T S (CONT.•.) PAGE

3.2 Comparison of Computed Results with X-ray 30 Crystallography Data

3.3 N M R properties 33

3.3.1 Chemical Shifts 33

3.3.2 Spin-Spin Coupling Constants 38

3.4 Natural Bond Orbital (NB〇）Analysis 41

3.4.1 Determination of Three-centered H-bonds 41

3.4.2 N B O Analysis of Different Interaction of 43 Dimer Units

3.4.3 Detailed Analysis of C C and C G Dimers 64

3.5 Summary 68

C H A P T E R FOUR: C O N C L U D I N G R E M A R K S 69

R E F E R E N C E S 71

APPENDIX 76

viii

LIST O F T A B L E S

NUMBER DESCRIPTION PAGE

1.1 Differences between two-centered and three-centered 7 H-bonds.

2.1 Values for calculated bond lengths associated with 27 intermolecular H-bonds for D N A dimer.

2.2 Values for calculated bond angles associated with 28 intermolecular H-bonds for D N A dimer.

3.1 Comparison of three-centered H-bonds geometry of 31 Dickerson's and this thesis work for CC, AA，CA and A C dimer.

3.2 Summary of the difference between the calculated H 34 chemical shifts, A5 (in ppm) of D N A dimers and monomers.

3.3 Summary of the difference between the calculated C 35 chemical shifts, A5 (n ppm) of D N A dimers and monomers.

3.4 Summary of the difference between the calculated ^N 36 chemical shifts, A5 (in ppm) of D N A dimers and monomers.

3.5 Summary of the difference between the calculated O 37 chemical shifts, AS (in ppm) of D N A dimers and monomers.

3.6 Calculated scalar coupling constants, Jxh and Jxh, 39 (X二N or 〇）for the intermolecular H-bonds.

3.7 The summary of scalar coupling constants, Jxh, (X二N 40 or O) of the nuclei between two base pairs.

3.8 Values for energetic parameters of cross H-bonds for 42 AA, AC, CA, CC and C G dimer by N B O analysis with UB3PW91/6-311G** or UB3LYP/6-311G** method.

3.9 The geometry of three-centered H-bonds identified by 48 N B O analysis for CC, AA, C A and A C dimers.

ix

LIST O F TABLES (CONT...)

N U M B E R DESCRIPTION PAGE

3.10 Values for energetic parameters of intermolecular 50 H-bonds for AA, AC, CA, CC and C G dimers by N B O analysis with B3PW91/6-3IIG** method.

3.11 The E(2) energy, deletion energy and Wiberg's bond 52 index of cross-strand H-bonds identified by second-order perturbative analysis from B3PW91 and B3LYP-optimixed structures of dimers

3.12 E(2) energy of intermolecular H-bonds for AA, AC, CA, 54 CC and C G dimers and their corresponding monomers by N B O analysis with B3PW91/6-311G** method.

3.13 Values for energetic parameters of intermolecular 57 H-bonds for AA, AC, CA, CC and C G dimers by N B O analysis with B3LYP/6-311G** method.

3.14 Results of natural charge differences (AQ, e') for the CC 59 dimer.

3.15 Values for energetic parameters of orbital interaction for 62 CC dimer by N B O analysis with B3PW91/6-3IIG** method.

3.16 Results of natural steric analysis (NSA) of 63 intermolecular H-bonds for AA, AC, CA, CC and C G dimers by N B O analysis with B3PW91/6-3IIG** method.

3.17 Values for second order perturbation energy, E(2) of 65 intermolecular H-bonds for models by N B O analysis with B3PW91/6-311G** method.

3.18 Values for second order perturbation energy, E(2) of 66 intermolecular hydrogen bonds for hss-monomer models for CC dimer with different distances by N B O analysis using B3PW91/6-311G** method.

3.19 Values for natural steric analysis (NSA) of 67 intermolecular H-bonds for models by N B O analysis with B3PW91/6-311G** method.

V

LIST O F F I G U R E S

N U M B E R DESCRIPTION PAGE

1.1 Schematic diagram of a three-centered H-bond system. 7

2.1 Schematic N B O perturbation diagram for '2-e 15 stabilizing' interaction between a lone pair and antibonding orbital.

2.2 Sequence of d(CCAACGTTGG ) 2 duplex. 17

2.3 Nomenclature of D N A . 18

2.4 Structures of the models. 24

3.1 The cross H-bond presented in the C C dimer. 44

3.2 The cross H-bond presented in the C A dimer. 44

3.3 The cross H-bond presented in the A A dimer. 45

3.4 The cross H-bond presented in the A C dimer. 46

3.5 The cross H-bond presented in the C G dimer. 47

3.6 The relationship between Wiberg bond index and E(2) 55 energy of intermolecular H-bonds of the dimers optimized using B3PW91 functional.

3.7 The relationship between Wiberg bond index and E(2) 58 energy of intermolecular H-bonds of the dimers optimized using B3LYP functional.

3.8 Top view of the C C dimer. 60

xi

ABBREVIATION

1 JxH One-bond J coupling between atom X and atom H bp Basepair

5 Chemical shift .

A5 Chemical shift difference

AQ Natural charge difference

A Deoxyadenine

C Deoxycytidine

DFT Density functional theory •.

G Deoxyguanosine

D N A Deoxyribonucleic acid

T Deoxythymine

E(2) Energy lowering due to second order perturbation analysis

Edei Deletion energy

FPT Finite Perturbation Theory

GIAO Gauge Including Atomic Orbitals

H-bond Hydrogen bond

HF Hartree-Fock

H K Hong Kong

JxY J coupling value between atom X and atom Y

Lone pair of hydrogen bond acceptor

N B O Natural Bond Orbital

N D B Nucleic Acid Database

N M R Nuclear magnetic resonance

NPA Natural Population Analysis

N S A Natural Steric Analysis

a*AH Antibonding orbital of A—H bond

W B I Wiberg's bond index

xii

C H A P T E R O N E

I N T R O D U C T I O N A N D B A C K G R O U N D

1.1 Introduction

Hydrogen bonding has been classified as an important type of intermolecular

interaction and its phenomenon has been studied for more than 70 years. This

interaction can be found from simple hydrogen-bonded complex to

biomacromolecules. Hydrogen bonds (H-bonds) are commonly found in

biopolymers such as proteins and nucleic acids. This type of interaction plays an

important role in the stability of their secondary structure. One of the most

important biopolymers is deoxyribonucleic acid (DNA). D N A commonly exists in

double helix form, which is maintained by the formation of hydrogen bondings

between Watson-Crick base pairs. H-bonds have a wide diversity and different

definitions on this topic have been made. In this chapter, a brief summary on the

natures and general features of various types of H-bonds will be given.

1.2 Definition of Hydrogen Bonds (H-bonds)

A simple definition to a H-bond, is the weak interaction

between a hydrogen atom attached to an electronegative donor atom A and an

electronegative acceptor atom B. The electronegative atoms are commonly nitrogen

and oxygen. This type can be categorized as "classical" or "conventional" H-bond.

1

In general, several common features are found in conventional hydrogen bondings:

(i) both donor and acceptor atoms are negatively charged;

(ii) H-bond angle is close to linear; and

(iii) the interatomic distance of the donor and acceptor is substantially shorter than

the sum of their van der Waals radii.

Moreover, C-H bonds can form H-bonds with electronegative O atom:

Although normally weaker than its conventional H-bond, the C—H..0 interaction is

thought to be crucial in a large number of crystal structures (1.1-1.2) and biological

systems such as peptides (1.3-1.5) and nucleic acids (1.6-1.7). This type bears

positive charges on both C and H atoms and the H > " 0 distance may not be shorter

than the sum of the van der Waals radii of H and O atoms. This hydrogen bridge is

referred to as a “non-classical” H-bond. Both experimental and theoretical studies

showed that its nature is quite different from the classical one (1.8-1.10).

In general, H-bond has been widely accepted as a weak bond mediated by the

electrostatic interactions. This is the interaction between the unperturbed nuclei and

electron clouds of the atoms involving H-bond. This contribution includes the

interactions of all permanent charges and multipoles. However, the pure simple

electrostatic model has limitations in explaining some phenomena such as the

increases of molecular polarity. In fact, the H-bond is a complex interaction

composed of several constituents including electrostatics, polarization, charge

transfer, dispersion, and exchange repulsion (1.11). Recently, Buckingham (1.12)

presented that the H-bond should be thought of as a strong van der Waals interaction.

This interaction consists of long-range attractive intermolecular forces i.e. a

combination of electrostatic, induction and dispersion interaction, and short-range

repulsive forces coming from the exchange interaction when the electron clouds

2

overlap significantly. This description of H-bond includes most of the important

systems in clusters, liquids, and in molecular biology.

1.3 Experimental Evidences of Hydrogen Bonding

Formation of hydrogen bonding can be observed from the change of physical

properties of compounds (1.13). These changes can be summarized as below:

(i) abnormal melting and boiling points;

(ii) abnormal enthalpies of mixing;

(iii) abnormal dipole moments;

(iv) abnormal ionization constants of acids;

(v) excess viscosities;

(vi) decrease of solubilities; and

(vii) deviations from Raout's law.

Moreover, hydrogen bonding phenomena can be detected experimentally by

both spectroscopic and non-spectroscopic techniques. The common methods include

x-ray/neutron diffraction, infrared (IR) and nuclear magnetic resonance (NMR)

spectroscopy. X-ray diffraction experiments determine electron-density distributions

and locate the maxima of the atoms. The presence of H-bond is usually inferred

from the distance of the donor and acceptor groups. A H-bond is considered to be

present in the structures solved by x-ray crystallography when there is a shortening

of the sum of van der Waals radii for both the donor and acceptor atoms. Due to the

weak scattering density of the hydrogen atom, it is difficult to obtain precise

information on its position within the H-bonds. On the other hand, neutron

diffraction can locate the nuclei of the atoms and is capable of providing more

3

reliable information on the hydrogen nuclei position within the H-bonds of

biomacromolecules (1.14-1.15).

IR spectroscopy is also an important method because of the sensitivity of

vibrational modes to the presence of H-bonds. The frequency of the donor A - H

stretching vibrational band is frequently studied in hydrogen-bonded complex. The

major characteristic of a H-bond is indicated by the shift to lower frequencies of the

A - H stretch band (red shift). The bandwidth and the integrated band intensity also

increase strongly upon the formation of a H-bond (1.13). These parameters are more

reliable indicators of weak H-bond formation than the frequency red-shifting (1.16).

The abnormal behavior is observed for a subset of C—H".〇 H-bonds. The

“improper blue-shifting" of stretching frequency is the result of change of electronic

density of the remote parts of the donor molecule.

Moreover, high resolution N M R spectroscopy has contributed significantly to

the understandings of H-bonds. A number of different N M R observables, give

indirect evidence for H-bonds (1.13). There is always a change in the chemical shift

of the H-bonded hydrogen nucleus to higher frequencies (downfield shift).

Chemical shifts of the heavy atoms and differences in the H and H signals in H/D

exchange experiments can provide additional information on hydrogen bondings.

Direct evidence has also been found by the presence of cross bond scalar couplings

between the nuclei on both sides of the H-bond in biomacromolecules and in small

chemical compounds (1.17).

4

1.4 Three-Centered H-bonds

Besides the simple H-bonds, three-center H-bonds are often found in the

solid state of many compounds (1.18-1.19) and the crystal structures of biologically

relevant systems such as nucleic acids. The three-center H-bonds in nucleic acids

were often characterized by x-ray crystallography (1.20-1.21) and other experimental

methods (1.22-1.23).

The majority of hydrogen bondings involve one donor and one acceptor

group only. This type of hydrogen bridges is referring to as simple two-center H-

bonds. Since the H-bond has a long range, a donor can interact with two or more

acceptors simultaneously. The schematic diagram of three-center H-bond systems is

shown in Figure 1.1. In fact, two types of three-center hydrogen bond interaction

can be distinguished: (i) one that involves one hydrogen atom and two acceptor

atoms, and (ii) one that involves one acceptor atom and two H atoms (1.24). Only

type (i) hydrogen bonding interactions are discussed in this study since the three-

center H-bonds found in D N A belong to this category. In this three-center H-bond

system, a hydrogen atom is located between three electronegative atoms, being

covalently bound to one donor atom and hydrogen bonded to the other two acceptor

atoms. In order to give a better representation for atoms involving three-center H-

bond，another nomenclature is applied. The acceptor, which is not located in

complemtary base pair, is denoted as atom 1 while for that located in complemtary

base is denoted as atom 2. The donor and the hydrogen atom are labeled as atom 3

and 4 respectively. The distance between atom x and y is denoted as Rxy and the

angle formed by intersection of two bonds is denoted as Axy. If the two H—B

separations are distinctly different, the shorter interaction is called the major

5

component, and the longer one the minor component of three-center H-bond. For

the three-center H-bond system in nucleic acids, the major component is assumed to

be intermolecular H-bond and the minor component is the cross-strand H-bond.

Based on the general features of the typical two-center and three-center H-

bonds, their differences are summarized in the Table 1.1.

1.5 Scope of the Thesis

Recently, intramolecular and intermolecular three-center H-bonds have been

investigated at a theoretical level. Rozas et al. (1.25) has applied the theory of atoms

in molecules (AIM) to show that three-center interactions do exist in simple

molecular structure and that they are energetically weaker than two-center hydrogen

bonds. Parra et al. (1.26) also carried out ah initio calculations on diacetamide-HCN

and diacetamide-methanol dimers models for investigating the intermolecular three-

center H-bonding, For D N A molecules, Sponer et al (1.27) has studied the

bifurcated hydrogen bond with the A p A B - D N A step with the use of simplified

model. The adenine forming the three-center H-bonds was replaced by cytosine,

while the other adenine was removed. The two thymines were replaced by two

formamides that mimic the intermolecular and cross-strand H-bonds with cytosine

respectively. From recent U V resonance Raman studies of D N A duplex, the

enthalpy of three-center H-bond is approximately 0.46 kcal/mol, which is obtained

by estimating the frequency shift of the H-acceptor bond (1.23). However, no

detailed studies on three-center H-bonds in various D N A dimers have been

performed so far.

This thesis is the first effort studying the three-center H-bonds interaction of

D N A molecules using dimer units with backbones. To identify the existence of

6

these types of H-bonds, Density Functional Theory (DFT) method combined with

the Natural Bond Orbital (NBO) analysis are applied.

/ base (5') j j base (3,) / L A(3)-H(4)；-……-B(2) /

....

