Quantum Chemistry
Free Global Shipping
No minimum orderDescription
Quantum Chemistry covers the basic principles, methods, and results of quantum chemistry, providing insights on electron behavior. This book is organized into 14 chapters that focus on ground state molecular orbital theory. After briefly dealing with some of the concepts of classical physics, the book goes on describing some simple but important particle systems. It then examines several systems with discontinuous potential energies, such as the simple harmonic oscillator and the hydrogen-like ion system. A chapter presents a set of postulates and theorems that form the formal foundation of quantum mechanics. Considerable chapters are devoted to various quantum chemical methods, as well as their basic features and application to molecular orbital evaluation. These methods include Huckel molecular orbital, variation, linear variation, extended Huckel, and SCF-LCAO-MO. The concluding chapters deal with the development of theories for molecular orbital, including time-independent Rayleigh-Schrodinger perturbation, group, and qualitative molecular orbital theories. Supplemental texts of the more complicated derivations or proofs and problems encountered in quantum chemistry are also provided. This book is an introductory text intended for organic, inorganic, and physical chemists, as well as for graduate and undergraduate students.
Table of Contents
Preface
Chapter 1 Classical Waves and the Time-Independent Schrödinger Wave Equation
1-1 Introduction
1-2 Waves
1-3 The Classical Wave Equation
1-4 Standing Waves in a Clamped String
1-5 Light as an Electromagnetic Wave
1-6 The Photoelectric Effect
1-7 The Wave Nature of Matter
1-8 A Diffraction Experiment with Electrons
1-9 Schrödinger's Time-Independent Wave Equation
1-10 Conditions on ψ
1-11 Some Insight into the Schrödinger Equation
1-12 Summary
Problems
Chapter 2 Quantum Mechanics of Some Simple Systems
2-1 The Particle in a One-Dimensional "Box"
2-2 Detailed Examination of Particle-in-a-Box Solutions
2-3 The Particle in a One-Dimensional "Box" with One Finite Wall
2-4 The Particle in an Infinite "Box" with a Finite Central Barrier
2-5 The Free Particle in One Dimension
2-6 The Particle in a Ring of Constant Potential
2-7 The Particle in a Three-Dimensional Box: Separation of Variables
2-8 Summary
Problems
Reference
Chapter 3 The One-Dimensional Harmonic Oscillator
3-1 Introduction
3-2 Some Characteristics of the Classical One-Dimensional Harmonic Oscillator
3-3 The Quantum-Mechanical Harmonic Oscillator
3-4 Solution of the Harmonic Oscillator Schrödinger Equation
3-5 Quantum-Mechanical Average Value of the Potential Energy
Problems
Chapter 4 The Hydrogenlike Ion
4-1 The Schrödinger Equation and the Nature of Its Solutions
4-2 Separation of Variables
4-3 Solution of the R, Θ, and Φ Equations
4-4 Atomic Units
4-5 Angular Momentum and Spherical Harmonics
4-6 Summary
Problems
References
Chapter 5 Many-Electron Atoms
5-1 The Independent Electron Approximation
5-2 Simple Products and Electron Exchange Symmetry
5-3 Electron Spin and the Exclusion Principle
5-4 Slater Determinants and the Pauli Principle
5-5 Singlet and Triplet States for the ls2s Configuration of Helium
5-6 The Self-Consistent Field, Slater-Type Orbitals, and the Aufbau Principle
Problems
References
Chapter 6 Postulates and Theorems of Quantum Mechanics
6-1 Introduction
6-2 The Wavefunction Postulate
6-3 The Postulate for Constructing Operators
6-4 The Time-Dependent Schrödinger Equation Postulate
6-5 The Postulate Relating Measured Values to Eigenvalues
6-6 The Postulate for Average Values
6-7 Hermitian Operators
6-8 Proof That Eigenvalues of Hermitian Operators Are Real
6-9 Proof That Eigenfunctions of an Hermitian Operator Form an Orthonormal Set
6-10 Proof That Commuting Operators Have Simultaneous Eigenfunctions
6-11 Completeness of Eigenfunctions of an Hermitian Operator
6-12 The Variation Principle
6-13 Measurement, Commutators, and Uncertainty
6-14 Summary
Problems
References
Chapter 7 The Variation Method
7-1 The Spirit of the Method
7-2 Nonlinear Variation: The Hydrogen Atom
7-3 Nonlinear Variation: The Helium Atom
7-4 Linear Variation: The Polarizability of the Hydrogen Atom
7-5 Linear Combination of Atomic Orbitals: The H2+ Molecule-Ion
7-6 Molecular Orbitals of Homonuclear Diatomic Molecules
7-7 Basis Set Choice and the Variational Wavefunction
7-8 Beyond the Orbital Approximation
Problems
References
Chapter 8 The Simple Hückel Method and Applications
8-1 The Importance of Symmetry
8-2 The Assumption of σ-π Separability
8-3 The Independent π-Electron Assumption
8-4 Setting up the Hückel Determinant
