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Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theoryby Attila Szabo
Synopses & ReviewsPublisher Comments:The aim of this graduatelevel textbook is to present and explain, at other than a superficial level, modem ab initio approaches to the calculation of the electronic structure and properties of molecules. The first three chapters contain introductory material culminating in a thorough discussion of the HartreeFock approximation.The remaining four chapters describe a variety of more sophisticated approaches, which improve upon this approximation. Among the highlights of the seven chapters are (1) a review of the mathematics (mostly matrix algebra) required for the rest of the book, (2) an introduction to the basic techniques, ideas, and notations of quantum chemistry, (3) a thorough discussion of the HartreeFock approximation, (4) a treatment of configuration interaction (Cl) and approaches incorporating electron correlation, (5) a description of the independent electron pair approximation and a variety of more sophisticated approaches that incorporate coupling between pairs, (6) a consideration of the perturbative approach to the calculation of the correlation energy of manyelectron systems and (7) a brief introduction to the use of the oneparticle manybody Green's function in quantum chemistry. Over 150 exercises, designed to help the reader acquire a working knowledge of the material, are embedded in the text. The book is largely selfcontained and requires no prerequisite other than a solid undergraduate physical chemistry course; however, some exposure to quantum chemistry will enhance the student's appreciation of the material. Clear and wellwritten, this text is ideal for the second semester of a twosemester course in quantum chemistry, or for a special topics course. Synopsis:This graduatelevel text explains the modern indepth approaches to the calculation of electronic structure and the properties of molecules. Largely selfcontained, it features more than 150 exercises. 1989 edition. Synopsis:This graduatelevel text explains the modern indepth approaches to the calculation of electronic structure and the properties of molecules. Largely selfcontained, it features more than 150 exercises. 1989 edition. Table of Contents Preface to Revised edition
Preface 1. Mathematical Review 1.1 Linear Algebra 1.1.1 Threedimensional vector algebra 1.1.2 Matrices 1.1.3 Determinants 1.1.4 NDimensional Complex Vector spaces 1.1.5 Change of Basis 1.1.6 The Eigenvalue Problem 1.1.7 Functions of Matrices 1.2 Orthogonal functions, Eigenfunctions, and Operators 1.3 The Variation Method 1.3.1 The Variation principle 1.3.2 The Linear Variational Problem Notes, Further Reading 2. Many Electron Wave functions and operators 2.1 The Electronic Problem 2.1.1 Atomic Units 2.1.2 The BornOppenheimer Approximation 2.1.3 The Antisymmetry or Pauli Exclusion Principle 2.2 Orbitals, Slater Determinants, and Basis functions 2.2.1 Spin Orbitals and Spatial Orbitals 2.2.2 Hartree Products 2.2.3 Slater Determinants 2.2.4 The HartreeFock Approximation 2.2.5 The Minimal Basis H subscript 2 Model 2.2.6 Excited Determinants 2.2.7 Form of the Exact Wave function and Configuration Interaction 2.3 Operators and Matrix Elements 2.3.1 Minimal Basis H subscript 2 matrix Elements 2.3.2 Notations for One and TwoElectron Integrals 2.3.3 General Rules for Matrix Elements 2.3.4 Derivation of the Rules for Matrix Elements 2.3.5 Transition from Spin Orbitals to Spatial Orbitals 2.3.6 Coulomb and Exchange Integrals 2.3.7 PseudoClassical interpretation of Determinantal Energies 2.4 Second Quantization 2.4.1 Creation and annihilation Operators and Their Anticommutation Relations 2.4.2 SecondQuantized Operators and Their Matrix Elements 2.5 SpinAdapted Configurations 2.5.1 Spin Operators 2.5.2 Restricted Determinants and SpinAdapted Configurations 2.5.3 Unrestricted Determinants Notes, Further Reading 3. The HartreeFock Approximation 3.1 The HartreeFock Equations 3.1.1 The Coulomb and Exchange Operators 3.1.2 The Fock Operator 3.2 Derivation of the HartreeFock Equations 3.2.1 Functional Variation 