/ 7 、 ⑴ 7

丨 base 丨 ！ base j

-……-intermolecular H-bond cross H-bond

Figure 1.1 Schematic diagram of a three-center hydrogen bond system

Table 1 • 1 Differences between two-center and three-center H-bonds

Two-center H-bond Three-center H-bond

Number of acceptors One Two

H-bond distance Shorter than the van der Equal/Longer than the van

Waals radii sum of H and der Waals radii sum of H and

acceptor atom acceptor atom

H-bond angle Close to linear Bent to around 90°

7

C H A P T E R T W O

T H E O R Y A N D C O M P U T A T I O N A L D E T A I L S

2.1 Introduction

In order to study the three-center H-bonds in D N A molecules, DFT method

and N B O analysis are applied. The use of DFT is due to its computational simplicity

compared with the Hartree-Fock (HF)-based ab initio quantum mechanical methods,

especially at the correlated levels of ah initio methods. Gauge Including Atomic

Orbitals (GIAO) method is used to calculate the chemical shifts of the nuclei of the

D N A molecules. The combination of DFT and the finite perturbation theory (FPT)

methods is needed for calculating the spin-spin coupling constants involving the H-

bonds.

N B O analysis is a quantum-chemical methodology that emphasizes the

importance of orbital interaction and charge-transfer effects in van der Waals

complexes distinguishable from classical electrostatic effects. Charge transfer

interaction is the interaction caused by charge transfer from occupied molecular

orbitals to vacant molecular orbitals. This method has been successfully applied to a

number of small systems including ones with intramolecular H-bonds (2.1-2.2) and

molecular clusters where intermolecular hydrogen bonding takes place (2.2-2.3).

This method was also used to study orbital interactions and stabilities of molecular

structures (2.4-2.5).

The brief summary of theories and the methodologies of various computation

methods are mentioned in this chapter.

8

2.2 Theory

2.2.1 Density Functional Theory (DFT)

In Hartree-Fock (HF) theory, the energy of a many-electron system as given

by:

gHF _ gnuclear + gcore + Coulomb + exchange (2_1)

where

Enudear nuclear repulsioii energy,

Ecore is the one-electron (kinetic plus potential) energy,

ECouiomb is the classical coulomb repulsion of the electrons,

exchange (he exchange energy resulting from the quantum (fermion) nature of

electrons.

The energy according to DFT includes the same nuclear, core and Coulomb

as the H F energy, the exact exchange in HF method for a single determinant is

replaced by a more general expression, the exchange-correlation functional, which

include terms accounting for both exchange energy, E (P), and the electron

correlation which is omitted in Hartree-Fock theory, E^(P):

gOFT 二 gnuclear + gcore + gCoulomb + gX^p) + (2-2)

Both of the latter are functions of the electron density, P.

For different density functionals used in DFT computations, the notation

B, is used to denote the use of A functional for exchange and B functional for

correlation. In this study, B3LYP (Becke's Three Parameter Hybrid Functional (2.6)

Using the LYP Correlation Functional (2.7)) and B3PW91 (Becke's Three Parameter

Hybrid Method Functional with Perdew/Wang 91 (2.8-2.9)) functionals are used.

9

Both are hybnd functionals which include a mixture of HF exchange with DFT

exchange-correlation and are available via keywords:

B3LYP is Becke's three parameter functional, which has the form:

A*E^(Slater)+(l.A)*E^(HF)4-B*AE^(Becke88)+E^(VWN)+

C*AE^(non-local) (2-3)

where the non-local correlation is provided by the LYP expression.

The constants A, B, and C are those determined by Becke by fitting to the G1

molecule set, computing values of A=0.80, B=0.72，and 00.81.

B3PW91 is Becke's three parameter functional as above, with the non-local

correlation provided by the Perdew/Wang 91 expression. The constants A, B, and C

are again those determined by Becke. B3LYP is chosen since this is the most

common used DFT method whereas for B3PW91, Barfield (2.10) has applied the

same functional to the study of D N A structures.

2.2.2 Chemical Shifts

In molecules, the nuclear magnetic shielding constant at nucleus N has a

matrix form:

= 御 (2-4) iJ

where

i and j are the direction components (x, y, and z),

E is the total energy of the molecule,

mNj stands for the j-th component of magnetic moment of nucleus N.

10

In experiments, the shielding constant of a nucleus is usually expressed by its

difference from that of a nucleus in a reference molecule. Thus, instead of the

absolute a value, the chemical shift is usually measured.

A common difficulty in the calculation of magnetic properties is that gauge

invariance is not guaranteed, i.e., the computational result may depend on the

position of the molecule in the Cartesian frame (2.11). Gauge including atomic

orbital (GIAO) formulation (2.12) overcomes this problem, this type of orbitals are

defined as:

Xp(B) = Xp(0) exp [-0.5iB-RpXri] (2-5)

where

B is the magnetic flux density,

Xp(0) is an unperturbed atomic basis function,

Rp is its center.

2.2.3 Spin-Spin Coupling Constants

Normally, scalar spin-spin coupling interaction is caused by three individual

nuclear magnetic moments (2.13) from

(1) the orbital motion of the surrounding electrons (electron orbital term);

(2) the spins of the electrons (electron spin term); and

(3) electrons that have a non-zero-probability density at the position of the nucleus

(Fermi contact term, FC).

However, the FC contribution is dominant in the scalar spin-spin coupling

involving the hydrogen atom and the other terms can be neglected.

11

In the finite perturbation theory (FPT) (2.14-2.15) approach, the reduced

nuclear spin-spin coupling constant for the Fermi contact term Kab can be expressed

as

Kab = 字 r 1 D p v (lie) < (M § (re) I v > (2-6) ^ fiV

where

(3 is the Bohr magneton,

\ is the perturbation parameter which to measure the perturbation added to nucleus B

and resulting interaction between the perturbed spin-density and the nucleus A,

p v (I B) is the spin-density matrix,

5 (fb) is the Dirac-delta function,

^^ and (|)v are the atomic orbitals.

The calculation of the term Z) p^ ([Xb) < 〜I 5 (re) | (t)v > is implemented

using the FIELD option of the Gaussian 98 program.

The relationship between the reduced coupling constant Kab and the ordinary

nuclear spin-spin coupling constant Jab is

JAB 二 {H / 47I') 丫A yg 你 (2-7)

where

h is Planck constant,

丫A and yb are the nuclear magnetogyric ratio for the nuclei A and B respectively.

Finally, the nuclear scalar coupling constant Jab is obtained using eq. (2-7)

with unit conversion (2.16-2.17).

12

2.2.4 Natural Bond Orbital (NBO) Analysis

The concept of natural orbitals has been used by Reed and Weinhold (2.18)

and constitutes the basis of the natural population analysis (NPA). Its starting point

is a partitioning of the density matrix, P, and the overlap matrix, S, into atomic

blocks. These blocks are then diagonalized independently, thereby forming natural

atomic pre-orbitals (2.18). The pre-orbitals are separated into two distinct classes:

the orbitals corresponding to the maximum degree of occupancy, which form the

natural minimal basis (NMB), and all other orbitals, forming the natural Rydberg

basis (NRB). The latter is orthogonalized utilizing Schmidt's technique, with respect

to the N M B . Both the N M B and the N R B subsequently use a symmetrical

orthogonalization procedure, weighted by the degree of occupancy of the orbitals.

The generated orbitals are rearranged into blocks and further diagonalized, thus

leading to the natural atomic orbitals (NAO). The diagonal elements of the density

matrix built from the NAOs correspond to the atomic population of each NAO. The

summation of these populations over all atomic orbitals centered on a given atom is

called the natural atomic population (NAP). The calculation details can be referred

to Ref. 2.19.

Their 'natural' populations qi(A) (diagonal elements of the density operator in

the N A O basis),

qi⑷二〈没{A)昨;A)〉 (2.8)

which may be summed to give the total number of electrons tVa,

tVa 二 2qi(A) (2.9)

And "natural charge" QA on atom A (with atomic number ZA)

QA = ZA-iVA (2.10)

13

While atomic charges cannot be determined experimentally, the polarity of

the molecule can be deduced from the direction of its electric dipole moment.

Whereas the constituent nuclear charges are clearly atom-centered, the electron

charge distribution is spread out over the entire molecule.

The N B O algorithm transforms all the orbitals into two categories: high-

occupancy "Lewis-type" and low-occupancy "non-Lewis-type" orbitals. The former

orbitals refer to core orbitals (CR, unhybridized core-type NAO)，valence lone pairs

(LP), G or 71 bonds (BD), and the latter refer to a* or 7t* antibonds (BD*) and extra-

valence-shell Rydberg orbitals (RY*). The N B O theory generally describes the

formation of a A-H."B hydrogen bond as the charge transfer (CT) from the lone pair,

of the acceptor B into the antibonding orbital a*(AH) of the donor A. Two

methods are used to estimate the relative strength of intermolecular and cross-strand

hydrogen bonds. One by calculating the energy lowering effect of E(2), due to

„(A)-^a*(DH) delocalization from the second order perturbation analysis. The

N B O Fock matrix E can be separated into diagonal and off-diagonal terms,

E(o) 二 diag(E), E⑴ 二 off-diag(E) (2-11)

The occupied eigenfunctions of E(o) are simply the Lewis-type N B O s {«b}, with

eigenvalues s =〈《B F "B〉. By mixing a lone pair hb with an empty antibond G*AH,

two new hybrid orbitals are generated. It leads to the estimated second order energy

lowering. This lowering is given by the equation (4-1)

⑵ （nB 间。"*AH〉2 E( •) — = -2- — (2-12) “^ As(n, (J*) V

where

F is the Fock operator,

14

A8(«, a*) is the N B O orbital energies difference between antibonding orbital of the

H-bond donor and lone pair of the H-bond acceptor.

This type of donor- acceptor ('2-e stabilizing') interaction is depicted

schematically in Figure 2.1.

''2-e Stabilizing" C T Interaction • •

• • • • 木

• ： ^ A H «

奢 «

#

瞎

n-D A • B — 一 厂 • 、

. • I AE * #

• • .HI / \Y

Figure 2.1 Schematic N B O perturbation diagram for ‘2-e stabilizing, interaction

between a lone pair and antibonding orbital

The other method starts with deleting the specific off-diagonal matrix

(ng Fct^ah) elements of the effective one-electron Hamiltonian in the N B O basis

and then recalculating the approximate SCF energy without cr* interaction. The

resultant energy change Edei, also called deletion energy, measures the loss of

stabilization related to the deleted interactions.

Natural steric analysis (NSA) (2.20) is also used for studying the repulsive

forces between the molecular orbitals. NSA provides a numerical estimate of steric

15

exchange energy from the sum of energy differences between the filled orthonormal

N B O s and their "pre-orthogonalized" N B O counterparts.

Wiberg's bond index (WBI) (2.21) is used to measure the M O bond order,

obtained from the sum of squared off-diagonal density matrix elements between

atoms. The result yielded by such a scheme will be called the covalent bond index.

The equation of bond index of a bond A-B is:

BIAB = SSppq' (2.13)

where

Ppq is a density matrix.

2.3 Methodology

2.3.1 Geometry Optimization

DFT methods were utilized to calculate the structures of D N A base pairs.

The computations of geometry optimized D N A dimers were carried out using the

GAUSSIAN 98 (2.22) program running on a SGI Origin 2000 and PC cluster.

Coordinates for the heavy atoms were taken from the 1.4 A X-ray crystal structure of

self-complementary decamer B-DNA d(CCAACGTTGG )2 duplex (NDB entry

BDJ019) (2.23). This crystal structure was chosen because its resolution was high

and detailed studies of three-center hydrogen bonds were performed on this duplex.

The sequence of the duplex is shown in Fig. 2.2. All the water molecules and metal

ions were removed because studies were focused primarily on the interaction

between base pairs.

It is not applicable to perform fiill optimization for the whole D N A strands

because the computational resources are expensive. The models calculated were

16

extracted for the exploration of the possibility of three-center hydrogen bonding.

Several D N A dimers [C1-C2 (CC), C2-A3 (CA), A3-A4 (AA), A4-C5 (AC) and C5-

G6 (CG)] were clipped from the decamer. The standard nomenclature of D N A

dimers is shown in Fig. 2.3 (a)-(e) and each dimer unit consists of two base pairs.

For convenience, an abbreviated nomenclature XX'YY' is used to indicate the

specific atom in the D N A duplex. X X ' represents the number of residue X’ for a

base X (A/C/G/T) in this duplex and YY' represents the atom Y in the position Y’

i.e. C2H2' refers to the H2' atom in the cytosine (C2) residue.

Since positions of hydrogen atoms cannot be obtained from crystallographic

data, the hydrogen atoms were included using SYLBL 6.2 (2.24). Coordinates for

the heavy atoms were fixed during partial optimization. For the CC, CA, A A and

A C dimers, the coordinates of hydrogen atoms were partially optimized at the

HF/ST0-3G or HF/6-31G level to obtain a better starting geometries and hence to

increase the efficiency of calculation. Then they were followed by partial

optimization using unrestricted UB3PW91/6-31IG**, as well as UB3LYP/6-

31IG** level. For the C G dimer, the coordinates of hydrogen atoms were optimized

at the UB3PW91/6-311G** directly because it is well known that the inclusion of

electron correlation is necessary for the accurate description of hydrogen-bonding

interactions.

5’-Ci C 2 A 3 A 4 C 5 G , T, Tg G9 Gio

G20G19T18T17G16C15A14A13C12C11-3

Figure 2.2 Sequence of dfCCAACGTTGG)? duplex

17

(a)

CI G20

H ^ / >3-……Ht"N; ) r \ > = N 3 \

r ^ 〇 2 . … … Y sugar 、 H2b I sugar

/ V r H 4 a … … . O . N ^ H . \

backbone | h ^ ' \.".…Ht"N〈 ^ ^ | backbone

\ z N r ^ \ / \ 〇2……H—N2 ^ r

sugar '' u sugar I 2b “ “

C2 G19

(b) C2 G19

… . . . � H y 3

> = N 3 \ 〇2……H —N2 \

sugar ^ '' sugar 、 2b

/ H 丫 N ^ ^ N 「 H f … 9 ^ C H 3 \

backbone N^^^、/^^^ u m ^ A — u backbone

\ / 乂 I Z H2 〇2 ]

sugar sugar A3 T18

Figure 2.3 Nomenclature o f D N A (a) CC dimer. fb) C A dimer

18

(C)

A3 T18 H《b -

/ — f H, 〇2

sugar sugar

、 ^^ / ^ V ^ N N^H,,…..0^CH3 \

backbone ^ 》5 A \ backbone \ / — Z sugar H2 〇2 | sugar

A4 T17 (d)

A4 T17

H t > ^ “ 6 ‘ . … . . v c / — 1 H2 〇2 ^

sugar ^ sugar

/ H5 H,……o^ N k / H 8 f \__/ 4a ^ \

backbone I backbone

\ , - - ^ H \ z I 1 O , … … H — N , 1 f sugar 2a \ sugar

C5 G16

Figure 2.3(cont'd) Nomenclature of D N A (c) A A dimer, fd) A C dimer

19

(e)

C5 G16

v j ^ " . . . . . . uy H ^ / V-……h「N(—

N t ^ sugar

1 〇 2 . … … ^ ^ . sugar Y zb \

\ backbone ^ ^ ^ 『s……^ n. ^ ^ ^ H5 backbone

旧「Hi.……NfV^.

sugar Nf^s / N厂H……02 1 / 2a sugar

G6 C15

(f)

H 5 " 、

R - 0 5 - C 5 - H 5 '

^ B a s e C 1 ,

H 4 ' H 2 y 、 H r

C 3 ' _ C 2 '

0 3 ' - R H 2 "

Figure 2.3fcont'd) Nomenclature o f D N A (q) CG dimen (f) ribose sugar ring

20

2.3.2 Nuclear Magnetic Resonance (NMR) Properties

The molecular structures of D N A dimers were optimized at UB3PW91/6-

31IG** level. Each of the dimer units was divided into two monomer base-pair

units. The monomer units were used in calculation of N M R properties without

further geometry optimization, therefore the change of parameters could not be

caused by any alternations of monomers' local structures.

