Mathematical Physics in Theoretical Chemistry

Front Cover -- Mathematical Physics in Theoretical Chemistry -- Copyright -- Contents -- Contributors -- Mathematical physics in theoretical chemistry -- Introduction -- References -- Chapter 1: Introduction to the Hartree-Fock method -- 1 Hartree self-consistent field theory -- 2 Determinantal wavefunctions -- 3 Hartree-Fock equations -- 4 Hartree-Fock equations using second quantization -- 5 Roothaan equations -- 6 Atomic HF results -- 7 Post-HF methods -- References -- Chapter 2: Slater and Gaussian basis functions and computation of molecular integrals -- 1 Introduction -- 2 General representation of molecular orbitals -- 3 Slater- and Gaussian-type orbitals: mathematics -- 4 Basis set types for quantum mechanical calculations -- 5 Pseudopotentials or ECPs and relativistic effects -- 6 Basis Sets for density functional approaches -- 7 Basis set superposition error -- 8 Solution of the integrals over atomic orbitals -- 8.1 One-Electron Integrals -- 8.2 Two-Electron Integrals -- 8.3 Resolution of the Identity and Density Fitting -- 8.4 Auxiliary Basis Sets -- 9 Summary -- Acknowledgments -- References -- Chapter 3: Post-Hartree-Fock methods: configuration interaction, many-body perturbation theory, coupled-cluster theory -- 1 Introduction -- 1.1 The Many-Body Problem of Electron Correlation -- 1.2 Fermi Correlation -- 1.3 Coulomb Correlation and Limitations of Hartree-Fock Theory -- 2 Basics of second quantization -- 2.1 Fock Space -- 2.2 Elementary Operators -- 2.3 Representation of One- and Two-Electron Operators -- 2.4 One- and Two-Electron Density Matrices -- 2.5 Spin-Free Operators -- 3 Configuration interaction theory -- 3.1 HF Theory and the Dissociation of H2 -- 3.2 FCI Theory -- 3.2.1 Determinant-based CI -- 3.2.2 CI Eigensolver -- 3.3 Truncated CI -- 3.3.1 Single-reference CI.

3.3.2 Multireference CI -- 3.4 Multiconfigurational Self-Consistent Field -- 3.4.1 Complete active space self-consistent field -- 4 Many-Body perturbation theory -- 4.1 Rayleigh-Schrödinger Perturbation Theory -- 4.1.1 Møller-Plesset perturbation theory -- 4.1.2 Epstein-Nesbet perturbation theory -- 4.2 Multireference Perturbation Theory -- 5 Coupled-cluster theory -- 5.1 General Considerations -- 5.2 Exponential Parametrization -- 5.3 Size-Extensivity and Coupled-Cluster Theory -- 5.4 Derivation of the Coupled-Cluster Equations -- 5.5 Coupled-Cluster Doubles -- 5.6 Coupled-Cluster Models and Convergence to the FCI/CBS Limit -- 5.7 Coupled-Cluster Theory for Excited States -- 6 Conclusions and outlook -- References -- Further Reading -- Chapter 4: Density functional theory -- 1 Introduction -- 2 Fundamentals of density functional theory -- 2.1 Wavefunction Theory -- 2.2 Wavefunction Variational Principle -- 2.3 Hellmann-Feynman Theorem -- 2.4 Hartre-Fock Approximation -- 2.5 Density Variational Principle -- 2.6 Kohn-Sham Noninteracting System -- 2.7 Exchange Energy and Correlation Energy -- 2.8 Coupling-Constant Integration -- 2.9 Uniform Electron Gas and Slowly Varying Densities -- 3 Approximations of exchange and correlation energy density functional -- 3.1 Approaches of Developing Approximations -- 3.2 Jacob's Ladder of Density Functional Theory -- 4 The strongly constrained and appropriately normed meta-generalized gradient approximation -- 5 Outlook -- References -- Further Readings -- Chapter 5: Vibrational energies and partition functions -- 1 Introduction -- 2 Molecular vibrations and the harmonic approximation -- 2.1 Harmonic Approximation -- 2.2 Normal Modes -- 3 Vibrational analysis on anharmonic potential surfaces -- 3.1 Effective Hamiltonians and Perturbation Theory -- 3.2 Model Potentials.

