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Informationen zum Autor Trygve Helgaker, Department of Chemistry, University of Oslo, Norway. Poul Jorgensen and Jeppe Olsen Department of Chemistry, University of Aarhus, Denmark. Klappentext Ab initio quantum chemistry has emerged as an important tool in chemical research and is applied to a wide variety of problems in chemistry and molecular physics. Recent developments of computational methods have enabled previously intractable chemical problems to be solved using rigorous quantum-mechanical methods. This is the first comprehensive up-to-date and technical work to cover all the important aspects of modern molecular electronic-structure theory. Topics covered in the book include: Second quantization with spin adaptation Gaussian basis sets and molecular-integral evaluation Hartree-Fock theory Configuration-interaction and multi-configurational self-consistent theory Coupled-cluster theory for ground and excited states Perturbation theory for single- and multi-configuration states Linear-scaling techniques and the fast multiple method Explicitly correlated wave functions Basis-set convergence and extrapolation Calibration and benchmarking of computational methods, with applications to molecular equilibrium structures, atomization energies and reaction enthalpies. Molecular Electronic-Structure Theory makes extensive use of numerical examples, designed to illustrate the strengths and weaknesses of each method treated. In addition, statements about the usefulness and deficiencies of the various methods are supported by actual examples, not just model calculations. Problems and exercises are provided at the end of each chapter, complete with hints and solutions. This book is a must for researchers in the field of quantum chemistry as well as for nonspecialists who wish to acquire a thorough understanding of ab initio molecular electronic-structure theory and its applications to problems in chemistry and physics. It is also highly recommended for the teaching of graduates and advanced undergraduates. Zusammenfassung Molecular electronic-structure theory uses quantum mechanics to calculate the energies and wave functions of molecules and their molecular properties. It uses sophisticated mathematics and computers to solved the wave equations. The calculations can be used to find out how the atoms of the molecule are linked together in a molecule. Inhaltsverzeichnis Preface xxi Overview xxv Programs used in the preparation of this book xxix 1. Second Quantization 1 1.1 The Fock space 1 1.2 Creation and annihilation operators 2 1.3 Number-conserving operators 6 1.4 The representation of one- and two-electron operators 9 1.5 Products of operators in second quantization 14 1.6 First- and second-quantization operators compared 18 1.7 Density matrices 19 1.8 Commutators and anticommutators 25 1.9 Nonorthogonal spin orbitals 27 2. Spin in Second Quantization 34 2.1 Spin functions 34 2.2 Operators in the orbital basis 35 2.3 Spin tensor operators 41 2.4 Spin properties of determinants 46 2.5 Configuration state functions 51 2.6 The genealogical coupling scheme 53 2.7 Density matrices 61 3. Orbital Rotations 80 3.1 Unitary transformations and matrix exponentials 80 3.2 Unitary spin-orbital transformations 86 3.3 Symmetry-restricted unitary transformations 89 3.4 The logarithmic matrix function 93 4. Exact and Approximate Wave Functions 107 4.1 Characteristics of the exact wave function 107 4.2 The variation principle 111 4.3 Size-extensivity 126 4.4 Symmetry constraints 135 5. The Standard Models 142 5.1 One- and N-electron expansions 143 5.2 A model system: the hydrogen...