The magnetic shielding tensors of both dimer and monomer units were

obtained via the GIAO formulation at the UB3PW91/6-31IG** level using Gaussian

98 (2.25). All H, C, ^N, ^O chemical shifts reported here are isotropic values.

Also, all H and ^ C chemical shifts are indirectly referenced to tetramethylsilane

(TMS) by subtracting the calculated magnetic shielding for the nuclei of interest

from the shielding of the reference compound. '^N and ^^O chemical shifts are

referenced to NH3 and H2O respectively using the same method. Molecular

structures for TMS, NH3 and H2O were optimized at the UB3PW91/6-31IG** level,

and the ^H, C, ^N, ^O isotropic magnetic shieldings are calculated to be 31.67,

182.56, 271.37 and 340.52 ppm respectively, at the UB3PW91/6-31IG** level. The

chemical shift differences between D N A dimers and the corresponding monomers

were determined.

The Fermi contact (FC) contributions to the scalar coupling constants for the

optimized structures were computed using the unrestricted UB3PW91/6-31IG**

triple-split level with polarization functions on hydrogen and heavier elements (2.26-

2.27). This approach makes use of DFT and FPT methods.

21

2.3.3 NBO Analysis

N B O analysis was used to analyze the orbital interactions of the D N A base

pairs. A N B O analysis of optimized D N A dimers was performed at the

UB3PW91/6-311G** or UB3LYP/6-31IG** levels by using NPA. Then the dimer

units were divided into the corresponding monomer units. N o optimization is

needed for the monomer units before the N B O analysis. The calculations of E(2) and

deletion energy of dimers and monomers were performed. The cut-off value of E(2)

energy is 0.03kcal/mol which is suitable for identifying cross-strand H-bond. The

N B O 3.1 program linked to Gaussian 98 was used for these calculations.

Natural steric analysis (NSA) is also used for studying the repulsive forces

between the molecular orbitals. Unlike the calculations of E(2) and deletion energy,

the sugar and phosophodiester linkages of dimer molecules were removed in the

N S A studies in order to overcome the limitation of computational capacities. A

stand-alone N B O 5.0 program was used for N S A calculations. The corresponding

NAO-Wiberg's bond index can be obtained with the B N D I D X keyword in N B O

program.

For the detailed studies of CC and C G dimers, different models based on

these two dimers optimized at B3PW91/6-31IG** level were constructed. Starting

from the dimer molecules, the m-dimer models of CC and C G dimers (Figure 2.4

(a)-(b)) were constructed by eliminating the phosphodiester backbones and replacing

the 2'-deoxyribose moiety with the methyl groups. This is followed by replacing all

the methyl groups of the two m-dimer models by hydrogen atoms to form another

smaller dimer molecules, donated as h-dimer (Figure 2.4 (c)-(d)).

22

In order to study the effects of constituents of nucleobases in the charge

transfer process, the N1 atoms of cytosines and N9 atoms of guanines for the h-

dimers were removed to form the hss-dimer molecules (Figure 2.4 (e) and (g)). The

hs-dimers of C C and C G dimers were further reduced to the 40-atom fragments; and

were donated as the hss-dimer models (Figure 2.4 (f) and (h)). The hss-dimer

models consist of the H-bonded regions only and they are the simplest structures that

mimic the G*C base pair.

A N B O analysis of different models of C C and C G dimers was performed at

the UB3PW91/6-311G** or UB3LYP/6-31IG** levels using N P A and N S A

method.

2.4 Geometry Optimization

The bond distances and bond angles of N — N — H " . N and C-H...0 H-

bonds in CC, CA, AA, A C and C G dimers are shown in Tables 2.1-2.2 respectively.

In general, the A - H bonds are shorter and thus H".B distances are longer for the

structures calculated at HF/ST0-3G when comparing with those calculated by DFT

methods except in A C dimers. There is not much difference in the structural

parameters when using either B3PW91 or B3LYP methods in comparing the

calculated results. The mean values of imino N-H, amino N - H and C-H bonds

calculated using B3PW91 functional are 1.047, 1.027 and 1.083 A respectively. For

the interatomic distances between a hydrogen atom and the acceptor, those refer to

C—H"-0 H-bonds are around 2.600 A, which are longer than the N—H*"0 and N—

H".N H-bonds. Bond angles of the conventional N - H—0 and N—H."N hydrogen

bonds are close to linear, but non-linearity is observed for all C - H—0 H-bonds and

23

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Table 2.1 Values for calculated bond lengths associated with intermolecular

hydrogen bond for D N A dimers

- d(A-H)(A)a d(H.’.B)(A)b HF7 HF/ UB3LYP/ UB3PW91/ HFV HF/ UB3LYP/ UB3PW91/

ST0-3G 6-3IG 6-311G** 6-311G** ST0-3G 6-3IG 6-31IG** 6-311G** C C dimer

C1H4-G2006 1.037 - 1.031 1.031 1.878 -- 1.890 1.889 G20H2--C102 1.034 -- 1.019 1.020 1.760 -- 1.775 1.774 G20H1-C1N3 1.045 -- 1.035 1.037 1.877 -- 1.885 1.885 C2H4--G1906 1.042 -- 1.036 1.037 1.816 -- 1.819 1.820 G19H2...C202 1.031 -- 1.018 1.018 1.826 -- 1.840 1.840 G19H1-C2N3 1.043 -- 1.034 1.036 1.889 -- 1.898 1.898

C G dimer C5H4 …G1606 -- -- -- 1.035 -- -- - 1.854 G16H2-C502 -- -- -- 1.026 -- -- -- 1.791 G16H1 …C5N3 -- -- -- 1.041 -- -- -- 1.863 G6H2"-C1502 -- -- -- 1.026 -- -- - 1.784 G6H1-C15N3 -- -- -- 1.041 -- -- -- 1.856 C15H4---G606 -- -- -- 1.036 -- -- -- 1.846

A C dimer A4H6...T1704 1.001 -- 1.020 1.019 2.184 -- 2.164 2.164 T17H3-A4N1 1.024 -- 1.051 1.054 1.801 -- 1.774 1.772 A4H2 …T1702 1.067 -- 1.083 1.084 2.575 -- 2.559 2.560 C5H4-G1606 1.015 -- 1.041 1.042 1.838 -- 1.813 1.811 G16H2-C502 1.003 -- 1.024 1.025 1.757 -- 1.744 1.741 G16H1-C5N3 1.014 -- 1.036 1.038 1.867 -- 1.845 1.842

A A dimer A3H6...T1804 1.028 -- 1.019 1.019 1.971 -- 1.982 1.982 T18H3-A3N1 1.052 -- 1.066 1.066 1.756 -- 1.743 1.742 A3H2-T1802 1.090 -- 1.083 1.083 2.639 -- 2.638 2.637 A4H6 …T1704 1.027 -- 1.020 1.020 2.143 -- 2.149 2.149 T17H3-A4N1 1.047 -- 1.056 1.056 1.779 -- 1.770 1.770 A4H2-T1702 1.092 -- 1.084 1.084 2.558 -- 2.565 2.564

C A dimer C2H4-G1906 1.038 1.007 1.031 1.031 1.820 1.851 1.827 1.826 G19H2...C202 1.032 1.002 1.021 1.022 1.817 1.848 1.830 1.828 G19H1 …C2N3 1.047 1.017 1.039 1.041 1.884 1.914 1.892 1.890 A3H6-T1804 1.030 1.002 1.023 1.023 1.971 1.999 1.978 1.978 T18H3-A3N1 1.048 1.024 1.053 1.056 1.761 1.785 1.756 1.752 A3H2-T1802 1.090 1.065 1.081 1.082 2.638 2.653 2.640 2.637 a. d(A-H) denotes the bond length between the hydrogen and the hydrogen bond donor. b. d(H...B) denotes the interatomic distance between the hydrogen and the hydrogen bond acceptor.

27

Table 2.2 Values for calculated bond angles associated with intermolecular

hydrogen bond for D N A dimers

— A—H…B(o)a

r ^ HFV HF/ UB3LYP/ U B 3 P W 9 1 / ST0-3G 6-3IG “ 6-311G** 6-311G**

C C dimer C1H4-G2006 171.4 -- 167.8 168.2 G20H2-C102 177.7 -- 179.3 179.5 G20H1...C1N3 177.8 -- 177.9 177.9 C2H4-G1906 176.1 -- 176.0 176.4 ‘ G19H2--C202 172.2 -- 171.7 171.9

G19H1-C2N3 177.1 -- 177.0 177.0 C G dimer

C5H4 …G1606 -- -- -- 177.6 G 1 6 H 2 - C 5 0 2 -- -- -- 178.9

G 1 6 H 1 - C 5 N 3 -- -- -- 175.3 G 6 H 2 - C 1 5 0 2 -- -- -- 178.9

G 6 m …C15N3 -- - -- 175.2 C 1 5 H 4 - G 6 0 6 -- -- -- 177.8

A C dimer A4H6-T1704 161.6 -- 161.8 162.0 T17H3-A4N1 175.2 -- 175.1 175.3 A4H2...T1702 134.1 -- 134.1 134.1 C5H4...G1606 177.9 -- 178.5 178.8 G16H2-C502 175.4 -- 170.8 171.1 G 1 6 H 1 - C 5 N 3 173.8 - 174.3 174.3

A A dimer A3H6"-T1804 171.4 -- 170.0 169.9 T18H3 …A3N1 176.0 -- 176.3 176.3 A3H2-T1802 129.7 -- 130.3 130.3 A 4 H 6 …T1704 166.5 -- 166.9 166.9 T17H3-A4N1 175.7 -- 175.3 175.3 A4H2 …T1702 133.7 -- 133.6 133.6

C A dimer C2H4-G1906 176.0 175.0 175.6 176.0 G19H2-C202 176.9 176.3 176.1 176.5 G19H1-C2N3 178.1 177.8 178.1 178.2 A3H6-T1804 171.4 171.2 171.3 171.7 T18H3-A3N1 176.1 175.9 176.3 176.3 A3H2-T1802 129.8 130.4 130.4 130.5

a. A—H"-B denotes the hydrogen bond angle.

28

their bond angles are 132.1 士2.0°. The calculated results of C—H."0 H-bonds are

consistent with the previous work from Leonard and coworkers (2.28). They found

that sp2 hybridization of the carbonyl group of adenine results in bending of the bond

angle to approximately 120°.

2.5 Summary

In this chapter, the theory and methodology of different computational

methods including DFT and N B O were briefly reviewed. Furthermore, the geometry

optimizations of different dimers were determined.

29

C H A P T E R T H R E E

R E S U L T S A N D DISCUSSION

3.1 Introduction

The details on theory and computational methods for performing geometry

optimization and N B O analysis, as well as calculating the chemical shifts and spin-

spin coupling constants have been presented in the previous chapter. In this chapter,

the results of the different methods utilized for studying the three-center H-bonds are

reported. The computed structural optimization results are compared with the x-ray

crystallography data followed by results obtained from the calculations of N M R

properties and N B O studies of three-center H-bonds. J

3.2 Comparison of Computed Results with X-ray Crystallography Data

In order to demonstrate the reproducibility of the experimental results with

the DFT calculation, the geometry of three-center hydrogen bond atoms obtained

from calculation are compared with those of Dickerson's x-ray work (3.1). A

comparison of the calculated data from this study and Dickerson's work is shown in

Table 3.1. The nomenclature of the parameters is based on Section 1.4. It

demonstrates that DFT calculations could predict the positions of hydrogen atoms in

the major groove successfully, with small deviations in both values of hydrogen

bond distances (smaller than 0.06 人）and angles (smaller than 5。). For the H-bonds

found in the minor groove i.e. G20H2, the distance between a hydrogen atom and an

acceptor atom at the next base pair is 0.17 A longer for the calculated values and all

30

Table 3.1 Comparison of three-centered H-bonds geometry of Dickerson's and this work for CC, AA, C A and A C dimer

u , Distance (A) Angles (。） …w。、c Hatom — R i ) Ai2b A . ^ S A N ()

(i) CC dimer “ C1H4 (this work) d 1.889 2.934 88.3 101.8 168.2 358.3 C1H4 (this work) e 1.890 2.933 88.3 102.0 167.8 358.1

C1H4 (Dickerson's work) 1.880 2.890 90.0 104.0 164.0 358.0

Deviation, A^ 0.010 0.044 -1.7 -2.2 4.2 0.3 G20H2 (this work) d 1.770 3.690 89.3 91.2 179.5 360.0

• G20H2 (this work) e 1.775 3.688 89.3 91.2 179.3 359.8 G20H2 (Dickerson's work) f 1.780 3.520 95.0 100.0 162.0 357.0

Deviation, A^ -0.010 0.170 -5.7 -8.8 17.5 3.0

(ii) A A dimer A3H6 (this work) d 1.980 2.980 88.9 99.7 169.9 358.5 A3H6 (this work) e 1.982 2.976 88.9 99.7 170.0 358.6

A3H6 (Dickerson's work) f 1.950 2.990 89.0 98.0 171.0 358.0 Deviation, A^ 0.032 -0.014 -0.1 1.7 -1.1 0.6

(iii) C A dimer C2H4 (this work) d 1.830 3.870 120.8 58.2 176.0 355.0 C2H4 (this work) e 1.827 3.876 120.6 58.1 175.6 354.3

C2H4 (Dickerson's work) f 1.810 3.820 124.0 62.0 171.0 357.0 Deviation, A^ 0.020 0.056 -3.4 -3.9 5.0 -2.7

(iv) A C dimer A4H6 (this work) d 2.160 2.950 97.4 94.6 162.0 354.0 A4H6 (this work) e 2.164 2.947 97.4 94.6 161.8 353.8

A4H6 (Dickerson's work) f 2.130 2.970 97.0 92.0 163.0 352.0 Deviation, A^ 0.034 -0.023 0.4 2.6 -1.2 2.0

a. Rxy denotes the distance between atoms number x and y. b. Axy denotes the central angle defined by atoms x, H-4 and y. c. S A N denotes the sum of three angles about the hydrogen atom. d. Results obtained by UB3PW91/6-31IG** calculation. e. Results obtained by UB3LYP/6-3IIG** calculation. f. Ref.3.1. g. Deviation, A = calculated value - experimental value.