3.2.2 Minimization of the Energy of a Single Determinant 3.2.3 The Canonical HartreeFock Equations 3.3 Interpretation of Solutions to the HartreeFock Equations 3.3.1 Orbital energies and Koopmans' Theorem 3.3.2 Brillouin's Theorem 3.3.3 The HartreeFock Hamiltonian 3.4 Restricted ClosedShell hartreeFock: The Roothaan Equations 3.4.1 ClosedShell HartreeFock: Restricted Spin Orbitals 3.4.2 Introduction of a Basis: The Roothaan Equations 3.4.3 The Charge Density 3.4.4 Expression for the Fock Matrix 3.4.5 Orthogonalization of the Basis 3.4.6 The SCF Procedure 3.4.7 Expectation Values and Population Analysis 3.5 Model Calculations on H subscript 2 and HeH superscript + 3.5.1 The 1s Minimal STO3G Basis Set 3.5.2 STO3G H subscript 2 3.5.3 An SCF Calculation on STO3G HeH superscript + 3.6 Polyatomic Basis Sets 3.6.1 Contracted Gaussian functions 3.6.2 Minimal Basis Sets: STO3G 3.6.3 Double Zeta Basis Sets: 431G 3.6.4 Polarized Basis Sets: 631G and 631G 3.7 Some Illustrative ClosedShell Calculations 3.7.1 Total Energies 3.7.2 Ionization Potentials 3.7.3 Equilibrium Geometries 3.7.4 Population Analysis and Dipole Moments 3.8 Unrestricted OpenShell HartreeFock: The PopleNesbet Equations 3.8.1 OpenShell HartreeFock: Unrestricted Spin Orbitals 3.8.2 Introduction of a Basis: The PopleNesbet Equations 3.8.3 Unrestricted Density Matrices 3.8.4 Expression for the Fock Matrices 3.8.5 Solution of the Unrestricted SCF Equations 3.8.6 Illustrative Unrestricted Calculations 3.8.7 The Dissociation Problem and its Unrestricted Solution Notes, Further Reading 4. Configuration Interaction 4.1 Multiconfigurational Wave Functions and the Structure of the Full CI Matrix 4.1.1 Intermediate Normalization and an Expression for the Correlation Energy 4.2 Doubly Excited CI 4.3 Some Illustrative Calculations 4.4 Natural Orbitals and the OneParticle Reduced Density Matrix 4.5 The Multiconfiguration SelfConsistent Field (MCSCF) and Generalized Valence Bond (GVB) Methods 4.6 Truncated CI and the SizeConsistency Problem Notes, Further Reading 5. Pair and CoupledPair Theories 5.1 The Independent Electron Pair Approximation (IEPA) 5.1.1 Invariance under Unitary Transformations: an example 5.1.2 Some Illustrative Calculations 5.2 CoupledPair Theories 5.2.1 The Coupled Cluster Approximation (CCA) 5.2.2 The Cluster Expansion of the Wave Function 5.2.3 Linear CCA and the Coupled Electron Pair Approximation (CEPA) 5.2.4 Some Illustrative Calculations 5.3 ManyElectron Theories with Single Particle Hamiltonians 5.3.1 The Relaxation Energy via CI, IEPA, CCA, and CEPA 5.3.2 The Resonance Energy of Polyenes in Hückel Theory Notes, Further Reading 6. ManyBody Perturbation Theory 6.1 RayleighSchrödinger (RS) Perturbation Theory 6.2 Diagrammatic Representation of RS Perturbation Theory 6.2.1 Diagrammatic Perturbation Theory for 2 States 6.2.2 Diagrammatic Perturbation Theory for N States 6.2.3 Summation of Diagrams 6.3 Orbital Perturbation Theory: OneParticle Perturbations 6.4 Diagrammatic Representation of Orbital Perturbation Theory 6.5 Perturbation Expansion of the Correlation Energy 6.6 The NDependence of the RS Perturbation Expansion 6.7 Diagrammatic Representation of the Perturbation Expansion of the Correlation Energy 6.7.1 Hugenholtz Diagrams 6.7.2 Goldstone Diagrams 6.7.3 Summation of Diagrams 6.7.4 What Is the Linked Cluster Theorem? 6.8 Some Illustrative Calculations Notes, Further Reading 7. The Oneparticle ManyBody Green's Function 7.1 Green's Functions in single Particle Systems 7.2 The OneParticle ManyBody Green's Function 7.2.1 The SelfEnergy 7.2.2 The solution of the Dyson Equation 7.3 Application of the formalism to H subscript 2 and HeH superscript + 7.4 Perturbation Theory and the Green's Function Method 7.5 Some Illustrative Calculations Notes, Further Reading Appendix A. Integral Evaluation with 1s Primitive Gaussians Appendix B. TwoElectron SelfConsistentField Program Appendix C. Analytic Derivative methods and Geometry Optimization Appendix D. Molecular Integrals for H subscript 2 as a Function of Bond Length Index What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
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