Computational Atomic Structure

An MCHF Approach

Charlotte Froese-Fischer

• Publisher: CRC Press
• Year: 2019
• eBook ISBN: 9781351458955
• Topic: Physical Sciences
• Subtopic: Atomic & Molecular Physics

Computational Atomic Structure: An MCHF Approach deals with the field of computational atomic structure, specifically with the multiconfiguration Hartree-Fock (MCHF) approach and the manner in which this approach is used in modern physics. Beginning with an introduction to computational algorithms and procedures for atomic physics, the book describes the theory underlying nonrelativistic atomic structure calculations (making use of Brett-Pauli corrections for relativistic effects) and details how the MCHF atomic structure software package can be used to this end. The book concludes with a treatment of atomic properties, such as energy levels, electron affinities, transition probabilities, specific mass shift, fine structure, hyperfine-structure, and autoionization. This modern, reliable exposition of atomic structure theory proves invaluable to anyone looking to make use of the authors' MCHF atomic structure software package, which is available publicly via the Internet.

Chapter 1

Introduction

1.1 Introduction

According to quantum mechanics (Messiah 1965) a stationary state of an N- electron atom is described by a wave function $\psi \left(q_1,\dots ,q_N\right),$, where $q_i=$ represents the space and spin co-ordinates^† of the electron labelled $\mathit{i}$. The wave function is assumed to be continuous with respect to the space variables and is a solution to the wave equation

$\mathscr{H}\psi \left(q_1,\dots ,q_n\right)=E\psi \left(q_1,\dots ,q_n\right),$

(1.1)

where $\mathscr{H}$ is the Hamiltonian operator for the atomic system. The wave equation is an eigenvalue problem, and solutions exist only for certain values of $\mathit{E}\mathrm{.}$ These values are known as the eigenvalues of the operator, and they represent the possible values of the total energy of the system. Following the mathematical terminology, the set of all eigenvalues is known as the eigenvalue spectrum of the operator.

The operator $\mathscr{H}$ depends on the atomic system as well as on the underlying quantum mechanical form alism. For non-relativistic calculations, the norm al starting point is Schrödinger’s equation where the Hamiltonian, in atomic units (see appendix C) is given as

$\mathscr{H}={\displaystyle \sum _{i=1}^N\left(-\frac{1}{2}{\nabla }_i^2-\frac{z}{r_i}\right)+}{\displaystyle \sum _{i>j}^N\frac{1}{r_{ij}}.}$

(1.2)

Here $\mathit{Z}$ is the nuclear charge of the atom, ${\mathit{r}}_{\mathit{i}}$ is the distance of electron $\mathit{i}$ from the nucleus and $r_{ij}$ is the distance between electron $\mathit{i}$ and electron $\mathit{j}$. The above Hamiltonian is valid under the a...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Table of Contents
• Preface
• Acknowledgments
• 1 Introduction
• 2 Configuration State Functions and Hamiltonian
• 3 Hartree–Fock Calculations
• 4 Multiconfiguration Hartree–Fock Wave Functions
• 5 Two-Electron Systems
• 6 Correlation in Many-Electron Systems
• 7 Relativistic Effects
• 8 Isotope and Hyperfine Effects
• 9 Allowed and Forbidden Transitions
• 10 MCHF Continuum Wave Functions
• Appendices
• References
• Index