31

three angles centered at H atom deviate by more than 5°. Furthermore, the sums of

three angles formed by the H atom and the other three atoms are close to 360°. In

short, the four atoms are nearly on the same plane, thus satisfying the condition that

a planar structure is required for three-center hydrogen bond system to occur (3.2).

Earlier on in the discussion in Section 1.3，it has been pointed out that one of

the H-bond phenomena is that the intemuclear A*'*B distance is less than the sum of

van der Waals radii of the A and B atoms. Donohue (3.3) has showed using

different examples of crystal structures with three-center H-bonds that the hydrogen

atom is markedly closer to one of the two acceptor atoms and that both distances

being shorter than the van der Waals radii sum by about 0.2 A. But from the results

shown in Table 3.1, the smallest value of R31 is 3.190 A indicating that the

interatomic distance of two heavy atoms is even but larger than their van der Waals

radii sum (the van der Waals radius of nitrogen and oxygen atom is 1.5 and 1.4 A

respectively) (3.4). So it is rather difficult to identify the three-center H-bond for

D N A molecules based on the use of distance.

A less stringent definition of a H-bond has been provided by Steiner and

Saenger (3.5). They defined H-bond as “any cohesive interaction X - H— Y where H

carries a positive charge and Y a negative (partial or full) charge, and the charge on

X is more negative than on H". Such a definition has been widely applied to x-ray

structures and molecular modeling. However, it remains difficult to prove the

formation of three-center H-bonds by charge distribution since the charge on the

acceptor atom can be affected by both the intermolecular H-bond and the three-

centered one.

32

3.3 N M R Properties

3.3.1 Chemical Shifts

The calculated H, ' C, ^N and「〇 chemical shift of all atoms in the CC,

CA, AA, A C and CC dimers are listed in the Supp. Tables 3.1-3.4. The range of H

chemical shift of HI atoms of guanine, 5(^H1), is within 13.01 to 13.59 ppm whereas

the values of 5(^H3) of thymine are between 15.31 and 16.86 ppm. These results are

in agreement with the experimental results (3.6), i.e. the average values of 5(^H1)

and 5(^H3) are 12.6 and 14.4 ppm respectively. The ranges of calculated of

A and G are 257.74-265.25 and 170.69-173.95 ppm. The ranges of calculated

5(i5N3) of T and C are 186.75-198.48 and 237.59-247.70 ppm.

The ^H, 13c，i5n and「0 chemical shift differences between D N A dimers

and corresponding monomers are listed in Tables 3.2-3.5 respectively. Not much

information on the formation of three-center H-bond could be extracted from ^H

chemical shift differences. However, the most notable evidences were observed

from the chemical shift change of heavy atoms. For the cross-strand amino N -

H."0 H-bonds, the CC dimer demonstrate a remarkable change. The「O chemical

shift changes of 06 atoms for G19 and G20 residues were -18.90 ppm and 10.50

ppm respectively (Table 3.5) and ^ N chemical shift change of N4 atom for CI

residue was -8.07 ppm in the CC dimer (Table 3.4)。This result suggests that the

electron density of both donor and acceptor atoms have changed after removal of the

lower part of the C-G base pair. It is suggested that cross-strand H-bond has been

broken and the H atom hydrogen-bonded to an oxygen atom on the complementary

base only. Moreover, the chemical shift change of the acceptor involving the major

33

Tab

le

3.5

Sum

mar

y of

the

dif

fere

nces

bet

wee

n th

e ca

lcul

ated

^O

che

mic

al s

hift

s. A

S^ (i

n pp

m)

of D

NA

dim

ers

and

mon

omer

s''

""Residue

HI,

H2'

H2"

H3'

H4'

H5'

H5"

H6/H8

H2/H5

H1/H3

H2a/H4a/H6aC H2b/H4b/H6b

CC dimer

CI

0.25

0.39

-0.67

0.15

-0.09

0.02

0.06

0.21

0.04

- -0.27

-0.25

C2

-0.07

0.20

-0.04

0.13

-0.15

-0.08

-0.32

0.19

0.34

- -0.09

0.36

G19

0.10

0.30

-0.41

0.15

0.01

0.08

0.05

0.20

- 0.25

0.19

0.02

G20

0.07

0.17

0.06

0.25

-0.10

-0.29

-0.26

0.43

- 0.22

^ 0.02

CA dimer

C2

1.64

0.53

-1.26

0.14

0.16

0.27

-0.05

0.14

-0.02

- 0.53

0.23

A3

-0.07

0.14

-0.03

0.08

-0.13

-0.34

-0.14

0.14

-0.46

- 0.23

0.42

T18

1.14

0.52

-1.98

0.06

0.09

0.27

-0.08

-0.02

- 0.28

- -

G19

-0.11

0.13

-0.06

0.11

-0.16

-0.43

-0.28

0.13

- -0.09

-0.44

AA dimer

A3

0.07

0.33

-0.65

0.14

-0.01

0.11

0.07

0.32

0.40

- 0.10

-0.03

A4

0.14

0.24

0.06

0.15

-0.24

-0.18

-0.49

0.50

0.30

- 0.00

0.21

T17

0.22

0.28

-0.66

0.13

-0.03

0.01

0.02

0.23

- 0.06

- -

T18

-0.07

0.18

-0.02

0.15

-0.14

-0.08

-0.37

0.22

- 0.00

- -

AC dimer

A4

-0.19

0.26

-0.37

0.11

-0.20

0.00

-0.01

0.26

0.04

- -0.28

-0.10 .

C5

0.08

0.28

0.16

0.27

-0.13

-1.59

-0.18

0.51

0.67

- 0.32

0.33

G16

0.03

0.13

-1.12

-0.30

0.12

0.03

0.04

0.04

- 0.49

0.23

0.00

T17

0.00

-0.05

0.05

0.09

-0.07

-0.08

0.00

0.25

- 0,17

- -

CG dimer

C5

0.35

-0.32

-2.04

-0.44

-0.04

0.00

-0.02

0.03

0.00

- 0.38

0.30

G6

-0.03

0.09

-0.06

0.19

-0.12

-0.22

0.12

-0.15

0.18

0.34

0.02

C15

0.33

-0.24

-1.69

-0.07

-0.02

0.01

-0.08

0.07

0.03

- 0.34

0.31

G16

-0.01

0.26

0.00

0.09

-0.12

-0.35

-0.34

0.08

- 0.14

^ -0.02

a. A

b - 5(atom in dimer) - 5 (atom in monomer).

b. The nomenclature of the atoms is based on Figure 2.2.

c. The amino proton involves in Watson-Crick bp.

d. The amino proton does not involve in Watson-Crick bp.

34

Tabl

e 3.

5 Su

mm

ary

of th

e di

ffer

ence

s bet

wee

n th

e ca

lcul

ated

^O

che

mic

al s

hift

s. A

S^ (

in p

pm)

of D

NA

dim

ers

and

mon

omer

s''

Residue

C1'

C2'

C3'

C4'

C5'

C2

C4

C5

C6

C8

CC

dimer

CI

0.54

3.92

0.00

-0.41

0.41

0.11

-0.14

-0.16

1.89

-

C2

0.30

0.38

0.34

0.59

-2.51

0.39

0.60

0.40

0.01

-

G19

0.81

3.25

-1.44

-0.08

0.32

0.58

-0.23

-0.07

-0.17

-1.59

G2Q

0.69

0.45

-0.76

0.55

-2.53

-0.21

0.73

-0.71

0.87

2.49

CA

dimer

C2

1.21

5.40

0.06

-1.67

0.83

0.12

-0.29

-1.08

0.44

-A3

0.08

-0.02

-0.08

-0.05

-3.48

-3.62

-0.76

0.65

0.08

-0.07

T18

0.41

5.12

-1.93

-2.19

0.44

-0.29

-0.86

1.95

“ -2.14

-G19

0.18

-0.01

0.04

-0.08

-6.14

-1.11

-1.23

0.10

-0.37

-0.69

AA

dimer

A3

0.90

3.64

0.48

-0.08

0.20

-0.30

0.61

0.63

0.15

-0.96

A4

0.57

0.21

-0.11

0.46

-2.68

-1.68

0.69

0.32

0.34

2.65

T17

0.22

5.90

-0.38

1.02

0.40

0.14

-0.63

-1.80

1.12

-T18

0.27

0.19

-0.31

0.43

-2.03

0.29

0.02

0.74

-0.11

-AC

dimer

A4

0.69

2.95

-0.94

0.61

0.49

-2.48

0.40

-0.08

-0.44

1.90

C5

0.31

0.46

-0.74

0.02

-4.13

0.82

0.70

0.17

2.01

-G16

-0.11

3.83

-0.91

-0.43

0.26

-0.12

-0.82

-0.70

-0.24

-0.43

T17

-0.22

0.60

-0.46

0.80

-1.25

0.20

0.69

-1.61

1.81

-CG

dimer

C5

-0.55

0.79

-4.12

0.90

0.25

0.11

-0.48

-0.11

-0.50

-G6

-0.20

0.88

-0.09

1.03

-0.94

-0.58

-0.83

-0.26

-0.34

-1.00

C15

-0.42

0.69

-0.90

0.86

0.30

0.43

-0.70

-0.09

-0.08

-G16

-0.13

0.75

Q.Ql

0.43

-3.88

-0.76

-1.08

-0.23

-0.40

-0.20

a. A5 = 5(atom in dimer) - 5 (atom in monomer).

b. The nomenclature of the atoms is based on Figure 2.2.

35

Tabl

e 3.

5 Su

mm

ary

of th

e di

ffer

ence

s bet

wee

n th

e ca

lcul

ated

^^O

che

mic

al s

hift

s. A

S^ (i

n pp

m)

of D

NA

dim

ers

and

mon

omer

s''

Residue

N1

N3

N7

N9

N2/N4/N6

CC

dimer

CI

2.83

-2.61

- -

-8.07

C2

1.16

-5.76

- -

-3.08

G19

-0.66

-4.25

-1.86

1.17

-1.21

G2Q

AM

^ LZ2

-3.04

CA

dimer

C2

-0.63

-2.25

- -

1.48

A3

-3.12

0.59

2.17

-0.11

0.23

T18

-4.97

-0.69

- -

-G19

-2.78

-2.00

^ ^

-7.09

AA

dimer

A3

-1.20

-0.74

2.61

1.64

-5.81

A4

-1.35

0.30

-3.13

1.73

-4.06

T17

1.49

-1.35

- -

-T18

q^

-_L9

4 -

：

-

AC

dimer

A4

-2.43

3.87

-0.46

1.83

-9.40

C5

1.41

-1.55

- -

-1.77

G16

-1.01

-2.25

-2.18

1.08

-5.32

T17

- -

-

CG

dimer

C5

-0.83

-0.67

- -

2.46

G6

-1.86

-0.57

1.61

1.00

-8.56

C15

-0.26

-0.93

- -

2.07

G16

-2.03

-0.67

OM

-9.24

a. A5 二

5(atom in dimer) - 5 (atom in monomer).

b. The nomenclature of the atoms is based on Figure 2.2.

36

Tab

le 3

.5

Sum

mar

y of

the

dif

fere

nces

bet

wee

n th

e ca

lcul

ated

^^O

che

mic

al s

hift

s. A

S^ (

in p

pm)

of D

NA

dim

ers

and

mon

omer

s''

— Residue

03'

04'

05'

02

04/06

—

CC

dime

r

CI

- 3.90

0.61

-2.77

-C2

0.12

1.27

- -8.61

-G19

- 5.36

0.43

- 10.50

G2Q

0.18

1.64

- -

-18.90

CA

dime

r C2

- 3.94

0.83

-2.47

-A3

-0.32

0.08

- -

-T18

- 2.86

0.01

0.61

17.99

G19

-0.52

-0.67

- -

4.82

A A

dime

r A3

~ 4.

75

-0.74

- -

A4

-1.11

-0.25

- -

-T17

- 3.24

1.09

-4.68

-2.04

T18

-0^

- -7.33

AC

dime

r A4

- 5.23

0.65

-C5

-0.14

1.44

- -6.82

-G16

- 2.02

-0.33

- 0.36

T17

-0.54

-2.12

- 2.61

-13.62

CG

dime

r C5

- 1.97

-0.59

1.72

-G6

0.13

0.92

- -

-2.45

C15

- 0.34

0.21

1.25

-G16

0.33

-0.62

- -

-3.11

a. A5 = 5(atom in dimer) - 5 (atom in monomer).

b. The nomenclature of the atoms is based on Figure 2.2.

37

component of the three-center H-bond (intermolecular H-bond) is larger than that of

minor component (cross-strand H-bond). This is due to the strength of shorter

intermolecular H-bond being larger. A similar result is found in the A A dimer, but

the chemical shift differences of the electronegative atoms are smaller in this case.

For the cross bonds involving imino group, the locations of the three-center H-bonds

are difficult to assign based on chemical shift differences.

For the C A dimer, the change of the chemical shift for the C2 atom on

adenine (-3.62 ppm) is largest among all carbon atoms found in the aromatic rings.

The N 2 atom on the thymine has also yield a chemical shift change of—7.09 ppm.

Those observations indicate the existence of cross-strand C H— N bond between

two base pairs.

3.3.2 Spin-Spin Coupling Constants

When a hydrogen bond is formed, the scalar interaction is transmitted via the

electron cloud of the molecules and is usually observed through the one-bond trans-

hydrogen bond coupling. Both the covalent ( Jxh) and trans-hydxogQn bond J-

coupling constants ( Jxh) between the H and heavy atoms such as nitrogen and

oxygen for intermolecular H-bonds were calculated and listed in Table 3.6. The

range of % h is between -53.11 and -55.49 Hz which is smaller than the

experimental values determined from the N M R spectroscopy (3.6) i.e. the mean

value of % H is around -86 Hz. Although the covalent J-coupling between H and 0

atoms cannot be detected easily, the values of % h can be found by computations.

Its value are between -56.14 and -83.10 Hz. For the its value can be either

positive or negative, ranging from -3.30 to 1.08 Hz.