3.3 Calculation of Potential Energy Surfaces -- 3.4 Variational Methods -- 3.5 Vibrational SCF -- 4 Vibrational transition intensities -- 5 Vibrational partition function -- 6 Applications to thermodynamics -- 6.1 Equipartition Principle -- 6.2 Heat Capacities and Vibrations -- 6.3 Free Energies -- 7 Applications to kinetics -- 8 Conclusion -- References -- Chapter 6: Introduction to fixed-node quantum monte carlo -- 1 Introduction -- 2 Diffusion monte carlo -- 2.1 Importance Sampling -- 2.2 Short-Time Green's Function -- 2.3 Kinetic Branching -- 2.4 Fixed-Node Approximation -- 3 A pure-sampling quantum monte carlo method -- 3.1 Why Do Pure-Sampling? -- 3.2 A Pure-Sampling Algorithm -- 3.3 Independent Metropolis -- 3.4 Removing Biases -- 4 Molecular properties -- 4.1 Fixed-Node Energy -- 4.2 Other Electronic Properties -- 4.2.1 Electric moments -- 4.2.2 Diamagnetic shielding and susceptibility -- 4.2.3 Electric fields and electric field gradients -- 5 Application to ethene -- 6 Conclusion -- 7 Appendix -- 7.1 Derivation of the Modified Schrödinger Equation -- 7.2 Derivation of the Energy Estimator for Diffusion Monte Carlo -- References -- Further Readings -- Chapter 7: Personal computers in computational chemistry -- Preface -- Computing, computers, and the personal computer -- Examples of calculations on personal computers -- 1 An instructive example of the growth of computer speed -- 1.1 A note on factors affecting calculation times -- 2 Planar tetracoordinate carbon -- 2.1 Dimethano[2.2]Octaplane, 1 -- 2.2 A Smaller Planar-Carbon Molecule Than Dimethano[2.2]Octaplane: 3a -- 3 Pyramidal tetracoordinate carbon -- 4 Half-planar carbon, butterfly carbon: polyprismanes or prismanes -- 5 propellane carbon -- 6 Postscript -- References -- Chapter 8: Chemical applications of graph theory -- 1 Introduction.

2 Topological indices -- 3 Models -- 4 Conclusions -- References -- Chapter 9: Singularity analysis in quantum chemistry -- 1 Mathematical background -- 2 Avoided crossings of molecular potential energy -- 2.1 Born-Oppenheimer Approximation -- 2.2 Interpolation With Quadratic Approximants -- 3 Critical points in electronic structure -- 3.1 Ionization as a Critical Phenomenon -- 3.2 Finite-Size Scaling to Calculate Critical Parameters -- 4 Summation of perturbation series -- 4.1 The Effects of Singularities on Convergence -- 4.2 Summation Methods for Various Problems -- 4.2.1 Molecular vibrations -- 4.2.2 Dimensional perturbation theory -- 4.2.3 Møller-Plesset perturbation theory -- References -- Chapter 10: Diagrams in coupled-cluster theory: Algebraic derivation of a new diagrammatic method for closed shells -- 1 Introduction -- 2 The coupled-cluster method and its diagrammatic representations -- 2.1 Spin-Orbital Picture -- 2.2 Spin-Integration -- 2.3 Coupled Cluster -- 2.4 Brandow Diagrams -- 3 The closed-shell case -- 3.1 Reduction From Spin to Spatial Orbitals -- 3.2 Goldstone Diagrams -- 4 Nonorthogonally spin-adapted diagrams -- 4.1 Permutations and Antisymmetrizers -- 4.2 Diagrammatic and Algebraic Formalism -- 4.3 From Spin-Orbital to Orbital -- 4.4 Factorizing the Orbital Equations -- 4.5 Spin-Summation and Dealing With Cross-Products -- 5 Examples I: simple cases -- 6 New diagrammatic rules -- 7 Spin-summation revisited -- 8 Examples II: complex cases -- 9 Conclusions -- Acknowledgments -- 10 Appendix -- References -- Chapter 11: Quantum chemistry on a quantum computer -- 1 Qubits -- 2 Quantum gates and circuits -- 3 Quantum fourier transform -- 4 Phase estimation algorithm -- 5 Many-electron systems -- 6 Atomic and molecular Hamiltonians -- 7 Time-evolution of a quantum system.

8 Trotter expansions -- 9 Simulations of molecular structure -- References -- Index -- Back Cover.

Medienart:	E-Book

Erscheinungsjahr:	2018
Erschienen:	San Diego: Elsevier ; 2018

Reihe:	Developments in physical & theoretical chemistry Developments in Physical and Theoretical Chemistry Ser

Sprache:	Englisch

Beteiligte Personen:	Blinder, S. M. [VerfasserIn] House, J. E. [Sonstige Person]

Links:	Volltext [lizenzpflichtig]

ISBN:	978-0-12-813701-7

Themen:	Chemistry, Physical and theoretical ; Mathematics Electronic books

Umfang:	1 Online-Ressource (426 pages)

Förderinstitution / Projekttitel:

PPN (Katalog-ID):	104254929X