Multiconfigurational Quantum Chemistry

The first book to aid in the understanding of multiconfigurational quantum chemistry, Multiconfigurational Quantum Chemistry demystifies a subject that has historically been considered difficult to learn. Accessible to any reader with a background in quantum mechanics and quantum chemistry, the book contains illustrative examples showing how these methods can be used in various areas of chemistry, such as chemical reactions in ground and excited states, transition metal and other heavy element systems. The authors detail the drawbacks and limitations of DFT and coupled-cluster based methods and offer alternative, wavefunction-based methods more suitable for smaller molecules.

Table of Contents:
Preface xi Conventions and Units xiii 1 Introduction 1 1.1 References 4 2 Mathematical Background 7 2.1 Introduction 7 2.2 Convenient Matrix Algebra 7 2.3 Many-Electron Basis Functions 11 2.4 Probability Basics 14 2.5 Density Functions for Particles 16 2.6 Wave Functions and Density Functions 17 2.7 Density Matrices 18 2.8 References 22 3 Molecular Orbital Theory 23 3.1 Atomic Orbitals 24 3.1.1 The Hydrogen Atom 24 3.1.2 The Helium Atom 26 3.1.3 Many Electron Atoms 28 3.2 Molecular Orbitals 29 3.2.1 The Born–Oppenheimer Approximation 29 3.2.2 The LCAO Method 30 3.2.3 The Helium Dimer 34 3.2.4 The Lithium and Beryllium Dimers 35 3.2.5 The B to Ne Dimers 35 3.2.6 Heteronuclear Diatomic Molecules 37 3.2.7 Polyatomic Molecules 39 3.3 Further Reading 41 4 Hartree–Fock Theory 43 4.1 The Hartree–Fock Theory 44 4.1.1 Approximating the Wave Function 44 4.1.2 The Hartree–Fock Equations 45 4.2 Restrictions on The Hartree–Fock Wave Function 49 4.2.1 Spin Properties of Hartree–Fock Wave Functions 50 4.3 The Roothaan–Hall Equations 53 4.4 Practical Issues 55 4.4.1 Dissociation of Hydrogen Molecule 55 4.4.2 The Hartree-Fock Solution 56 4.5 Further Reading 57 4.6 References 58 5 Relativistic Effects 59 5.1 Relativistic Effects on Chemistry 59 5.2 Relativistic Quantum Chemistry 62 5.3 The Douglas–Kroll–Hess Transformation 64 5.4 Further Reading 66 5.5 References 66 6 Basis Sets 69 6.1 General Concepts 69 6.2 Slater Type Orbitals, STOs 70 6.3 Gaussian Type Orbitals, GTOs 71 6.3.1 Shell Structure Organization 71 6.3.2 Cartesian and Real Spherical Harmonics Angular Momentum Functions 72 6.4 Constructing Basis Sets 72 6.4.1 Obtaining Exponents 73 6.4.2 Contraction Schemes 73 6.4.3 Convergence in the Basis Set Size 77 6.5 Selection of Basis Sets 79 6.5.1 Effect of the Hamiltonian 79 6.5.2 Core Correlation 80 6.5.3 Other Issues 81 6.6 References 81 7 Second Quantization and Multiconfigurational Wave Functions 85 7.1 Second Quantization 85 7.2 Second Quantization Operators 86 7.3 Spin and Spin-Free Formalisms 89 7.4 Further Reading 90 7.5 References 91 8 Electron Correlation 93 8.1 Dynamical and Nondynamical Correlation 93 8.2 The Interelectron Cusp 94 8.3 Broken Bonds. (��)2→(��∗)2 97 8.4 Multiple Bonds, Aromatic Rings 99 8.5 Other Correlation Issues 100 8.6 Further Reading 102 8.7 References 102 9 Multiconfigurational SCF Theory 103 9.1 Multiconfigurational SCF Theory 103 9.1.1 The H2 Molecule 104 9.1.2 Multiple Bonds 107 9.1.3 Molecules with Competing Valence Structures 108 9.1.4 Transition States on Energy Surfaces 109 9.1.5 Other Cases of Near-Degeneracy Effects 110 9.1.6 Static and Dynamic Correlation 111 9.2 Determination of the MCSCF Wave Function 114 9.2.1 Exponential Operators and Orbital Transformations 115 9.2.2 Slater Determinants and Spin-Adapted State Functions 117 9.2.3 The MCSCF Gradient and Hessian 119 9.3 Complete and Restricted Active Spaces, the CASSCF and RASSCF Methods 121 9.3.1 State Average MCSCF 125 9.3.2 Novel MCSCF Methods 125 9.4 Choosing the Active Space 126 9.4.1 Atoms and Atomic Ions 126 9.4.2 Molecules Built from Main Group Atoms 128 9.5 References 130 10 The RAS State-Interaction Method 131 10.1 The Biorthogonal Transformation 131 10.2 Common One-Electron Properties 133 10.3 Wigner–Eckart Coefficients for Spin–Orbit Interaction 134 10.4 Unconventional Usage of RASSI 135 10.5 Further Reading 136 10.6 References 136 11 The Multireference CI Method 137 11.1 Single-Reference CI. Nonextensivity 137 11.2 Multireference CI 139 11.3 Further Reading 140 11.4 References 140 12 Multiconfigurational Reference Perturbation Theory 143 12.1 CASPT2 theory 143 12.1.1 Introduction 143 12.1.2 Quasi-Degenerate Rayleigh–Schrödinger Perturbation Theory 144 12.1.3 The First-Order Interacting Space 145 12.1.4 Multiconfigurational Root States 146 12.1.5 The CASPT2 Equations 148 12.1.6 IPEA, RASPT2, and MS-CASPT2 154 12.2 References 155 13 CASPT2/CASSCF Applications 157 13.1 Orbital Representations 158 13.1.1 Starting Orbitals: Atomic Orbitals 162 13.1.2 Starting Orbitals: Molecular Orbitals 164 13.2 Specific Applications 167 13.2.1 Ground State Reactions 167 13.2.2 Excited States–Vertical Excitation Energies 171 13.2.3 Photochemistry and Photophysics 184 13.2.4 Transition Metal Chemistry 194 13.2.5 Spin-Orbit Chemistry 202 13.2.6 Lanthanide Chemistry 207 13.2.7 Actinide Chemistry 209 13.2.8 RASSCF/RASPT2 Applications 212 13.3 References 216 Summary and Conclusion 219 Index 221

About the Author :
Björn O. Roos received his PhD inTheoretical Physics and is Professor Emeritus at Lund University. He is a former board member of the Swedish National Research Foundation, a member of the Swedish Royal Academy of Sciences, the Nobel Committee for Chemistry, the International Academy of Quantum Molecular Sciences, and is on the advisory editorial board for Chemical Physics Letter, Molecular Physics, International Journal of Quantum Chemistry, and Chemical Physics Physical Chemistry. Dr. Roos is the author of approximately 300 peer-reviewed articles in international journals, various book chapters, and is editor and co-author of text books for the European Summer School in Quantum Chemistry.