38

Table 3.6 Calculated scalar coupling constants, Jxh and ^Jy^ (X二N or 0) for

the intermolecular H-bonds

AH…B Donor A Acceptor ’ 'JXH (HZ)� " JXH (HZ)�

A A dimer

A3H2-T1802 A3C2 T1802 • - -0.26

A3H6...T1804 A3N6 T1804 -73.88 2.57

T18H3-A3N1 T18N3 A3N1 -54.30 -1.65

A4H2..-T1702 A4C2 T1702 - -0.26

A4H6 …T1704 A4N6 T1704 -56.14 0.82

T17H3-A4N1 T17N3 A4N1 -53.37 -3.30

A C dimer

A4H2--T1702 A4C2 T1702 - -0.26

A4H6 …T1704 A4N6 T1704 -68.66 1.18

T17H3 …A4N1 T17N3 A4N1 -53.64 0.50

C5H4-G1606 C5N4 G1606 -74.26 2.67

G16H1 …C5N3 G16N1 C5N3 -54.14 1.08

G16H2--C502 G16N2 C502 -74.19 3.29

C A dimer

C2H4 …G1906 C2N4 G1906 -83.10 4.01

G19H1--C2N3 G19N1 C2N3 -55.18 0.65

G19H2---C202 G19N2 C202 -76.61 2.62

A3H2...T1802 A3C2 T1802 - -0.21

A3H6 …T1804 A3N6 T1804 -58.83 1.64

T 1 8 H 3 - A 3 N 1 T 1 8 N 3 A 3 N 1 - 5 5 . 4 9 - 3 . 1 1

C C dimer

C1H4-G2006 C1N4 G2006 -74.53 3.34

G20H1...C1N3 G20N1 C1N3 -53.11 1.04

G20H2-C102 G20N2 C102 -58.75 3.03

C2H4-G1906 C2N4 G1906 -58.71 2.57

G19H1-C2N3 G19N1 C2N3 -54.07 1.04

G19H2-C2Q2 G19N2 C202 -57.48 2.52

C G dimer

C5H4 …G1606 C5N4 G1606 -82.02 3.60

G16H1-C5N3 G16N1 C5N3 -54.64 0.96

G16H2--C502 G16N2 C502 -75.45 2.82

C15H4-G606 C15N4 G606 -75.26 2.57

G6H1...C15N3 G6N1 C15N3 -55.41 1.04

G6H2 …C1502 G6N2 CI 502 -75.72 2.98

a. it refers to the H-bond donor. b. it refers to the H-bond acceptor. c. 1 JxH refers to the covalent scalar coupling constant between H and X atoms

d. ihjxH refers to the trans-hydxogQn bond scalar coupling constant between H and X atoms

39

The calculations of FC term of the J-coupling constant were performed

between the hydrogen atoms involving three-center H-bonds and the acceptors. The

scalar coupling constants for these cross-strand H-bonds are reported in Table 3.7.

The trans-hydrogQn bond one-bond J-coupling constants of the cross-strand amino

N—H…O and N—H…N H-bonds are very small, with value equals or smaller than —

0.10 Hz. One exception . is the calculated J-coupling constant of -2.11 Hz

corresponding to the T17H3"-G16N1 H-bond. Its H-donor and H-acceptor are

located within the same D N A strand in the duplex. The spin-spin coupling constant

for the cross-strand H-bond found in the C A dimer is the largest, -2.30 Hz, which

may be measurable by N M R spectroscopy.

All the calculated scalar coupling constants for the cross-strand hydrogen

bonds are very small. In fact, the nuclear spin-spin couplings are related to the

hydrogen bond geometries (3.7-3.9). The contribution of the Fermi contact term to

the spin-spin coupling constant is distance-dependent, which generally increases

Table 3.7 The summary of scalar coupling constants, ihj：^, (X=N or 0) of the nuclei between two base pairs

d(H---B) (A) a Scalar coupling constant (Hz)

i) A A dimer A3H6..-T1704 2.97 -0.10 T17H3 …A3N6 ^

ii) A C dimer T17H3-G16N1 3.41 -2.11 G 1 6 m …A4N1 3 M

iii) C A dimer A3H2-G19N2 ^ - 2 M

iv) C C dimer C1H4-G1906 2.93 -0.10 V) C G dimer C5H4-C15N4 3.26 -0.02 C15H4-C5N4 3 M ；

a. d(H-"B) denotes the interatomic distance between the hydrogen and the hydrogen

bond acceptor.

4 0

when the H-bond distance decreases, as cross-strand H-bonds are always longer than

intermolecular H-bonds in the D N A dimer molecules.

3.4 Natural Bond Orbital (NBO) Analysis

3.4.1 Determination of Three-center H-bonds

As mentioned in section 2.2.4，the cross-strand hydrogen bond A-H—:B can

be recognized from the n^ — g*ah interaction of the filled lone pair of the Lewis

base B with the vacant antibonding orbital of the Lewis acid A. A number of these

interactions have been detected existing between the two base pairs in D N A dimers.

The N B O analysis results calculated with B3PW91/6-31 IG** and B3LYP/6-

31 IG** basis sets are listed in Table 3.8. From the results calculated using B3PW91

optimized structures, a cross-strand H-bond exists between A3H6 and T1704 atoms

in the A A dimer. This H-bond has been reported by Dickerson (3.10). Recall that

the N B O study can also identify both cross-strand N-H—N and C-H—N hydrogen

bonds. Three cross-strand N-H—N H-bonds have been determined from the

different dimer sequences; they are C5H4...C15N4 and C15H4…C5N4 in the C G

dimer, and T17H3 …G16N2 in the A C dimer. In the case of the C G dimer, the amino

group hydrogens were found to participate in cross-strand hydrogen bondings.

These H atoms are usually bent away from the molecular plane of the bases resulting

in shortening of hydrogen bond distances. The formation of these out-of-plane H-

bonds is due to the partial sp hybridization on the amino group nitrogen atom. And

the N4 amino group nitrogen atom of both cytosines served as the H-acceptor. The

lone pair on the partially sp -hybridized nitrogen of the amino group is also needed

as an electron-donating source. So, the nonplanarity of the amino group has an

41

Table 3.8

Values for energetic parameters of cross-strand hydrogen bonds for AA, AC, CA，

CC and CG

dimer by NBO

analysis with

UB3PW91/6-3IIG** or UB3LYP/6-31IG** method

S(n,a*) a

A£(n.a*) (au) ‘

E(2) (kcal/mol)

~

B3PW91

B3LYP

B3PW91

B3LYP

B3PW91

B3LYP

AA

dimer

A3H6-T1704

-0.0225

-0.0232

0.69

0.69

0.01

0.01

T17H

3...

A3N6

-0.0184

-0.0187

0.65

0.65

0.01

0.01

AC

dimer

T17H3-G16N1

-0.0265

0.0334

0.66

0.66

0.01

0.01

G16H1-A4N1

- -0.0266

- 0.63

- 0.02

CA dimer

A3H2 ••G19N2

0.0248

-0.0600

0.70

0.58

0.06

0.02

CC dimer

C1H4-G1906

- 0.0205

- 1.07

- 0.01

CG

dimer

C5H4-C15N4

-0.0274

n.d/

0.69

n.d/

0.02

n.d.

C15H4-C5N4

0.0273

n.d.

0.69

n.d.

0.02

n.d.

a. Overlap integral of associated pre-orthogonalized NBOs.

b. N

BO

energy difference between n and a*.

c. Energy lowering effect due to «(B)-» a*(AH) delocalization from the second order perturbation analysis.

d. n.d. 二

not determined.

42

important role in the formation of cross-strand H-bonds. Amino acceptor

interactions of bases have also been identified in crystals of nucleobases (3.11). In

the A C dimer, the imino H3 atom of a thymine residue is H-bonded to N2 atom of

the guanine at the 5' position. The cross-strand H-bond whose both the donor and

acceptor atoms are located in the same D N A strand has been identified from the

results of theoretical calculations. A non-classical C — b o n d formation is

possible between the H2 atom of A3 residue and N2 atom of G19 residue in the C A

dimer.

All cross-strand H-bonds identified from the calculation using B3PW91

functional, have also been identified from results obtained from calculations using

B3LYP optimized structures. Some additional cross-strand H-bonds, C1H4...G1906

in the C C dimer and G16H2…A4N1 in the A C dimer are identified. The locations of

three-center H-bonds found in the different dimer units are shown in Figure 3.1-3.5.

A summary of the geometric parameters of three-center hydrogen bonds

identified by computational method is listed in Table 3.9. No special pattern is

observed for the bond distance parameters. The bond angle between two acceptor

atoms is usually between 80° and 90° because the acceptors are located in the same

strand. The sum of three angles centered at H atom are always around 360° except

for one involving C-H bond.

3.4.2 NBO Analysis of Different Interactions of Dimer Units

The results of N B O analysis for the intermolecular hydrogen bonds for AA,

AC, CA, CC and C G dimer with B3PW91/6-3IIG** are listed in Table 3.10. The

43

H H I Figure 3.1 The cross-strand H-bond presented in the C C dimer

H^HPS

Figure 3.2 The cross-strand H-bond presented in the C A dimer

44

Figure 3.3 The cross-strand H-bond presented in the A A dimer

45

m m

m Figure 3.4 The cross-strand H-bond presented in the A C dimer

46

•

Figure 3.5 The cross-strand H-bond presented in the C G dimer

47

Table 3.9

The geometry of three-center H-bonds identified by NBO

analysis for CC, AA, CA

and AC

dimers

H atom

Distances (A)

Angles (。）

San (。)‘

Ri2 a

R23 a

R3I a

R14

丨(24

R34

Al2 ‘

八31 ‘

八

2厂

(i) CC

dimer

C1H4-G1906

3.442

2.906

3.303

2.934

1.889

1.031

88.28

168.16

101.81

358.25

(ii) A

A dimer

A3H6 …

T1704

3.544

2.991

3.303

2.975

1.982

1.019

88.93

169.94

99.69

358.56

T17H3-A3N6

3.751

2.824

4.029

3.628

1.770

1.056

80.00

175.25

104.74

359.99

(iii) C

A dimer

A3H2 …

G19N2

3.948

3.440

3.295

2.748

2.637

1.082

94.27

1 11.00

130.47

335.74

(iv) A

C dimer

T17H3 …

Gi6Nl

3.792

2.823

3.543

3.407

1.772

1.954

88.27

88.70

175.32

352.29

G16m …

A4N1

3.499

2.877

3.792

3.358

1.842

1.038

78.67

174.27

106.89

359.83

(V) C

G dimer

C5H4 …

C15N4

3.622

2.889

3.492

3.255

1.854

1.035

85.66

94.51

177.60

357.77

C15114 •

-C5N4

3.621

2.882

3.492

3.258

1.846

1.036

85.65

94.33

177.76

357.74

a. Rxy denotes the distance between at

oms number x and y.

b. Axy denotes the central angle defined by atoms x, H-4 and y.

c. S

AN

denotes the sum of 3 angles about the hydrogen atom.

48

E(2) energy quantifying the energy lowering of n^ - > CJ*AH delocalization effect can

be used to estimate the relative strength of hydrogen bonds. There are two

nonequivalent lone-pairs on the 0 atom; one of the oxygen lone pairs, nsp(O), is a spX

hybrid whereas the other,〜(O), is almost a pure p-type orbital. Since the "p(0) lone

pairs always have more overlapping with the antibonding orbitals, the E(2) energy

lowerings corresponding to 72p(0) lone pairs would be the larger one. For H-bonds

involving an oxygen atom as acceptor, their E(2) energies are calculated by the total

of energies from the two lone pairs. From the results in this table, it is concluded

that charge transfer processes are involved in both conventional and non-

conventional H-bonds.

The general trend for different types of H-bonds in descending strength

follows the order is imino N-H—N » amino N—H".0 » C-H—0. The E(2)

energy of imino N-H—N H-bond (-10-15 kcal/mol) is 50-fold larger than that of

the C—H…O H-bond (-0.2 kcal/mol). The E(2) energies for the H-bonds found in

A-T and C'G base pairs are also non-equivalent. The imino N-H—N H-bond

formed in A-T base pair is 1.5 times larger than that found in C-G base pair. The

hydrogen bonding interactions of amino N-H."0 are nearly as strong as the imino

H-bonds in the C-G base pairs. In the A*T base pairs, the strength of

amino N-H*"0 H-bonds are only one-fifth to one-third when compared as in the

imino N-H*"N bonds.

When the E(2) energy is counted in the dimer units, the trend follows in

descending order is CG〉CC > CA 〜AC > AA. Both the A C and CA dimers have

five H-bonds and the values for the total E(2) energy of intermolecular H-bonds of

these two dimers are within the same magnitude. The A A dimer, which has one H-

49

Table 3.10 Values for energetic parameters of intermolecular hydrogen bonds for AA, AC, CA, CC and C G dimers by N B O analysis with B3PW91/6-3IIG** method^

AH...B S(n.a*) - As(n.a*) (au) - ^ ^ ^ 。。�(；；；； Bond m d e ~

A A dimer

A3H2-T1802 0.025/0.024 1.16/0.71 0.05/0.15 0.113/0.292 0.0029

A 3 H 6 - T 1 8 0 4 -0.160/-0.198 1.14/0.72 1.45/3.04 3.471/6.540 0.0310 T18H3...A3N1 0.502 0.72 16.57 38.739 0.1126

A4H2-T1702 -0.031/-0.033 1.15/0.72 0.07/0.20 0.161/0.400 0.0031

A4H6-T1704 -0.118/-0.139 1.11/0.68 0.78/1.77 1.909/3.849 0.0226

T17H3 …A4N1 0.480 0.73 14.62 33.995 0.0977

38.70 f 89.483 ^

A C dimer

A4H2-T1702 0.032/0.034 1.14/0.71 0.07/0.21 0.153/0.409 0.0034

A4H6...T1704 0.112/0.131 1.11/0.68 0.70/1.55 1.687/3.346 0.0209

T17H3 …A4N1 -0.478 0.74 14.33 33.222 0.0945

C5H4 …G1606 0.200/0.284 1.04/0.67 2.65/7.15 6.227/ 15.344 0.0703

G16H1-C5N3 -0.440 0.79 10.96 25.554 0.0708

G16H2-C502 -0.221/-0.296 1.15/0.74 3.23/6.48 3.709/13.420 0.0582

47.33 f 103.067 ^

C A dimer C2H4 …G1906 0.208/0.267 1.09/0.70 2.69/5.93 6.380/12.739 0.0572 G19H1-C2N3 -0.415 0.76 9.86 23.142 0.0683 G19H2-C202 -0.208/-0.257 1.14/0.73 2.64/4.84 6.257/10.073 0.0451

A3H2 …T1802 0.028/0.027 1.15/0.70 0.06/0.16 0.130/0.324 0.0028 A3H6...T1804 -0.159/-0.205 1.11/0.70 1.46/3.42 3.519/7.448 0.0359

T18H3-A3N1 -0.494 0.75 15.44 36.018 0.1011 46,50 r 106.138 ^

CC dimer C1H4-G2006 0.198/0.227 1.08/0.68 2.34/4.32 5.595/9.147 0.0479 G20H1-C1N3 -0.418 0.79 9.62 22.593 0.0632 G20H2…C102 -0.221/-0.279 1.16/0.75 3.09/5.52 7.251/11.475 0.0491 C2H4 …G1906 0.208/0.276 1.06/0.68 2.74/6.55 6.520/14.235 0.0638 G19H1-C2N3 -0.408 0.78 9.19 21.512 0.0608 G19H2-C202 -0.203/-0.249 1.16/0.75 2.47/4.39 5.831/9.115 0.0403

50.23 f 113.274 f

C G dimer C5H4 …G1606 0.198/0.253 1.06/0.67 2.48/5.60 5.894/11.961 0.0585 G16H1-C5N3 -0.430 0.77 10.61 24.973 0.0726 G16H2-C502 -0.211/-0.266 1.13/0.72 2.91/5.42 6.858/11.233 0.0548 C15H4…G606 -0.198/-0.258 1.05/0.67 2.53/5.85 5.990/12.507 0.0606 G6H1-C15N3 0.433 0.78 10.79 25.379 0.0731 G6H2-C1502 0.213/0.270 1.13/0.72 2.97/5.57 6.978/11.534 0.0555

54.73 123.317 r

a. For NH…O and CH…O intermolecular hydrogen bonds, the charge transfer with both lone pairs on the oxygen atom are given and separated by a slash [nsp(0)/np(0)]. b. Overlap integral of associated pre-orthogonalized NBOs. c. N B O energy difference between n and a*. d. Energy change associated with deletion of off-diagonal matrix elements of effective one-electron Hamiltonian for the corresponding charge-transfer interaction. e. Refers to Wiberg's Bond Index. f. The sum of E(2) or deletion energy of all intermolecular hydrogen bonds in the dimer unit.

