**Meet the editor**

Dr. Tomofumi Tada is a Project Lecturer at the Global COE for Mechanical Systems Innovation, University of Tokyo. He obtained his Doctor of Science degree at the Hiroshima University in 2002. The same year he started a Postdoctoral Fellowship at the Basic Organic Chemistry Research Center, Kyushu University, followed by another Fellowship in 2003 at the Institute for Materials

Chemistry of the same University. In 2004 Dr. Tada became a Research Associate at the Department of Materials Engineering, University of Tokyo, taking the role of Assistant Professor in 2006. He has authored and coauthored many articles in esteemed scientific journals and is a coauthor of the book "Simulation for Measurements of Electric Properties of Surface Nanostructures" published in 2007. His expertise lies in the fields of Quantum Mechanics, Quantum Chemistry, Electronic Structure Theory, and Computational Materials Science.

Contents

**Preface IX** 

Chapter 1 **Numerical Solution of Linear** 

Chapter 2 **Composite Method Employing** 

Nelson Henrique Morgon

Chapter 3 **Quantum Chemical Calculations** 

Chapter 4 **Elementary Molecular Mechanisms of** 

**the Classical Understanding 59** 

Chapter 5 **Quantum Chemistry and Chemometrics** 

**Part 3 Molecules to Nanodevices 131** 

Tomofumi Tada

**Part 1 Theories in Quantum Chemistry 1** 

**Ordinary Differential Equations in** 

**Pseudopotential at CCSD(T) Level 11** 

**Part 2 Electronic Structures and Molecular Properties 23** 

**for some Isatin Thiosemicarbazones 25**  Fatma Kandemirli, M. Iqbal Choudhary, Sadia Siddiq, Murat Saracoglu, Hakan Sayiner, Taner Arslan, Ayşe Erbay and Baybars Köksoy

**the Spontaneous Point Mutations in DNA: A Novel Quantum-Chemical Insight into** 

**Applied to Conformational Analysis 103**  Aline Thaís Bruni and Vitor Barbanti Pereira Leite

**Processing in Single Molecular Junctions 133** 

Chapter 6 **Quantum Transport and Quantum Information** 

Ol'ha O. Brovarets', Iryna M. Kolomiets' and Dmytro M. Hovorun

**Quantum Chemistry by Spectral Method 3**  Masoud Saravi and Seyedeh-Razieh Mirrajei

## Contents

#### **Preface XI**

**Part 1 Theories in Quantum Chemistry 1** 


#### **Part 2 Electronic Structures and Molecular Properties 23**

	- **Part 3 Molecules to Nanodevices 131**

#### Chapter 8 **Theoretical Study for High Energy Density Compounds from Cyclophosphazene 175**  Kun Wang, Jian-Guo Zhang, Hui-Hui Zheng, Hui-Sheng Huang and Tong-Lai Zhang

## Preface

Molecules, small structures composed of atoms, are essential substances for lives. However, we didn't have the clear answer to the following questions until the 1920s: why molecules can exist in stable as rigid networks between atoms, and why molecules can change into different types of molecules. The most important event for solving the puzzles is the discovery of the quantum mechanics. Quantum mechanics is the theory for small particles such as electrons and nuclei, and was applied to hydrogen molecule by Heitler and London at 1927. The pioneering work led to the clear explanation of the chemical bonding between the hydrogen atoms. This is the beginning of the quantum chemistry. Since then, quantum chemistry has been an important theory for the understanding of molecular properties such as stability, reactivity, and applicability for devices.

Quantum chemistry has now two main styles: (i) the precise picture (computations) and (ii) simple picture (modeling) for describing molecular properties. Since the Schrodinger equation, the key differential equation in quantum mechanics, cannot be solved for polyatomic molecules in the original many-body form, some approximations are required to apply the equation to molecules. A popular strategy is the approximation of the many-body wave functions by using single-particle wave functions in a single configuration. The single-particle wave function can be represented with the linear combination of atomic orbitals (LCAOs), and the differential equation to be solved is consequently converted to a matrix form, in which matrices are written in AO basis. This strategy immediately leads to the Hartree-Fock Roothaan equation, and this is an important branching point toward the precise computations or appropriate modeling. Since the approximations made in the Hartree-Fock Roothaan equation can be clearly recognized, the descriptions of many-body wave functions are expected to be better and better by using much more AOs, multiconfigurations, and more rigorous treatment for many-body interactions. Prof. J. A. Pople was awarded the Novel prize in Chemistry at 1998 for his pioneering works devoted for the development of the wave function theory toward the precise picture of molecular properties. The style is of course quite important, especially when we roughly know what are the interesting properties in a target molecule, because our efforts in those cases must be made to obtain more quantitative description of the target properties. However, when we don't know what the interesting properties of

