Molecular electronic-structure theory / / Trygve Helgaker, Poul Jorgensen, Jeppe Olsen

• Record Nr.: UNINA9910208845103321
• Autore: Helgaker Trygve
• Pubbl/distr/stampa: Chichester, England : , : John Wiley & Sons Ltd., , 2012; ©2000
• ISBN: 1-119-01957-5; 1-119-01955-9; 1-119-01956-7
• Descrizione fisica: 1 online resource (940 p.)
• Disciplina: 541.28
• Soggetti: Molecular structure; Electronic structure; Electronic books.
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Cover; Title Page; Copyright; Contents; Preface; Overview; Programs used in the preparation of this book; 1 Second Quantization; 1.1 The Fock space; 1.2 Creation and annihilation operators; 1.2.1 Creation operators; 1.2.2 Annihilation operators; 1.2.3 Anticommutation relations; 1.3 Number-conserving operators; 1.3.1 Occupation-number operators; 1.3.2 The number operator; 1.3.3 Excitation operators; 1.4 The representation of one- and two-electron operators; 1.4.1 One-electron operators; 1.4.2 Two-electron operators; 1.4.3 The molecular electronic Hamiltonian; 1.5 Products of operators in second quantization1.5.1 Operator products; 1.5.2 The canonical commutators; 1.6 First- and second-quantization operators compared; 1.7 Density matrices; 1.7.1 The one-electron density matrix; 1.7.2 The two-electron density matrix; 1.7.3 Density matrices in spin-orbital and coordinate representations; 1.8 Commutators and anti commutators; 1.9 Nonorthogonal spin orbitals; 1.9.1 Creation and annihilation operators; 1.9.2 One- and two-electron operators; 1.9.3 Biorthogonal operators; References; Further reading; Exercises; Solutions; 2 Spin in Second Quantization; 2.1 Spin functions2.2 Operators in the orbital basis; 2.2.1 Spin-free operators; 2.2.2 Spin operators; 2.2.3 Mixed operators; 2.3 Spin tensor operators; 2.3.1 Spin tensor operators; 2.3.2 Creation and annihilation operators; 2.3.3 Two-body creation operators; 2.3.4 Excitation operators; 2.3.5 Singlet excitation operators; 2.4 Spin properties of determinants; 2.4.1 General considerations; 2.4.2 Spin projection of determinants; 2.4.3 Total spin of determinants; 2.5 Configuration state functions; 2.6 The genealogical coupling scheme; 2.6.1 Representations of determinants and CSFs; 2.6.2 Genealogical coupling2.6.3 Coupling coefficients; 2.6.4 An example: three electrons in three orbitals; 2.6.5 Completeness and orthonormality; 2.6.6 Transformations between determinant and CSF bases; 2.6.7 Genealogical coupling of operators; 2.7 Density matrices; 2.7.1 Orbital-density matrices; 2.7.2 Spin-density matrices; 2.7.3 Density functions; References; Further reading; Exercises; Solutions; 3 Orbital Rotations; 3.1 Unitary transformations and matrix exponentials; 3.1.1 Matrix exponentials; 3.1.2 Exponential representations of unitary matrices; 3.1.3 Special unitary matrices; 3.1.4 Orthogonal matrices3.1.5 Evaluation of matrix exponentials; 3.1.6 Nonunitary transformations; 3.2 Unitary spin-orbital transfonnations; 3.2.1 Unitary matrix expansions of creation and annihilation operators; 3.2.2 Exponential unitary transfonnations of the elementary operators; 3.2.3 Exponential unitary transfonnations of states in Fock space; 3.3 Symmetry-restricted unitary transfonnations; 3.3.1 The need for symmetry restrictions; 3.3.2 Symmetry restrictions in the spin-orbital basis; 3.3.3 Symmetry restrictions in the orbital basis; 3.4 The logarithmic matrix function; 3.4.1 Definition of the logarithmic matrix function
• Sommario/riassunto: Ab initio quantum chemistry has emerged as an important tool in chemical research and is appliced 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* H