50

bond less, differs from CA/AC dimer by around 8 kcal/mol. Approximately the

same energy difference is also found when comparing the E(2) energy of C G and

CA/AC dimer. However, the E(2) energy of the CC dimer is less than the C G dimer

by 4.5 kcal/mol, though both C G and CC dimers have the same numbers and types

of H-bonds, i.e. each O G base pair consists of one imino N - H—N H-bond and two

amino N - H—0 H-bonds. A detailed analysis of CC and C G dimers will be

performed in the next section of this chapter. Deletion energies，Edei, characterizes

？2b -> a*AH charge transfer interactions (from both lone pairs for C—H*"0 and N -

H".0 H-bonds) are also listed in Table 3.10, and are comparable to those calculated

for the E(2) energy.

For the cross-strand H-bonds identified from the second-order perturbative

analysis, their E(2) energies, deletion energies and W B I values have been calculated

and are listed in Table 3.11. The E(2) energy of almost all cross-stranded H-bonds

are between 0.01 and 0.02 kcal/mol, which are much smaller than normal

intermolecular H-bonds. Their deletion energies are also always smaller than 0.02

kcal/mol, which translates to 〜4o/o of the measured cross-stranded H-bond energy

i.e. 0.5 kcal/mol for d(CGCAAATTTGCG )2 (3.12).

Referring to the three-center H-bonds suggested in Dickerson's work (3.1),

only two of them, i.e. C1H4 and A3H6, can be identified by -> CT*AH interaction.

Moreover, the E(2) energy and deletion energy of the C1H4...G1906 and

A3H6…T17〇4 cross-strand H-bonds may be too weak to be accepted as hydrogen

bondings. So all of the possible three-center H-bonds proposed by x-ray

crystallography study of the D N A cannot be confirmed based on the N B O analysis.

However, one of the cross-strand H-bond identified by computation method

i.e.A3H2…G19N2 show a relatively large E(2) energy (0.06 kcal/mol) when

51

Table 3.11

The E(2) energy, deletion energy and Wiberg,s bo

nd index of cross-strand

H-bonds identified by second-order perturbative

analysis from

B3P

W91 and B3LYP-optimixed structures of dimers

AH…

B E(2) (kcal/mol) ‘

Edei (kcal/mol)

bond index ‘

B3PW

91

B3L

YP

B3P

W91

B

3LY

P B

3PW

91

B3L

YP

AA

dimer

A3H

6...T

1704

0.

01

0.01

n.

d.^

0.02

1 0.

0006

0.

0007

T1

7H3-

A3N

6 0.

01

0.01

0.

014

0.01

1 0.

0001

0.

0002

AC dimer

T17H

3...

G16N

1 0.01

0.01

-0.004

n.d/

0.0002

0.0002

G16

H1-

A4N

1 -

qm

：

n.d

.d

0.0

00

5

0.0

00

5

CA dimer

A3

H2

-G1

9N

2

0.0

6

0.0

2

0.1

08

n.d

/ 0

.00

12

0.0

01

3

CC dimer

C1

H4

-G1

90

6

- q

m

- 0

.02

0

0.0

01

0

0.0

01

3

CG dimer

C5

H4

-C1

5N

4

0.0

2

- 0.0

04

- 0

.00

03

-

C1

5H

4-C

5N

4

0.0

2

- 0.0

04

- 0

.00

03

-

a. Energy lowering effect due to

(j*(AH) delocalization from the second order perturbation analysis.

b. Energy change associated with deletion of off-diagonal matrix elements of effective one-electron Hamiltonian for the corresponding charge-

transfer interaction.

c. Refers to Wiberg's Bond Index.

d. The «(

B)-^

a*(A

H) interaction is only existed in alpha or beta spin. 52

compared with the others. This value is in the same order of magnitude as that of

intermolecular C—H…O H-bond between A*T base pair in the C A dimer (Table

3.10). In fact, the H-bond distance of the cross-stranded H-bond (2.75A) in this 3-

center H-bond system is almost the same as that of intermolecular H-bond (2.64 A)

(Table 3.9). Therefore, the A3H2---G19N2 should be classified as a cross-strand H-

bond. •

The N B O studies of the individual monomers corresponding to the dimer

units have been carried out and the values of the E(2) energy for H-bonds between a

base pair are listed in Table 3.12. The E(2) energy of H-bonds calculated from the

monomer units is usually smaller than those calculated from the dimer units except

for the C C dimer. The E(2) energy of the intermolecular H-bonds can be influenced

by the presence of cross strand H-bond. But the pattern about describing effect of

cross-strand H-bond to the intermolecular H-bond is very complicated.

Although H-bonds are not the actual bonds formed by sharing of electrons,

but bond indices have been determined in all intermolecular (Tables 3.10) and cross-

strand hydrogen bonds (Table 3.11). Because the Wiberg's bond index (WBI)

measures the covalency of a bond，it indicates that hydrogen bonding processes

covalent character. The covalent contribution arises from the overlap of the orbital

on hydrogen with those on distant atoms. The W B I shows a linear relationship with

the E(2) energy of the intermolecular H-bonds for the dimers calculated using the

B3PW91 functional (Figure 3.6). These intermolecular H-bonds include all the

conventional and non- conventional H-bonds found in G*C and A-T base pairs.

53

Table 3.12 E(2) energy of intermolecular hydrogen bonds for AA, AC, CA, CC and C G dimers and their corresponding monomers by N B O analysis with B3PW91/6-311G** method^

ah…B E(2), dimer (kcal/mol) & E(2), monomer (kcal/mol) & A A dimer

A3H2-T1802 0.05/0.15 0.05/0.15 A3H6-T1804 1.45/3.04 1.42/3.17 T18H3 …A3N1 16.57 16.32 A4H2-T1702 0.07/0.20 0.07/0.21 A4H6-T1704 0.78/1.77 0.76/1.75 T17H3-A4N1 14.62 14.49

38.70 c 38.39 '

AC dimer A4H2-T1702 0.07/0.21 0.08/0.22 A4H6-T1704 0.70/1.55 0.69/1.56 T17H3-A4N1 14.33 14.27 C5H4 …G1606 2.65/7.15 2.61/7.12 G16H1-C5N3 10.96 10.90 G16H2...C502 3.23/6.48 3.22/6.56

47.33 c 47.23。

CA dimer C2H4-G1906 2.69/5.93 2.66/6.13 G19H1...C2N3 9.86 9.63 G19H2 …C202 2.64/4.84 2.59/4.74 A3H2-T1802 0.06/0.16 0.05/0.15 A3H6-T1804 1.46/3.42 1.45/3.29 T18H3...A3N1 15.44 15.64

46.50 c 46.33。

CC dimer C1H4-G2006 2.34/4.32 2.29/4.42 G20H1-C1N3 9.62 9.60 G20H2-C102 3.09/5.52 3.08/5.61 C2H4 …G1906 2.74/6.55 2.71/6.22 G19H1-C2N3 9.19 9.38 G 1 9 H 2 - C 2 0 2 2.47/4.39 2.45/4.59

50.23 c 50.35 '

CG dimer C5KW…G1606 2.48/5.60 2.43/5.81 G16H1-C5N3 10.61 10.29 G16H2-C502 2.91/5.42 2.86/5.28 C15H4 …G606 2.53/5.85 2.47/6.04 G6H1-C15N3 10.79 10.54 G6H2 …C1502 2.97/5.57 2.93/5.49

54.73 c 54.14。

a. For NH…O and CH…〇 intermolecular hydrogen bonds, the charge transfer with both lone pairs on the oxygen atom are given and separated by a slash [nsp(〇)/np(〇)_ • b. Energy lowering effect due to «(B)->a*(AH) delocalization from the second order

perturbation analysis. c. The sum of E(2) energy of all intermolecular hydrogen bonds in the dimer unit.

54

18

,

16 -

3 14

丨

^^

I 丨

^

^

呈

10

；

y^

I 8

丨

舌

R i

<D

6 1

Z S

4 I

Z LU

1 Z

：丨

z U

！^

圓 _—

_ _ _ _

f I

_ ！

0 0.

05

0.1

0.15

b

on

d in

dex

Figure 3.6

The relationship between Wiberg,s bond index and

E(2) energy of intermolecular H-bonds of the dimers optimized

using B3PW91 functional

55

The corresponding equation. (3-1) is:

E(2) energy (kcal/mol) = 152.62x(WBI)-0.2164, (3-1)

R2=0.9865,n 二 30.

The stabilization energy of intermolecular H-bonds of AA, AC, C A and CC

dimers using B3LYP/6-31IG** were also calculated and reported in Table 3.13.

Their E(2) energies are slightly different from those obtained using B3PW91

because the positions of hydrogen atoms are slightly different after partial

optimization using different DFT functional. The Wiberg's bond index also shows a

good relationship with the E(2) energy of the intermolecular H-bonds for the dimers

calculated using B3LYP functional (Figure 3.7). The corresponding equation (3-2)

is:

E(2) energy (kcal/mol) = 153.86x(WBI)-0.292, (3-2)

r2 二 0.9872, n = 24.

In order to show how charges transfer between two base pairs, the natural

charge analysis of the CC dimer was performed. This is done by comparing the

charge difference of the dimer with the corresponding monomer units. The result is

listed in Table 3.14. The top view of the CC dimer is also shown in Figure 3.8 to

illustrate the stacking of the base pairs. The natural charges for the atoms of both

dimer and monomer units are shown in Supp. Table 3.5.

56

Table 3.13 Values for energetic parameters of intermolecular hydrogen bonds for AA, AC, CA, CC and C G dimers by N B O analysis with B3LYP/6-3IIG** method^

A H - B S(n,a*) As(n’cT*) (au)。 bond index -

A A dimer

A3H2-T1802 0.025/0.024 1.16/0.71 0.05/0.15 0.0034 A3H6-T1804 -0.160/-0.198 1.14/0.72 1.47/3.06 0.0317 T18H3-A3N1 0.502 0.73 16.27 0.1113 A4H2 …T1702 -0.031/-0.033 1.15/0.72 0.08/0.21 0.0036 A4H6-T1704 -0.118/-0.139 1.11/0.68 0.81/1.80 0.0237 T17H3-A4N1 0.480 0.73 14.42 0.0969

38.32 f

A C dimer A4H2-T1702 0.032/0.034 1.14/0.71 0.08/0.22 0.0039 A4H6...T1704 0.112/0.131 1.11/0.68 0.72/1.58 0.0220

T17H3-A4N1 -0.478 0.74 14.13 0.0937 C5H4 …G1606 0.200/0.284 1.04/0.67 2.64/7.10 0.0704 G16H1-C5N3 -0.440 0.79 10.81 0.0703

G16H2-C502 -0.221/-0.296 1.15/0.74 3.23/6.44 0.0583 46.95 f

C A dimer C2H4-G1906 0.208/0.268 1.08/0.70 2.69/5.94 0.0577 G19H1-C2N3 -0.414 0.76 9.86 0.0682 G19H2-C202 -0.208/-0.257 1.14/0.73 2.64/4.84 0.0456 A3H2 …T1802 0.029/0.027 1.15/0.70 0.06/0.16 0.0033 A3H6-T1804 -0.159/-0.207 1.11/0.70 1.48/3.45 0.0368 T 1 8 H 3 - A 3 N 1 -0.492 0.75 15.44 0.1002

46.56 r

CC dimer C1H4 …G2006 0.198/0.228 1.07/0.68 2.36/4.33 0.0487 G 2 0 H 1 - C 1 N 3 -0.417 0.79 9.59 0.0635

G20H2-C102 -0.222/-0.280 1.16/0.75 3.12/5.53 0.0497 C2H4-G1906 0.208/0.278 1.06/0.68 2.76/6.60 0.0646 G19H1-C2N3 -0.408 0.78 9.17 0.0612 G19H2 …C202 -0.203/-0.249 1.16/0.75 2.49/4.41 0.0410

50.36 r

a. For NH…O and CH…O intermolecular hydrogen bonds, the charge transfer with both lone pairs on the oxygen atom are given and separated by a slash [nsp(〇)/np(〇X • b. Overlap integral of associated pre-orthogonalized NBOs. c. N B O energy difference between n and a*. d. Energy change associated with deletion of off-diagonal matrix elements of effective one-electron Hamiltonian for the corresponding charge-transfer interaction. e. Refers to Wiberg's Bond Index. f. The sum of E(2) or deletion energy of all intermolecular hydrogen bonds in the dimer unit

57

18

n R2

= 0

.9872

X

16

] ^

^

？

14

I 12

1 Z

呈

10

t ：.!

X

§

4!

Z

0 奢

1

—1

1

0 0.05

0.1

0.15

bo

nd

ind

ex

Figure 3.7 The relationship between Wiberg's bond index and E(2) energy of intermolecular H-bonds of the dimers optimized using

B3LYP functional

58

Tabl

e 3.

