Practical Density Functional Approaches in Chemistry and Biochemistry
Density functional methods [1] are becoming increasingly popular in chemistry and biochemistry [2, 3, 4]. Their ability to incorporate the effects of electron correlation in a molecular orbital approach that is even simpler than HartreeFock has made densi
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Practical Density Functional Approaches in Chemistry and Biochemistry A. St-Amant
Department of Chemistry, University of Ottawa 10 Marie Curie, Ottawa, Ontario, KIN 6N5 Canada
1.
INTRODUCTION
Density functional methods [1] are becoming increasingly popular in chemistry and biochemistry [2, 3, 4]. Their ability to incorporate the effects of electron correlation in a molecular orbital approach that is even simpler than HartreeFock has made density functional theory very attractive to modellers in these fields. The search for improved exchange-correlation energy functionals and the development of efficient density functional codes continues to be an active field of research among the density functional experts. In this paper, we will focus on the practical aspects of modern density functional methods. Though we will point the reader to the appropriate literature, we will not focus on results obtained from density functional approaches. In our study of the methodology, we will also limit ourselves to linear combination of atomic orbitals approaches as these types of approaches are those to be most likely used by a chemist or biochemist. This assumption will become less valid as progress continues to be made with plane wave approaches [5], traditionally restricted to problems in physics, and fully numerical, or basis-set-free, approaches [6]. We will first go through the two fundamental works of modern density functional theory: the Hohenberg-Kohn theorem [7] and the Kohn-Sham equations [8]. The solution of the Kohn-Sham equations will be the focus of the rest of the paper. We will first look at approximations, particularly the simple,
D. Bicout et al. (eds.), Quantum Mechanical Simulation Methods for Studying Biological Systems © Springer-Verlag Berlin Heidelberg 1996
A. St-Amant
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yet accurate, local spin density approximation [9], to the true, but unknown, exchange-correlation potential which appears in these equations. We will then address the issue of choosing a basis set in which to expand the Kohn-Sham molecular orbitals. We will also deal with the construction of the required Kohn-Sham matrix elements, paying particular attention to their coulomb and exchange-correlation potential components. We will look at the grids that must be used in all density functional approaches as a result of the complexity of the exchange-correlation terms. While doing all of this, we will attempt to highlight the similarities and differences in the various linear combination of atomic orbitals approaches used today. The number of viable approaches is a sharp contrast to conventional ab initio electronic structure methods, where the linear combination of gaussian-type orbitals method clearly dominates [10]. 2.
THE HOHENBERG-KOHN THEOREM
All of modern density functional theory (DFT) is based on Hohenberg and Kohn's 1964 proof [7] that the energy of a system in its ground state is uniquely determined by, or is a functional of, its ground state electronic density, p(r),
E
= E[p(r)].
(1)
It was shown that this approach wa
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