Mathematical Physics in Theoretical Chemistry

S.M. Blinder, James E. House, S. M. Blinder

• Publisher: Elsevier
• Year: 2018
• Print ISBN: 9780128136515
• eBook ISBN: 9780128137017
• Topic: Physical Sciences
• Subtopic: Physical & Theoretical Chemistry

Mathematical Physics in Theoretical Chemistry deals with important topics in theoretical and computational chemistry. Topics covered include density functional theory, computational methods in biological chemistry, and Hartree-Fock methods. As the second volume in the Developments in Physical & Theoretical Chemistry series, this volume further highlights the major advances and developments in research, also serving as a basis for advanced study. With a multidisciplinary and encompassing structure guided by a highly experienced editor, the series is designed to enable researchers in both academia and industry stay abreast of developments in physical and theoretical chemistry.- Brings together the most important aspects and recent advances in theoretical and computational chemistry- Covers computational methods for small molecules, density-functional methods, and computational chemistry on personal and quantum computers- Presents cutting-edge developments in theoretical and computational chemistry that are applicable to graduate students and research professionals in chemistry, physics, materials science and biochemistry

Chapter 1

Introduction to the Hartree-Fock method

S.M. Blinder University of Michigan, Ann Arbor, MI, United States

Abstract

Introduction to the Hartree-Fock (HF) methods is the starting point for the vast majority of computational work on the electronic structure of atoms and molecules. The basic idea is that each electron in an atom or molecule interacts with the average field of every other electron. This leads to a set of simultaneous integro-differential equations for the electron spin-orbitals, which can be solved iteratively, until a self-consistent field is attained. The Roothaan equations transform a HF computation to a problem in matrix algebra, for which modern computers are highly adept. Good HF results can account for over 99% of the total energy. But the remaining 1% error, due to electron correlation, is essential to account for the chemical properties of atoms and molecules. Computation of the correlation energy is then the objective of several post-HF methods.

Keywords

Hartree-Fock method; Self-consistent field; Slater determinant; Coulomb ...

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright
• Contributors
• Mathematical physics in theoretical chemistry
• Chapter 1: Introduction to the Hartree-Fock method
• Chapter 2: Slater and Gaussian basis functions and computation of molecular integrals
• Chapter 3: Post-Hartree-Fock methods: configuration interaction, many-body perturbation theory, coupled-cluster theory
• Chapter 4: Density functional theory
• Chapter 5: Vibrational energies and partition functions
• Chapter 6: Introduction to fixed-node quantum monte carlo
• Chapter 7: Personal computers in computational chemistry
• Chapter 8: Chemical applications of graph theory
• Chapter 9: Singularity analysis in quantum chemistry
• Chapter 10: Diagrams in coupled-cluster theory: Algebraic derivation of a new diagrammatic method for closed shells
• Chapter 11: Quantum chemistry on a quantum computer
• Index