Multiconfigurational Quantum Chemistry

Björn O. Roos, Roland Lindh, Per �ke Malmqvist, Valera Veryazov, Per-Olof Widmark

• Publisher: Wiley
• Year: 2016
• ISBN:
  9781119277880
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Physical & Theoretical Chemistry

The first book to aid in the understanding of multiconfigurational quantum chemistry, Multiconfigurational Quantum Chemistry demystifies a subject that has historically been considered difficult to learn. Accessible to any reader with a background in quantum mechanics and quantum chemistry, the book contains illustrative examples showing how these methods can be used in various areas of chemistry, such as chemical reactions in ground and excited states, transition metal and other heavy element systems. The authors detail the drawbacks and limitations of DFT and coupled-cluster based methods and offer alternative, wavefunction-based methods more suitable for smaller molecules.

Chapter 1
Introduction

How do we define multiconfigurational (MC) methods? It is simple. In Hartree–Fock (HF) theory and density functional theory (DFT), we describe the wave function with a single Slater determinant. Multiconfigurational wave functions, on the other hand, are constructed as a linear combination of several determinants, or configuration state functions (CSFs)—each CSF is a spin-adapted linear combination of determinants. The MC wave functions also go by the name Configuration Interaction (CI) wave function. A simple example illustrates the situation. The

molecule (centers denoted A and B) equilibrium is well described by a single determinant with a doubly occupied

orbital:

1.1

where

is the symmetric combination of the

atomic hydrogen orbitals (

; the antisymmetric combination is denoted as

). However, if we let the distance between the two atoms increase, the situation becomes more complex. The true wave function for two separated atoms is

1.2

which translates to the electronic structure of the homolytic dissociation products of two radical hydrogens. Two configurations,

and

, are now needed to describe the electronic structure. It is not difficult to understand that at intermediate distances the wave function will vary from Eq. 1.1 to Eq. 1.2, a situation that we can describe with the following wave function:

1.3

where

and

, the so-called CI-coefficients or expansion coefficients, are determined variationally. The two orbitals,

and

, are shown in Figure 1.1, which also gives the occupation numbers (computed as

and

) at a geometry close to equilibrium. In general, Eq. 1.3 facilitates the description of the electronic structure during any

bond dissociation, be it homolytic, ionic, or a combination of the two, by adjusting the variational parameters

and

accordingly.

Figure 1.1 The

and

orbitals and associated occupation numbers in the

molecule at the equilibrium geometry.

This little example describes the essence of multiconfigurational quantum chemistry. By introducing several CSFs in the expansion of the wave function, we can describe the electronic structure for a more general situation than those where the wave function is dominated by a single determinant. Optimizing the orbitals and the expansion coefficients, simultaneously, defines the approach and results in a wave function that is qualitatively correct for the problem we are studying (e.g., the dissociation of a chemical bond as the example above illustrates). It remains to describe the effect of dynamic electron correlation, which is not more included in this approach than it is in the HF method.

The MC approach is almost as old as quantum chemistry itself. Maybe one could consider the Heitler–London wave function [1] as the first multiconfigurational wave function because it can be written in the form given by Eq. 1.2. However, the first multiconfigurational (MC) SCF calculation was probably performed by Hartree and coworkers [2]. They realized that for the

state of the oxygen atom, there where two possible configurations,

and

, and constructed the two configurational wave function:

1.4

The atomic orbitals were determined (numerically) together with the two expansion coefficients. Similar MCSCF calculations on atoms and negative ions were simultaneously performed in Kaunas, Lithuania, by Jucys [3]. The possibility was actually suggested already in 1934 in the book by Frenkel [4]. Further progress was only possible with the advent of the computer. Wahl and Das developed the Optimized Valence Configuration (OVC) Approach, which was applied to diatomic and some triatomic molecules [5, 6].

An important methodological step forward was the formulation of the Extended Brillouin's (Brillouin, Levy, Berthier) theorem by Levy and Berthier [7]. This theor...

Table of contents

• Cover
• Title Page
• Copyright
• Dedication
• Table of Contents
• Preface
• Conventions and Units
• Chapter 1: Introduction
• Chapter 2: Mathematical Background
• Chapter 3: Molecular Orbital Theory
• Chapter 4: Hartree–Fock Theory
• Chapter 5: Relativistic Effects
• Chapter 6: Basis Sets
• Chapter 7: Second quantization and multiconfigurational wave functions
• Chapter 8: Electron correlation
• Chapter 9: Multiconfigurational SCF Theory
• Chapter 10: The RAS State-Interaction method
• Chapter 11: The Multireference CI Method
• Chapter 12: Multiconfigurational Reference Perturbation Theory
• Chapter 13: CASPT2/CASSCF Applications
• Summary and Conclusion
• Index
• End User License Agreement