14

Res

ults

of n

atur

al c

harg

e di

ffer

ence

s^ (A

O. e

") fo

r the

CC

dim

er^

CI

C2

G19

G20

AQb

AQb

AQb

AQb

—

m

IOJO

O4

-0.0

03

-0.0

01

-0.0

02

N3

0.005

0.012

0.011

-0.002

N7

- -

0.007

0.008

N9

- -

0.002

-0.003

N2

- -

-0.002

0.001

N4

0.015

-0.004

- -

02

0.003

0.010

- -

06

- -

-0.015

0.019

HI

- -

-0.001

0.003

H5

-0.002

-0.001

- -

H6

-0.004

-0.002

- -

H8

- -

-0.001

-0.006

H2a

- -

-0.001

0.002

H2b

- -

0.001

0.000

H4a

0.009

0.005

- -

H4b

-0.001

-0.002

- -

C2

-0.002

0.000

-0.002

-0.001

C4

-0.001

-0.004

0.003

0.002

C5

-0.001

-0.001

0.001

0.004

C6

-0.009

-0.014

0.001

-0.001

O -

- 0.012

-0.018

a. AQ = Q (atom in dimer) - Q (atom in mon

omer

).

b. The nomenclature of the atoms is based on Figure 3.2.

59

Figure 3.8 Top view of the CC

dime

r

60

A large net charge difference, AQ, was observed at the 06 atom of G20

residue (AQ = 0.019), 06 atom of G19 residue (AQ 二 -0.015) and N4 atom of CI

residue (AQ 二 0.015). These three heavy atoms are involved in the three-center H-

bonds identified by the N B O approach. It indicates that this H-bond is formed with

the two guanine bases, therefore the charges can be transferred between these

nucleobases. The other amino N-H***0 H-bonds do not show significant changes in

their charges.

Instead of observing large net charge difference involving atoms participating

in three-center H-bonding, different kinds of charge transfer processes are involved.

The interactions of the atoms on the two separate bases were probed by N B O

analysis and the results listed in Table 3.15 demonstrate that three types of

interactions involving orbitals were recognized from the stacking of the two base

pairs. n-7I interaction is observed for the C-C and C-N bonds; the carbonyl group

of the CI residue is also involved. Other than the n-n interaction, the lone pair of

the C5 atom of the G20 residue is found to interact with the n bond of N3-C4 and

C5-N7 of the G20 residue. Moreover, a bond of C2'-H2' on the sugar ring is also

involved.

61

Table 3.15 Values for energetic parameters of orbital interaction for CC dimer by N B O analysis with B3PW91/6-31 IG** method

- o r N B O acceptor N B O feSol) - ？aS^^^ S 。

n-n interaction

^*G19C8-G19N9 兀 *G20N7~G20C8 0.19 0.05 0.006

兀 G19N3~G19C4 TI;*G20C4~G20N9 0 . 1 4 0.25 0.008

兀 *C2N3_C2C4 兀 *C1C2_C102 0.21 0.02 0.004

n->7r interaction NG20C5 7R*G19C5-G19N7 0 . 1 3 0.12 0.005 NG20C5 TR*G19N3-G19C4 0.37 0.11 0.008

a—>71 interaction crcic2'-ciH2' 兀 *C2C5-C2C6 0.14 0.54 0.012

a. E(2) refers to second order perturbation energy (estimated donor-acceptor stabilization energy). b. It refers to the orbital energy difference between the donor and acceptor NBOs. c. It refers to the interaction element between donor and acceptor orbitals.

62

Table 3.16 Results of natural steric analysis (NSA) of intermolecular hydrogen bonds for AA. AC. CA, CC and C G dimers by N B O analysis with B3PW91/6-311G** method^

a h o S(n,a*), dimer dE(n,a*), dimer S(n,a*), monomer dE(n’a*)，monomer (au) b (kcal/mol)。 (au)' (kcal/mol)。

A A dimer A3H2 …T1802 0.035/0.057 0.16/0.28 0.036/0.057 0.16/0.28 A3H6...T1804 -0.099/-0.140 1.20/1.99 -0.097/-0.140 1.17/2.02 T18H3-A3N1 0.331 11.88 0.331 11.91 A4H2-T1702 -0.044/-0.063 0.22/0.37 -0.045/-0.062 0.23/0.36 A4H6...T1704 -0.079/-0.105 0.68/1.03 -0.078/-0105 0.67/1.02 T17H3 …A4N1 0.310 10.50 0.310 • 10.52

28.31 r 28.34

A C dimer A4H2-T1702 0.044/0.063 0.22/0.37 0.045/0.063 0.23/0.37 A4H6-T1704 0.077/0.102 0.63/0.95 0.076/0.102 0.64/0.95

T17H3 …A4N1 -0.310 10.47 -0.309 10.47 C5H4 …G1606 0.122/0.197 1.86/4.18 0.117/0.195 1.78/4.12 G16H1-C5N3 -0.284 8.48 -0.290 8.68 G16H2-C502 -0.135/0.206 2.50/5.10 -0/137/-0.199 2.67/4.82

34.72 r 34.73 ‘

C A dimer C2H4…G1906 -0.127/-0.189 2.04/3.84 0.126/0.189 2.02/3.84 G19H1-C2N3 0.266 7.18 -0.265 7.16 G19H2-C202 0.131/0.175 2.20/3.46 -0.131/-0.173 2.24/3.39 A3H2-T1802 -0.041/-0.058 0.18/0.28 0.036/0.057 0.16/0.28 A3H6-T1804 0.101/0.146 1.21/2.14 -0.098/-0.141 1.18/2.07 T18H3 …A3N1 0.320 11.27 -0.328 11.57

33.80 f 33.91 f

CC dimer“

C1H4…G2006 -0.126/-0.164 1.84/2.70 0.121/0.161 1.80/2.71 G20H1 …C1N3 0.268 7.37 -0.275 7.59 G20H2-C102 0.138/0.190 2.58/4.30 -0.138/-0.187 2.63/4.17 C2H4…G1906 -0.127/-0.194 1.99/4.02 0.127/0.190 2.05/3.90 G19H1-C2N3 0.262 6.97 -0.262 6.98 G19H2 …C202 0.128/0.170 2.16/3.28 -0.129/-0.171 2.16/3.30

37.21 f 37.29

C G dimer C5H4 …G1606 0.122/0.178 1.79/3.28 0.117/0.177 1.69/3.28 G 1 6 H 1 - C 5 N 3 -0.276 7.89 -0.282 8.11 G16H2…C502 -0.129/-0.185 2.19/3.94 -0.131/-0.178 2.30/3.68 C15H4…G606 -0.122/-0.181 1.81/3.42 0.117/0.180 1.71/3.43 G6H1-C15N3 0.278 8.09 -0.285 8.32 G6H2-C1502 0.130/0.189 2.23/4.10 -0.132/-0.182 2.35/3.85

38.74 38.72 丨

a. For NH…O and CH…O intermolecular hydrogen bonds, the charge transfer with both lone pairs on the oxygen atom are given and separated by a slash [nsp(0)/np(0)]. b. Overlap integral of associated pre-orthogonalized NBOs. c. Steric exchange energy between n and a. d. The sum of steric repulsion energy of all intermolecular hydrogen bonds in the dimer unit.

63

The N S A analysis performed for the different dimer molecules (Table 3.16),

identified that the total steric exchange energies of all the dimer units are smaller

than the E(2) energies. So hydrogen bondings are energetically favorable.

3.4.3 Detailed Analysis of CC and CG Dimers

The sums of E(2) energy of the intermolecular H-bonds for the different

models of C C and C G dimers are listed in the Table 3.17. The E(2) energies of the

m-dimer models for the two dimers vary slightly when compared with those of the

dimer models. This indicates that charge transfer is not influenced by the sugar

moiety and the phosphodiester linkages. The E(2) energy of h-dimer models

increased by 0.13 and 0.56 kcal/mol for the CC and the C G dimer respectively.

These changes are probably due to the anomeric effect of C T atoms of the

nucleobases. The charge density of the atoms on the aromatic rings is influenced by

the Cl'-N bond distance. The charge transfer is enhanced after removing the methyl

groups of the m-dimer models.

When the h-dimer models of the CC and C G dimers were changed to hs-

dimer models and then to hss-dimer models, the E(2) energy for both dimers

increased but within the same magnitude. It has shown that the charge transfer

process of H-bonds can be affected by the constituents connected to the H-bonds, but

this effect is not related to the difference in the E(2) energy of both the CC and the

C G dimers.

To find out the major factor determining the E(2) energy difference between

the C C and C G dimers, the hss-dimer model of the CC dimer is divided into two

separate monomers. The E(2) energy of the two corresponding monomers is

64

Tabl

e 3.

17

Val

ues

for

seco

nd o

rder

per

turb

atio

n en

ergy

. E(

2) o

f in

term

olec

ular

hyd

roge

n bo

nds

for

mod

els

by N

BO

ana

lysi

s w

ith

B3P

W91

/6-3

11G

** m

etho

d"

E(2), dimer

E(2), m-dimer

E(2), h-dimer

E(2), hs-dimer

E(2), hss-dimer

E(2), monomer

D"

B 入

。

(kcal/mol)

(kcal/mol)

(kcal/inol)

(kcal/mol)

(kcal/mol)

(kcal/mol)

；

CC dimer

C1H4-G2006

2.34/4.32

2.35/4.39

2.33/4.38

2.32/3.71

2.38/4.26

2.29/4.42

1.89

G20H1 …

C1N3

9.62

9.56

9.51

10.24

9.25

9.60

1.88

G20H2-C102

3.09/5.52

3.1

0/5

.48

2.99/5.75

2.87/6.33

3.02/5.27

3.08/5.61

1.77

C2H 小..G1906

2.74/6.55

2.76/6.55

2.75/6.57

2.84/5.36

2.87/6.21

2.71/6.22

1.82

G19H1 …

C2N3

9.19

9.19

9.17

9.82

9.00

9.38

丨.90

G19H2-C202

2.47/4.39

2.46/4.41

2.45/4.48

2.38/4.92

2.49/4.18

2.45/4.59

1.84

50.2

3 b

50.2

5 ‘

50.3

8 ‘

50.8

0

48.7

3 ‘)

50.3

5 ‘

CG

dimer

C5H4-G1606

2.48/5.60

2.47/5.58

2.48/5.62

2.57/4.82

2.60/5.63

2.43/5.81

1.85

G16H 卜

.C5N3

10.61

10.55

10.56

11.23

10.10

10.29

1.86

G16H2 …

C502

2.91/5.42

2.91/5.36

2.78/5.70

2.60/6.25

2.79/5.12

2.86/5.28

1.79

C1

5H

4-G

60

6 2.

53/5

.85

2.52

/5.8

4 2.

52/5

.85

2.62

/5.2

2 2.

65/5

.86

2.47

/6.0

4 1.

85

G6H1-C15N3

10.79

10.83

10.82

1 1.10

10.33

10.54

1.86

G6H2 …

C1502

2.97/5.57

2.99/5.59

2.84/5.93

2.67/6.29

2.86/5.32

2.93/5.49

_ 1.78

54.7

7 b

54.6

4 ^

55.1

0^

55.3

7 ^

5

3.2

6。

5

4.1

4'

a. For NH…

O intermolecular hydrogen bonds, the charge transfer with both lone pairs on

the oxygen atom are given and separated by a slash

K(0)

/np(

0)].

b. The sum of E(2) energy of all intermolecular hydrogen bonds in the dimer unit.

c. D(H…

B) denotes the interatomic distance between the hydrogen and the hydrogen bond acceptor.

65

approximately equal to that of the hss-dimer. Since the interatomic distances

between the hydrogen and acceptor atom involving imino N-H***N H bonds are not

the same, the structure of hss-monomer models were then modified to match that of

the C G dimer by changing the distance between HI atom of guanine and N3 atom of

cytosine to 1.86 A. The resulting E(2) energy of the modified hss-monomers

together with both modified and unmodified models is listed in Table 3.18. The total

E(2) energy of modified monomer has increased by about 5 kcal/mol and this value

is nearly identical to the hss-dimer model of the C G dimer. So the crucial factor

influencing the charge transfer is identified to be the H-bond distance by elimination

because the overlap of donor and acceptor orbitals increase when H-bond distance

decrease.

Table 3.18 Values for second order perturbation energy, E(2) of intermolecular hydrogen bonds for hss-monomer models for C C dimer with different distances by N B O analysis using B3PW91/6-3IIG**^

“ E(2), hss-monomer (unmod.) E(2), hss-monomer(mod.) (kcal/mol) (kcal/mol)

C1-G20

C1H4-G2006 2.33/4.33 2.52/4.70

G20H1...C1N3 9.25 9.97

G20H2-C102 3.02/5.36 3.26/5.84

C2-G19

C2H4 …G1906 2.80/6.07 3.14/6.92

G19H1---C2N3 9.03 10.12

G19H2-C202 2.45/4.24 2.78/4.81

48.88 b 54.06 ‘

a. For NH…O intermolecular hydrogen bonds, the charge transfer with both lone pairs on the oxygen atom are given and separated by a slash [nsp(0)/np(0). b. The sum of E(2) energy of all intermolecular hydrogen bonds in the dimer unit

The Natural Steric Analysis (NSA) performed on the different model

structures (Table 3.19) confirms that the total steric repulsion energy remain nearly

constant in the all dimer models for both the CC and the C G dimers. The steric

exchange energy has also increased when H-bond distance decrease.

66

Table 3.19

Values for natural steric analysis fNSA) of intermolecular hydrogen bonds for models by

NBO

analysis with B3PW91/6-31 IG**

basis set

dE(n,G*),

dE(n,c*),

dE(n,a*),

dE(n,a*),

dE(n,a*),

dE(n,c*),

dE(n,a*),

dE(n,a*),

AH…

B dimer w/o sugar

m-dimer

h-dimer

hs-dimer

hss-dimer

monomer

hss-monomer

hss-monomer(mod.)

