Atoms and Molecules
1st Edition
Description
Atoms and Molecules describes the basic properties of atoms and molecules in terms of group theoretical methods in atomic and molecular physics. The book reviews mathematical concepts related to angular momentum properties, finite and continuous rotation groups, tensor operators, the Wigner-Eckart theorem, vector fields, and vector spherical harmonics. The text also explains quantum mechanics, including symmetry considerations, second quantization, density matrices, time-dependent, and time-independent approximation methods. The book explains atomic structure, particularly the Dirac equation in which its nonrelativistic approximation provides the basis for the derivation of the Hamiltonians for all important interactions, such as spin-orbit, external fields, hyperfine. Along with multielectron atoms, the text discusses multiplet theory, the Hartree-Fock formulation, as well as the electromagnetic radiation fields, their interactions with atoms in first and higher orders. The book explores molecules and complexes, including the Born-Oppenheimer approximation, molecular orbitals, the self-consistent field method, electronic states, vibrational and rotational states, molecular spectra, and the ligand field theory. The book can prove useful for graduate or advanced students and academicians in the field of general and applied physics.
Table of Contents
Preface
Part I Mathematical Background
Chapter 1 Angular Momentum
1.1 Orbital Angular Momentum
1.2 Spherical Harmonics and Related Functions
1.3 Generalized Angular Momentum
1.4 Spin
1.5 Coupling of Two Angular Momenta
1.6 Coupling of Three Angular Momenta
1.7 Summary and Examples
Chapter 2 Rotations
2.1 Coordinate Rotations and Scalar Functions
2.2 Rotations and Angular Momenta
2.3 Transformation Properties of Angular Momentum Eigenfunctions
Chapter 3 Elements of Group Theory
3.1 Definitions and Basic Properties
3.2 Representations and Characters
3.3 Reducible and Irreducible Representations
3.4 Basis Functions
3.5 Projection Operators
3.6 Product Representations
3.7 Matrix Elements
Chapter 4 Continuous Rotation Groups
4.1 Rotation Group in Two Dimensions, C∞
4.2 Rotation Group in Three Dimensions, 0+(3)
4.3 Special Unitary Group in Two Dimensions, SU(2)
4.4 Connection between 0+(3) and SU(2)
4.5 Irreducible Representations of 0+(3)
4.6 Summary and Examples
Chapter 5 Finite Groups
5.1 Point Groups—Symmetry Operations and Nomenclature
5.2 Double Groups
5.3 The Groups 0, D4 and D6h
5.4 Permutation Groups Sn — Young Diagrams
Chapter 6 Tensors
6.1 Irreducible Tensor Operators
6.2 Tensor Products
6.3 Wigner-Eckart Theorem
6.4 Cartesian Tensors
6.5 Tensors, Permutation Groups, Continuous Groups
Chapter 7 Vector Fields
7.1 Rotational Properties
7.2 Vector Spherical Harmonics
7.3 Plane Wave Expansion
7.4 Multipole Expansion of the Electromagnetic Field
Part II Quantum-Mechanical Background
Chapter 8 Symmetry Elements of the Hamiltonian
8.1 Connection Between Group Theory and Quantum Mechanics
8.2 Geometrical Symmetries
8.3 Time Reversal and Kramers' Theorem
8.4 Indistinguishability of Particles
Chapter 9 Time Development of a Quantum Syste
9.1 Schrödinger Representation
9.2 Heisenberg Representation
9.3 Interaction Representation
9.4 Infinite Limits
Chapter 10 Harmonic Oscillator
10.1 Schrödinger Solutions
10.2 Matrix Formulation
10.3 Heisenberg Representation
Chapter 11 Slater Determinants
11.1 Matrix Elements—General
11.2 Matrix Elements—Special Cases
Chapter 12 Second Quantization
12.1 Creation and Annihilation Operators
12.2 Matrix Elements of Operators
12.3 Diagrams
12.4 Field Operators