#### XII Preface

the target molecule are, we have to take care whether a quantum chemical method in your hand is really appropriate for your purpose because an expensive method using many AOs and configurations sometimes falls into a difficulty in the extraction of the intrinsic property of the target molecule. Thus, we have to turn to the second style, the simple picture, to capture the properties of the target molecule roughly. For example, a simple π orbital picture is useful to predict the reactivity of π organic molecules on the basis of the frontier orbital theory in which the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) are the key orbitals for the prediction of the chemical response of the target molecule. When symbolized AOs (i.e., AOs represented neither in analytical nor in numerical form) are adopted for calculations, the Hamiltonian matrix is simply represented only with the numbers "0" and "1". Despite the simple description for the molecule, the frontier orbitals calculated (sometimes by hand) from the Hamiltonian are quite effective for the prediction of the reactivity of the target molecule. Prof. K. Fukui, the pioneer of the frontier orbital theory, was awarded the Novel prize in Chemistry at 1981.

Nowadays, our target molecules are structured as more diverse atomic networks and embedded in more complicated environment. The molecular properties are thus inevitably dependent on the complicated situations, and therefore we need the balanced combination of both styles, simple-and-precise picture, for the target today. We have to consider how we should build the veiled third style. To keep this in mind, this book is composed of nine chapters for the quantum chemical theory, conventional applications and advanced applications. I sincerely apologize this book cannot cover the broad spectrum of quantum chemistry. However, I hope this book, *Quantum Chemistry – Molecules for Innovation*, will be a hint for younger generations.

#### **Tomofumi Tada**

Global COE for Mechanical Systems Innovation, Department of Materials Engineering, The University of Tokyo, Japan

**Part 1** 

**Theories in Quantum Chemistry** 

**1** 

*Iran* 

**Numerical Solution of Linear** 

Masoud Saravi1 and Seyedeh-Razieh Mirrajei2

*1Islamic Azad University, Nour Branch, Nour,* 

*2Education Office of Amol, Amol,* 

**Ordinary Differential Equations in** 

**Quantum Chemistry by Spectral Method** 

The problem of the structure of hydrogen atom is the most important problem in the field of atomic and molecular structure. Bahr's treatment of the hydrogen atom marked the beginning of the old quantum theory of atomic structure, and wave mechanics had its inception in Schrodinger 's first paper, in which he gave the solution of the wave equation for the hydrogen atom. Since the most differential equations concerning physical phenomenon could not be solved by analytical method hence, the solutions of the wave equation are based on polynomial (series) methods. Even if we use series method, some times we need an appropriate change of variable, and even when we can, their closed form solution may be so complicated that using it to obtain an image or to examine the structure of the system is impossible. For example, if we consider Schrodinger

��� + (���ℎ�� − ����)� � �, we come to a three-term recursion relation, which work with it takes, at least, a little bit time

����������(�),

As we can observe, working with this equation is tedious. Another two equations which occur in the hydrogen atom wave equations, are Legendre and Laguerre equations, which

In next section, after a historical review of spectral methods we introduce Clenshaw method, which is a kind of spectral method, and then solve such equations in last section. But, first of all, we put in mind that this method can not be applied to atoms with more electrons. With

<sup>ℎ</sup>� <sup>−</sup> �� �����

� � � ��

to get a series solution. For this reason we use a change of variable such as

��� ��� + ����

can be solved only by power series methods.

or when we consider the orbital angular momentum, it will be necessary to solve

�� �� + � �

**1. Introduction** 

equation, i.e.,