(kcal/mol) a

(kcal/mol)

(kcal/mol)'

(kcal/mol)'

(kcal/mol)

(kcal/mol) ‘

(kcal/mol)'

(kcal/mol)‘

CC

dimer

C1H4-G2006

1.84/2.70

1.86/2.71

1.84/2.70

1.99/2.49

1.80/2.57

1.80/2.71

1.79/2.60

1.94/2.87

G20H1-C1N3

7.37

7.40

7.37

7.48

7.81

7.59

7.82

8.49

G20H2-C102

2.58/4.30

2.74/4.15

2.59/4.31

2.40/4.58

2.76/4.29

2.63/4.17

2.74/4.31

2.95/4.76

C2H4"G1906

1.99/4.02

2.01/4.03

2.00/4.03

2.29/3.59

2.04/3.73

2.05/3.90

2.03/3.67

2.26/4.29

G19H1-C2N3

6.97

6.99

6.97

7.05

7.39

6.98

7.43

8.42

G19H2-C202

2.16/3.28

2.20/3.24

2.15/3.27

2.04/3.48

2.27/3.26

2.16/3.30

2.26/3.31

2.55/3.85

37

.2”

37.3

3 b

37.2

3 b

37

.39

b

37.9

2 b

37.2

9

37.9

6 &

42.3

8 &

CG

dimer

C5H4-G1606

1.79/3.28

1.80/3.28

1.79/3.27

1.99/3.01

1.77/3.11

1.69/3.28

G16H1-C5N3

7.89

7.91

7.86

7.99

8.38

8.11

G16H2-C502

2.1

9/3

.94

2.37/3.76

2.1

8/3

.91

2.01/4.18

2.3

5/3

.89

2.3

0/3

.68

C15H4-G606

1.81/3.42

1.82/3.42

1.81/3.42

1.99/3.17

1.79/3.25

1.71/3.43

G6H1...C15N3

8.09

8.09

8.08

8.18

8.59

8.32

G6

H2

-C1

50

2 2.

23/4

.10

2.41

/3.9

2 2.

23/4

.10

2.05

/4.3

7 2.

39/4

.07

2.35

/3.8

5 C5H4 …

C15N4

0.05

-C15H4 …

C5N4

0.05

-

38.8

4 b

38.7

8 b

38.6

5 ^

38.9

4 ^

39.5

9 ^

38.7

2 b

a. Steric exchange energy between n and a.

b. The

sum of steric repulsion energy of all intermolecular hydrogen bonds in the dimer unit.

67

3.5 Summary

The calculation performed by DFT method resembles the positions of three-

centered hydrogen atoms in major grooves successfully. The distances between the

H and acceptor atoms in the next base pair are always larger than their van der Waals

radii. The shortening of intemuclear distance is not strictly obeyed in three-center

H-bond system.

The chemical shift and spin-spin coupling constants of different dimers have

been determined. Moreover, chemical shift changes and scalar coupling constants

can provide supportive information in identifying the locations of three-center H-

bonds. All cross-stranded H-bonds have non-zero trans-hy&xogQn bond scalar

coupling constants indicating the presence of orbital interaction between hydrogen

and a heavy atom.

The locations of the three-center H-bonds in different dimer units of

Dickerson's decamer are identified by the n^ -> a*AH interaction. From the N B O

analysis, all of the possible three-center H-bonds identified by x-ray crystallography

of Dickerson's decamer cannot be confirmed in this study. But one cross-strand H-

bond A3H2…G19N2 is found to exist in the C A dimer. The strength of the charge

transfer of intermolecular H-bonds of D N A base pairs is discussed. Also, the factors

that influence the differences in the E(2) energy of CC and CG dimers are discussed.

The most important factor has been identified to be the H-bond distance between the

base pairs. Other reasons, substituents connected to the H-atoms and anomeric effect

can also affect the strength of H-bond, but to a lesser extent.

68

C H A P T E R F O U R

C O N C L U D I N G R E M A R K S

The study of three-center H-bonds in D N A has been demonstrated by

quantum-chemical methods. The chemical shift differences between dimer and the

corresponding monomers, and the /ra i'-hydrogen bond spin-spin coupling constants

have been shown to provide useful information on cross-strand H-bonds. The N B O

analysis on the dimer molecules could identify the locations of three-center H-bonds

by examining the n ^ g* orbital interactions as well as determining the strength of

H-bonds. Transfer of charges between base pairs is possible through three-center H-

bond. From a detailed analysis of CC and C G dimers, it has been identified that the

crucial factor determining for the differences in H-bond strength is the H-bond

distance.

Based on the results of N B O analysis, the proposed three-center H-bonds in

Dickerson's decamer cannot be confirmed Only one possible cross-stranded H-

bond IS found in this duplex. The presence of cross-strand H-bond may be further

confirmed by the determination of trans-hydrogen bond J-coupling constant from

N M R spectroscopy. Moreover, it is necessary to determine the cut-off value of

cross-stranded H-bonds in order to assign this type of bonding correctly.

This thesis has also identified the effect of cross-strand H-bond to the

intermolecular H-bonds in D N A dimers, but this observation requires confirmation.

In order to obtain a better understanding on this topic, there is a need to perform the

study on a large number of sequences of dimers and larger system such as trimer.

The results obtained may help to rationalize the charge transfer of hydrogen

69

bondings in long D N A duplex, thus contributing to the understanding of electric

conductivity in D N A .

70

R E F E R E N C E S

C H A P T E R O N E

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71

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75

A P P E N D I X

76

Supp

lem

enta

ry T

able

3.

2 T

he c

alcu

late

d ^^

C c

hem

ical

shi

fts

fin p

pm)

of

DN

A d

imer

s'

Residue

HTH2-

H2"

H3'

H4•一

H5'

H5"

H6/H8

H2/H5

H1/H3

H2a/H4a/H6a ‘

H2b/H4b/H^

CC dimer

CI

7.00

1.29

2.27

4.69

3.87

3.90

3.68

7.27

5.12

- 10.10

4.44

C2

6.58

2.00

1.69

4.29

3.88

3.93

3.97

6.82

4.65

_ 10.85

3.81

G19

6.23

2.66

1.95

4.49

3.91

3.30

3.40

7.10

- 13.14

8.52

•

3.80

G2Q

6.19

2.36

2.15

4.53

4.03

4.23

3.84

6.79

- 13.01

9.26

3.50

CA

dimer

C2

4.89

1.83

2.35

4.29

3.82

3.61

3.69

6.88

5.00

- 10.13

3.90

A3

7.09

2.74

1.63

4.69

4.00

3.93

3.73

7.76

9.65

- 8.42

4.60

T18

5.71

1.80

3.12

4.54

3.78

3.50

3.73

7.33

- 16.26

- -

G19

6.48

2.87

1.63

4.60

4.11

4.05

3.97

7.36

- 13.59

8.80

4.22

A A

dimer

A3

6.95

2.59

2.21

4.59

3.84

3.42

3.55

7.59

8.82

- 8.40

5.00

A4

6.50

2.07

1.51

4.54

4.13

4.08

4.17

7.09

8.92

- 7.62

5.07

T17

6.48

1.46

2.16

4.72

3.64

3.94

3.64

6.76

- 15.57

- -

T18

6.92

2.06

1.21

4.42

4.12

3.88

4.07

7.11

- 16.86

- -

AC

dimer

‘

A4

6.82

1.87

1.89

4.52

4.07

3.66

3.39

7.22

9.22

- 7.84

5.35

C5

7.02

1.03

1.52

4.39

3.72

5.42

3.93

6.52

4.42

- 1 1.23

4.12

G16

6.52

2.61

2.54

5.05

3.70

3.78

3.65

7.52

- 13.43

9.68

3.41

T17

6.67

1.76

1.59

4.75

3.70

4.10

3.63

6.70

- 15.32

- -

CG

dimer

C5

6.73

1.60

3.32

5.09

3.68

4.02

3.73

6.99

5.05

- 10.51

4.08

G6

6.49

2.62

1.56

4.63

3.97

4.07

3.53

7.66

- 13.46

9.03

3.52

C15

6.74

1.52

3.02

4.74

3.63

4.00

3.78

6.94

5.04

- 10.66

4.10

G16

6.49

2.43

1.55

4.71

3.99

4.19

4.03

7.41

- 13.42

^ 3.53

a. The nomenclature of the atoms is based on Figure 2.3.

b. The amino proton involves in Watson-Crick basepair.

c. The amino proton does not involve in Watson-Crick basepair.

77

Supp

lem

enta

ry T

able

3.2

T

he c

alcu

late

d ^

C c

hem

ical

shi

fts

fin

ppm

) of

DN

A d

imer

s'

Residue

C1'

C2,

C3'

C4'

C5'

C2

C4

C5

C6

C8

—

CC dimer

CI

89.3

8 31

.75

78.2

5 78

.97

66.0

3 15

4.16

16

6.12

90

.92

136.

43

-C2

81.63

36.66

71.40

85.45

67.46

154.61

163.56

89.02

134.94

-

G19

85

.55

30.5

1 79

.94

82.0

8 66

.18

153.

20

153.

62

116.

69

158.

28

130.

32

GW

78

.73

38.4

0 68

.05

85.5

5 63

.64

154.

38

151.

45

117.

69

152.

41

128.

88

CA

dimer

C2

81.14

36.48

71.85

82.38

64.54

154.81

164.41

90.46

134.73

-

A3

90.80

31.91

80.65

79.87

66.42

丨 57.04

147.49

120.03

152.49

137.17

T18

84.65

34.84

75.20

79.71

63.09

157.95

166.63

103.36

140.10

-

G19

85.92

33.69

77.24

79.85

73.49

153.95

154.25

1 15.66

158.51

133.09

AA

dimer

A3

90.16

28.15

80.38

80.62

62.56

154.06

146.28

119.88

152.10

137.85

A4

82.27

36.04

71.57

81.29

64.60

156.84

148.55

1 19.64

151.12

134.11

T17

87.27

28.84

74.49

76.60

62.17

148.06

166.55

107.98

131.51

-

T18

84.67

38.84

73.02

77.37

65.73

157.44

165.85

104.51

138.00

-

AC

dimer

A4

82.22

34.02

73.57

82.76

60.46

158.26

148.77

119.69

151.56

133.60

C5

82.75

38.97

69.70

82.53

65.62

153.15

165.01

88.31

137.72

-

G16

88.67

33.37

81.56

79.81

64.31

151.71

149.71

116.47

156.90

134.34

T17

87.80

33.77

74.21

76.71

63.88

148.19

165.48

107.79

130.90

-

CG

dimer

C5

83.82

37.91

73.97

82.10

59.81

150.83

166.16

88.12

140.54

-

G6

86.93

35.95

81.63

78.12

65.65

148.22

150.25

115.35

154.62

134.14

C15

83.94

38.16

70.50

82.05

59.70

150.79

166.16

88.26

140.24

-

G16

86

.90

36.1

0 81

.53

78.5

3 68

.51

148.

30

150.

36

1 15

.23

154.

66

133.

35

a.

The nomenclature of the atoms is based on Figure 2.3.

78

Supp

lem

enta

ry T

able

3.

2 T

he c

alcu

late

d ^^

C c

hem

ical

shi

fts

fin p

pm)

of D

NA

dim

ers'

”iT

esid

ue

N1

" N3

N7

N9

N2/N4/N6

CC

dimer

CI

185.28

244.47

- -

127.44

C2

181.32

247.70

- -

122.91

G19

170.69

207.88

309.94

208.20

98.49

G20

173.49

198.48

303.07

196.87

98.94

CA

dimer

C2

183.03

245.15

- -

1 18.16

A3

265.25

267.59

280.92

208.53

95.29

T18

184.08

196.21

- -

-

G19

172.36

204.82

295.28

206.73

103.34

AA

dimer

A3

262.96

269.78

280.76

207.23

100.89

•

A4

257.74

273.08

280.34

197.87

100.34

T17

171.98

188.13

- -

-

T18

178.73

198.48

- -

-

AC

dimer

,

A4

259.29

268.57

280.00

197.78

106.23

C5

183.06

239.72

- -

127.24

G16

173.95

196.76

302.17

204.14

103.23

T17

172.16

186.75

- -

-

CG

dimer

C5

185.00

237.59

- -

120.63

G6

171.03

188.24

299.00

201.57

103.45

C15

184.52

237.79

- .

- 121.42

G16

171.28

188.16

298.34

202.44

103.78

a.

The nomenclature of the atoms is based on Figure 2.3.

79

Supp

lem

enta

ry T

able

3.

2 T

he c

alcu

late

d ^^

C c

hem

ical

shi

fts

fin

ppm

) of

DN

A d

imer

s'

Residue

03'

04'

05'

02

04/06

CC dimer

CI

- 123.05

26.41

308.18

-C2

74.40

120.71

- 328.07

-G19

- 140.59

35.09

- 325.58

G2Q

71.12

131.20

- ：

340.78

CA dimer

C2

- 119.11

28.56

321.71

-A3

72.15

148.88

- -

-T18

- 128.06

24.25

345.74

381.33

G19

74.50

145.79

- -

325.99

AA dimer

A3

- 145.21

26.00

- -

A4

67.58

131.51

- -

-T17

- 153.74

25.31

323.57

400.98

T18

71.28

130.02

- 351.69

406.52

AC dimer

A4

- 123.59

23.90

- -

C5

61.81

111.90

- 302.32

-G16

- 133.66

27.87

- 31 1.61

T17

67.95

158.37

- 316.91

413.46

CG dimer

C5

- 112.46

27.29

286.11

-G6

66.53

134.80

- -

310.84

C15

- 114.40

26.29

286.95

-G16

66.13

135.60

- -

312.15

a. The nomenclature of the atoms is based on figure 2.3.

80

Supplementary Table 3.5

Results of natural charge for the CC

dimer and the corresponding monomers^

^ ^

^ G20

Qdimer

Qmoncner

Q—er

Qmonomer

Qd.mer

Q 酬

。隨

Qimer

Q 隱

。隨

Ml

_0.459

-0.455

-0.454

-0.451

-0.617

-0.616

-0.627

-0.625

N3

-0.663

-0.668

-0.653

-0.666

-0.603

-0.614

-0.627

-0.625

N7

- -

- -

-0.448

-0.455

-0.449

-0.457

N9

- -

- -

-0.4

18

-0.4

19

-0.424

-0.421

N2

- -

- -

-0.779

-0.777

-0.789

-0.790

N4

-0.721

-0.735

-0.750

-0.747

-

02

-0.690

-0.693

-0.667

-0.678

-

06

- -

- -

-0.701

-0.685

-0.653

-0.672

HI

- -

- -

0.454

0.455

0.455

0.452

H5

0.221

0.223

0.219

0.221

-

H6

0.231

0.235

0.212

0.214

-

H8

- -

- -

0.193

0.193

0.185

0.190

H2a

- -

- -

0.424

0.425

0.426

0.424-

H2b

- -

- -

0.394

0.393

0.390

0.390

H4a

0.454

0.445

0.450

0.445

-

H4b

0.385

0.386

0.382

0.384

- -

-

C2

0.822

0.824

0.833

0.832

0.645

0.647

0.649

0.650

C4

0.480

0.481

0.475

0.479

0.387

0.384

0.383

0.381

C5

-0.362

-0.361

-0.357

-0.356

-0.057

-0.058

-0.062

-0.066

C6

0.093

0.102

0.090

0.104

0.654

0.653

0.653

0.654

C8

- -

0.197

0.185

0.205

0.223

a. The nomenclature of the atoms is based on Figure 3.2.

81

CUHK L i b r a r i e s

l l l l l l l l l l l i • 0MD7flMm