This provides an advanced text introducing graduate students to the mathematical foundations of methods needed to do working applications in molecular quantum mechanics. It contains a consistent use of atomic units from the very beginning for simplifying mathematical formulae, and presents a unified presentation of basic elements of atomic and molecular interactions, with particular emphasis on practical use of second-order calculation techniques.
This provides an advanced text introducing graduate students to the mathematical foundations of methods needed to do working applications in molecular quantum mechanics. It contains a consistent use of atomic units from the very beginning for simplifying mathematical formulae, and presents a unified presentation of basic elements of atomic and molecular interactions, with particular emphasis on practical use of second-order calculation techniques.
Dr Valerio Magnasco, MRSC, is full Professor of Theoretical Chemistry at the University of Genoa, Italy, presently at the Department of Chemistry and Industrial Chemistry (DCCI) of the Faculty of Mathematical, Physical and Natural Sciences of the University. He is Member of the Royal Society of Chemistry (UK, RSC), the American Institute of Physics (US, AIP), the Physical Chemistry Division of the Italian Chemical Society (Italy, SCI), the Class of Sciences of Accademia Ligure di Scienze e Lettere (Italy, Genova). He is supervising a research group working on the theoretical study of atomic and molecular interactions, and is author or co-author of over 170 scientific papers mostly published on international journals, and of one book on Molecular Quantum Mechanics.
Inhaltsangabe
Preface 1 Principles 1.1 The Orbital Model 1.2 Mathematical Methods 1.3 Basic Postulates 1.4 Physical Interpretation of the Basic Principles 2 Matrices 2.1 Definitions and Elementary Properties 2.2 Properties of Determinants 2.3 Special Matrices 2.4 The Matrix Eigenvalue Problem 3 Atomic Orbitals 3.1 Atomic Orbitals as a Basis for Molecular Calculations 3.2 Hydrogen-Like Orbitals (HAOs) 3.3 Slater-Type Orbitals (STOs) 3.4 Gaussian-Type Orbitals (GTOs) 4 The Variation Method 4.1 Variational Principles 4.2 Non-Linear Parameters 4.3 Linear Parameters and the Ritz Method 4.4 Applications of the Ritz Method 5 Spin 5.1 The Zeeman Effect 5.2 The Pauli Equations for 1-Electron Spin 5.3 The Dirac Formula for N-Electron Spin 6 Antisymmetry of Many-Electron Wavefunctions 6.1 Antisymmetry Requirement and the Pauli Principle 6.2 Slater Determinants 6.3 Distribution Functions 6.4 Average Values of Operators 7 SCF Calculations and Model Hamiltonians 7.1 Elements of Hartree-Fock Theory for Closed Shells 7.2 Roothaan Formulation of the LCAO-MO-SCF Equations 7.3 Molecular SCF Calculations 7.4 Hückel Theory 7.5 A Model for the 1-Dimensional Crystal 8 Post-Hartree-Fock Methods 8.1 Configuration Interaction (CI) 8.2 Multiconfiguration SCF 8.3 Møller-Plesset (MP) Theory 8.4 MP-R12 Method 8.5 CC-R12 Method 9.6 Density Functional Theory (DFT) 9 VB Theory and the Chemical Bond 9.1 The Born-Oppenheimer Approximation 9.2 The Hydrogen Molecule H2 9.3 The Origin of the Chemical Bond 9.3 Valence Bond (VB) Theory and the Chemical Bond 9.4 Hybridization and Molecular Structure 9.5 Pauling's Formula for Conjugated and Aromatic Hydrocarbons 10 Elements of Rayleigh-Schroedinger (RS) Perturbation Theory 10.1 RS Perturbation Equations up to Third Order 10.2 First-Order Theory 10.3 Second-Order Theory 10.4 Approximate E2 Calculations: the Hylleraas' Functional 10.5 Linear Pseudostates and Molecular Properties 10.6 Quantum Theory of Magnetic Susceptibilities 11 Atomic and Molecular Interactions 11.1 The H-H Non-Expanded Interactions up to Second Order 11.2 The H-H Expanded Interactions up to Second Order 11.3 Molecular Interactions 11.4 Van der Waals and Hydrogen Bonds 11.5 The Keesom Interaction 12 Symmetry 12.1 Molecular Symmetry 12.2 Group Theoretical Methods 12.3 Illustrative Examples References Author Index Subject Index
Preface 1 Principles 1.1 The Orbital Model 1.2 Mathematical Methods 1.3 Basic Postulates 1.4 Physical Interpretation of the Basic Principles 2 Matrices 2.1 Definitions and Elementary Properties 2.2 Properties of Determinants 2.3 Special Matrices 2.4 The Matrix Eigenvalue Problem 3 Atomic Orbitals 3.1 Atomic Orbitals as a Basis for Molecular Calculations 3.2 Hydrogen-Like Orbitals (HAOs) 3.3 Slater-Type Orbitals (STOs) 3.4 Gaussian-Type Orbitals (GTOs) 4 The Variation Method 4.1 Variational Principles 4.2 Non-Linear Parameters 4.3 Linear Parameters and the Ritz Method 4.4 Applications of the Ritz Method 5 Spin 5.1 The Zeeman Effect 5.2 The Pauli Equations for 1-Electron Spin 5.3 The Dirac Formula for N-Electron Spin 6 Antisymmetry of Many-Electron Wavefunctions 6.1 Antisymmetry Requirement and the Pauli Principle 6.2 Slater Determinants 6.3 Distribution Functions 6.4 Average Values of Operators 7 SCF Calculations and Model Hamiltonians 7.1 Elements of Hartree-Fock Theory for Closed Shells 7.2 Roothaan Formulation of the LCAO-MO-SCF Equations 7.3 Molecular SCF Calculations 7.4 Hückel Theory 7.5 A Model for the 1-Dimensional Crystal 8 Post-Hartree-Fock Methods 8.1 Configuration Interaction (CI) 8.2 Multiconfiguration SCF 8.3 Møller-Plesset (MP) Theory 8.4 MP-R12 Method 8.5 CC-R12 Method 9.6 Density Functional Theory (DFT) 9 VB Theory and the Chemical Bond 9.1 The Born-Oppenheimer Approximation 9.2 The Hydrogen Molecule H2 9.3 The Origin of the Chemical Bond 9.3 Valence Bond (VB) Theory and the Chemical Bond 9.4 Hybridization and Molecular Structure 9.5 Pauling's Formula for Conjugated and Aromatic Hydrocarbons 10 Elements of Rayleigh-Schroedinger (RS) Perturbation Theory 10.1 RS Perturbation Equations up to Third Order 10.2 First-Order Theory 10.3 Second-Order Theory 10.4 Approximate E2 Calculations: the Hylleraas' Functional 10.5 Linear Pseudostates and Molecular Properties 10.6 Quantum Theory of Magnetic Susceptibilities 11 Atomic and Molecular Interactions 11.1 The H-H Non-Expanded Interactions up to Second Order 11.2 The H-H Expanded Interactions up to Second Order 11.3 Molecular Interactions 11.4 Van der Waals and Hydrogen Bonds 11.5 The Keesom Interaction 12 Symmetry 12.1 Molecular Symmetry 12.2 Group Theoretical Methods 12.3 Illustrative Examples References Author Index Subject Index
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