Atoms and Molecules

1st Edition - January 1, 1978
Author: Mitchel Weissbluth
Language: English
eBook ISBN:
9 7 8 - 0 - 3 2 3 - 1 4 2 9 4 - 6

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… Read more

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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.

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 FieldPart 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; SusceptibilityPart 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 InteractionPart 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 InteractionsPart 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 EffectsPart 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 OrbitalsAppendix 1 Dirac NotationAppendix 2 OperatorsAppendix 3 Eigenvalues and EigenfunctionsAppendix 4 Relationships Among Unit VectorsAppendix 5 Bessel FunctionsAppendix 6 Laguerre PolynomialsAppendix 7 Hermite PolynomialsAppendix 8 Dirac δ-FunctionsReferencesIndex