8-5 Solving the HMO Determinantal Equation for Orbital Energies
8-6 Solving for the Molecular Orbitals
8-7 The Cyclopropenyl System: Handling Degeneracies
8-8 Charge Distributions from HMOs
8-9 Some Simplifying Generalizations
8-10 HMO Calculations on Some Simple Molecules
8-11 Summary: The Simple HMO Method for Hydrocarbons
8-12 Relation between Bond Order and Bond Length
8-13 π-Electron Densities and Electron Spin Resonance Hyperfine Splitting Constants
8-14 Orbital Energies and Oxidation-Reduction Potentials
8-15 Orbital Energies and Ionization Potentials
8-16 π-Electron Energy and Aromaticity
8-17 Extension to Heteroatomic Molecules
8-18 Self-Consistent Variations of α and ß
8-19 HMO Reaction Indices
8-20 Conclusions
Problems
References
Chapter 9 Matrix Formulation of the Linear Variation Method
9-1 Introduction
9-2 Matrices and Vectors
9-3 Matrix Formulation of the Linear Variation Method
9-4 Solving the Matrix Equation
9-5 Summary
Problems
References
Chapter 10 The Extended Hückel Method
10-1 The Extended Hückel Method
10-2 Mulliken Populations
10-3 Extended Hückel Energies and Mulliken Populations
10-4 Extended Hückel Energies and Experimental Energies
Problems
References
Chapter 11 The SCF-LCAO-MO Method and Extensions
11-1 Ab Initio Calculations
11-2 The Molecular Hamiltonian
11-3 The Form of the Wavefunction
11-4 The Nature of the Basis Set
11-5 The LCAO-MO-SCF Equation
11-6 Interpretation of the LCAO-MO-SCF Eigenvalues
11-7 The SCF Total Electronic Energy
11-8 Basis Sets
11-9 The Hartree-Fock Limit
11-10 Correlation Energy
11-11 Koopmans' Theorem
11-12 Configuration Interaction
11-13 Examples of Ab Initio Calculations
11-14 Approximate SCF-MO Methods
Problems
References
Chapter 12 Time-Independent Rayleigh-Schrödinger Perturbation Theory
12-1 An Introductory Example
12-2 Formal Development of the Theory for Nondegenerate States
12-3 A Uniform Electrostatic Perturbation of an Electron in a "Wire"
12-4 The Ground-State Energy to First Order of Heliumlike Systems
12-5 Perturbation at an Atom in the Simple Hückel MO Method
12-6 Perturbation Theory for a Degenerate State
12-7 Polarizability of the Hydrogen Atom in the n = 2 States
12-8 Interaction between Two Orbitals: An Important Chemical Model
12-9 Connection between Time-Independent Perturbation Theory and Spectroscopic Selection Rules
Problems
References
Chapter 13 Group Theory
13-1 Introduction
13-2 An Elementary Example
13-3 Symmetry Point Groups
13-4 The Concept of Class
13-5 Symmetry Elements and Their Notation
13-6 Identifying the Point Group of a Molecule
13-7 Representations for Groups
13-8 Generating Representations from Basis Functions
13-9 Labels for Representations
13-10 Some Connections between the Representation Table and Molecular Orbitals
13-11 Representations for Cyclic and Related Groups
13-12 Orthogonality in Irreducible Inequivalent Representations
13-13 Characters and Character Tables
13-14 Using Characters to Resolve Reducible Representations
13-15 Identifying Molecular Orbital Symmetries
13-16 Determining in Which Molecular Orbital an Atomic Orbital Will Appear
13-17 Generating Symmetry Orbitals
13-18 Hybrid Orbitals and Localized Orbitals
13-19 Symmetry and Integration
Problems
References
Chapter 14 Qualitative Molecular Orbital Theory
14-1 The Need for a Qualitative Theory
14-2 Hierarchy in Molecular Structure and in Molecular Orbitals
14-3 H2+ Revisited
14-4 H2: Comparisons with 2+
14-5 Rules for Qualitative Molecular Orbital Theory
14-6 Application of QMOT Rules to Homonuclear Diatomic Molecules
14-7 Shapes of Polyatomic Molecules: Walsh Diagrams
14-8 Frontier Orbitals
14-9 Qualitative Molecular Orbital Theory of Reactions
Problems
References
Appendix 1 Useful Integrals
Appendix 2 Determinants
Appendix 3 Evaluation of the Coulomb Repulsion Integral over Is AOs
Appendix 4 Some Characteristics of Solutions of the Linear Variation Procedure
Appendix 5 The Pairing Theorem
Appendix 6 Hückel Molecular Orbital Energies, Coefficients, Electron Densities, and Bond Orders for Some Simple Molecules
Appendix 7 Derivation of the Hartree-Fock Equation
Appendix 8 The Virial Theorem for Atoms and Diatomic Molecules
Appendix 9 Details of the Solution of the Matrix Equation HC=SCE
Appendix 10 Computer Program Listings
Appendix 11 Bra-Ket Notation
Appendix 12 Values of Some Useful Constants and Conversion Factors
Appendix 13 Group Theoretical Charts and Tables
Appendix 14 Hints for Solving Selected Problems
Appendix 15 Answers to Selected Problems
Index
Product details
- No. of pages: 618
- Language: English
- Copyright: © Academic Press 1978
- Published: September 28, 1978
- Imprint: Academic Press
- eBook ISBN: 9780323141161