Multiconfigurational Quantum Chemistry

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.

• Preface xiConventions and Units xiii1 Introduction 11.1 References 42 Mathematical Background 72.1 Introduction 72.2 Convenient Matrix Algebra 72.3 Many-Electron Basis Functions 112.4 Probability Basics 142.5 Density Functions for Particles 162.6 Wave Functions and Density Functions 172.7 Density Matrices 182.8 References 223 Molecular Orbital Theory 233.1 Atomic Orbitals 243.1.1 The Hydrogen Atom 243.1.2 The Helium Atom 263.1.3 Many Electron Atoms 283.2 Molecular Orbitals 293.2.1 The Born–Oppenheimer Approximation 293.2.2 The LCAO Method 303.2.3 The Helium Dimer 343.2.4 The Lithium and Beryllium Dimers 353.2.5 The B to Ne Dimers 353.2.6 Heteronuclear Diatomic Molecules 373.2.7 Polyatomic Molecules 393.3 Further Reading 414 Hartree–Fock Theory 434.1 The Hartree–Fock Theory 444.1.1 Approximating the Wave Function 444.1.2 The Hartree–Fock Equations 454.2 Restrictions on The Hartree–Fock Wave Function 494.2.1 Spin Properties of Hartree–Fock Wave Functions 504.3 The Roothaan–Hall Equations 534.4 Practical Issues 554.4.1 Dissociation of Hydrogen Molecule 554.4.2 The Hartree-Fock Solution 564.5 Further Reading 574.6 References 585 Relativistic Effects 595.1 Relativistic Effects on Chemistry 595.2 Relativistic Quantum Chemistry 625.3 The Douglas–Kroll–Hess Transformation 645.4 Further Reading 665.5 References 666 Basis Sets 696.1 General Concepts 696.2 Slater Type Orbitals, STOs 706.3 Gaussian Type Orbitals, GTOs 716.3.1 Shell Structure Organization 716.3.2 Cartesian and Real Spherical Harmonics Angular Momentum Functions 726.4 Constructing Basis Sets 726.4.1 Obtaining Exponents 736.4.2 Contraction Schemes 736.4.3 Convergence in the Basis Set Size 776.5 Selection of Basis Sets 796.5.1 Effect of the Hamiltonian 796.5.2 Core Correlation 806.5.3 Other Issues 816.6 References 817 Second Quantization and Multiconfigurational Wave Functions 857.1 Second Quantization 857.2 Second Quantization Operators 867.3 Spin and Spin-Free Formalisms 897.4 Further Reading 907.5 References 918 Electron Correlation 938.1 Dynamical and Nondynamical Correlation 938.2 The Interelectron Cusp 948.3 Broken Bonds. (��)2→(��∗)2 978.4 Multiple Bonds, Aromatic Rings 998.5 Other Correlation Issues 1008.6 Further Reading 1028.7 References 1029 Multiconfigurational SCF Theory 1039.1 Multiconfigurational SCF Theory 1039.1.1 The H2 Molecule 1049.1.2 Multiple Bonds 1079.1.3 Molecules with Competing Valence Structures 1089.1.4 Transition States on Energy Surfaces 1099.1.5 Other Cases of Near-Degeneracy Effects 1109.1.6 Static and Dynamic Correlation 1119.2 Determination of the MCSCF Wave Function 1149.2.1 Exponential Operators and Orbital Transformations 1159.2.2 Slater Determinants and Spin-Adapted State Functions 1179.2.3 The MCSCF Gradient and Hessian 1199.3 Complete and Restricted Active Spaces, the CASSCF and RASSCF Methods 1219.3.1 State Average MCSCF 1259.3.2 Novel MCSCF Methods 1259.4 Choosing the Active Space 1269.4.1 Atoms and Atomic Ions 1269.4.2 Molecules Built from Main Group Atoms 1289.5 References 13010 The RAS State-Interaction Method 13110.1 The Biorthogonal Transformation 13110.2 Common One-Electron Properties 13310.3 Wigner–Eckart Coefficients for Spin–Orbit Interaction 13410.4 Unconventional Usage of RASSI 13510.5 Further Reading 13610.6 References 13611 The Multireference CI Method 13711.1 Single-Reference CI. Nonextensivity 13711.2 Multireference CI 13911.3 Further Reading 14011.4 References 14012 Multiconfigurational Reference Perturbation Theory 14312.1 CASPT2 theory 14312.1.1 Introduction 14312.1.2 Quasi-Degenerate Rayleigh–Schrödinger Perturbation Theory 14412.1.3 The First-Order Interacting Space 14512.1.4 Multiconfigurational Root States 14612.1.5 The CASPT2 Equations 14812.1.6 IPEA, RASPT2, and MS-CASPT2 15412.2 References 15513 CASPT2/CASSCF Applications 15713.1 Orbital Representations 15813.1.1 Starting Orbitals: Atomic Orbitals 16213.1.2 Starting Orbitals: Molecular Orbitals 16413.2 Specific Applications 16713.2.1 Ground State Reactions 16713.2.2 Excited States–Vertical Excitation Energies 17113.2.3 Photochemistry and Photophysics 18413.2.4 Transition Metal Chemistry 19413.2.5 Spin-Orbit Chemistry 20213.2.6 Lanthanide Chemistry 20713.2.7 Actinide Chemistry 20913.2.8 RASSCF/RASPT2 Applications 21213.3 References 216Summary and Conclusion 219Index 221

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