Chapter 13 Density Matrices
13.1 General Properties
13.2 Spin States
13.3 Reduced Density Matrices
13.4 Thermal Equilibrium
13.5 Equation of Motion
13.6 Multielectron Systems
13.7 Fock-Dirac Density Matrices
13.8 Spinless Density Matrices
Chapter 14 Approximations
14.1 Variational Methods
14.2 Time-Independent Perturbations
14.4 Fermi's Golden Rule
14.5 Density Matrices—Random Perturbations
14.6 Response Function; Susceptibility
Part III One-Electron Atoms
Chapter 15 Dirac Equation
15.1 Free Particle Equation
15.2 Dirac Equation with Electromagnetic Coupling
Chapter 16 Hydrogen Atom
16.1 Schrödinger Equation
16.2 One-Electron Wave Functions
16.3 Spin-Orbit Coupling
16.4 Other Interactions
Chapter 17 Static Fields
17.1 Magnetic Fields
17.2 Electric Fields
Chapter 18 Hyperfine Interactions
18.1 Hamiltonian for the Magnetic Hyperfine Interaction
18.2 Magnetic Hyperfine Interaction in One-Electron Systems
18.3 Electric Quadrupole Interaction
Part IV W-Electron Atoms
Chapter 19 Hartree-Fock Formulation
19.1 The Hamiltonian
19.2 Central Field Approximation
19.3 Hartiee-Fock Equations
19.4 Properties of the Hartree-Fock Solutions
19.5 Computational Methods
19.6 Correlation Error and Configuration Interaction
Chapter 20 Multiplet Wave Functions
20.1 Two-Electron Multiplets
20.2 Terms from a Configuration of n Electrons
20.3 Construction of Multiplet Wave Functions
20.4 Symmetry Properties
20.5 jj Coupling
Chapter 21 Matrix Elements
21.1 Electrostatic Matrix Elements—Two Electrons
21.2 Some n-Electron Matrix Elements
21.3 Electrostatic Matrix Elements—n Electrons
21.4 Spin- Orbit Interaction
21.5 Conjugate Configurations
21.6 Other Interactions
Part V Electromagnetic Interactions
Chapter 22 Interaction Between Atoms and Radiation
22.1 Hamiltonian of the Radiation Field
22.2 Quantization of the Radiation Field
22.3 Interaction Hamiltonian and Matrix Elements
22.4 Selection Rules and Angular Distributions
Chapter 23 Absorption and Emission
23.1 Transition Probabilities
23.2 Einstein Coefficients and Planck's Law
23.3 Oscillator Strengths and Sum Rules
23.4 Numerical Computations
23.5 Line Broadening
23.6 Cross Sections
23.7 Photoelectric Effect
23.8 Survey of Atomic Spectra
Chapter 24 Higher Order Electromagnetic Interactions
24.1 The Kramers-Heisenberg Formula
24.2 Scattering—Special Cases
24.3 Diagrams
24.4 Optical Susceptibility and Nonlinear Effects
Part VI Molecules
Chapter 25 General Properties of Molecules
25.1 Born-Oppenheimer Approximation
25.2 Molecular Orbitals and the Self-Consistent Field Method
25.3 Computational Methods
Chapter 26 Electronic States of Molecules
26.1 Hydrogen Molecule Ion (H2+)
26.2 Symmetry Considerations—H2+
26.3 Hydrogen Molecule
26.4 Diatomic and Linear Molecules
26.5 Hybrid Orbitals
26.6 The π-Electron Approximation
Chapter 27 Molecular Spectra
27.1 Vibrations and Rotations of Diatomic Molecules
27.2 Transitions in Diatomic Molecules
27.3 Vibration of Polyatomic Molecules
27.4 Transitions in Polyatomic Molecules
Chapter 28 Ligand Fields
28.1 Basic Ideas
28.2 Single d Electron in an Octahedral and Tetragonal Field
28.3 Multielectron Configurations
28.4 Magnetic Fields and the Spin Hamiltonian
28.5 Molecular Orbitals
Appendix 1 Dirac Notation
Appendix 2 Operators
Appendix 3 Eigenvalues and Eigenfunctions
Appendix 4 Relationships Among Unit Vectors
Appendix 5 Bessel Functions
Appendix 6 Laguerre Polynomials
Appendix 7 Hermite Polynomials
Appendix 8 Dirac δ-Functions
References
Index
Details
- No. of pages:
- 730
- Language:
- English
- Copyright:
- © Academic Press 1978
- Published:
- 1st January 1978
- Imprint:
- Academic Press
- eBook ISBN:
- 9780323142946