Density-based Hartree-Fock theory self-consistent field method

The focus then shifts to the delocalized side of Fig. 1.1, first discussing Hartree-Fock band-structure studies, that is, calculations in which the full translational symmetry of a solid is exploited rather than the point-group symmetry of a molecule. A good general reference for such studies is Ashcroft and Mermin (1976). Density-functional theory is then discussed, based on a review by von Barth (1986), and including both the multiple-scattering self-consistent-field method (MS-SCF-ATa) and more accurate basis-function-density-functional approaches. We then describe the success of these methods in calculations on molecules and molecular clusters. Advances in density-functional band theory are then considered, with a presentation based on Srivastava and Weaire (1987). A discussion of the purely theoretical modified electron-gas ionic models is... 

If we except the Density Functional Theory and Coupled Clusters treatments (see, for example, reference [1] and references therein), the Configuration Interaction (Cl) and the Many-Body-Perturbation-Theory (MBPT) [2] approaches are the most widely-used methods to deal with the correlation problem in computational chemistry. The MBPT approach based on an HF-SCF (Hartree-Fock Self-Consistent Field) single reference taking RHF (Restricted Hartree-Fock) [3] or UHF (Unrestricted Hartree-Fock ) orbitals [4-6] has been particularly developed, at various order of perturbation n, leading to the widespread MPw or UMPw treatments when a Moller-Plesset (MP) partition of the electronic Hamiltonian is considered [7]. The implementation of such methods in various codes and the large distribution of some of them as black boxes make the MPn theories a common way for the non-specialist to tentatively include, with more or less relevancy, correlation effects in the calculations. 

Although a wide variety of theoretical methods is available to study weak noncovalent interactions such as hydrogen bonding or dispersion forces between molecules (and/or atoms), this chapter focuses on size consistent electronic structure techniques likely to be employed by researchers new to the field of computational chemistry. Not stuprisingly, the list of popular electronic structure techniques includes the self-consistent field (SCF) Hartree-Fock method as well as popular implementations of density functional theory (DFT). However, correlated wave function theory (WFT) methods are often required to obtain accmate structures and energetics for weakly bound clusters, and the most useful of these WFT techniques tend to be based on many-body perturbation theory (MBPT) (specifically, Moller-Plesset perturbation theory), quadratic configuration interaction (QCI) theory, and coupled-cluster (CC) theory. 

Density functional theory based methods are now a very popular and rather inexpensive alternative to conventional correlated ab initio methods. However, none of the available DFT methods covers the dispersion energy" which limits their use for interactions of biomolecules. An other limitation to the application of DFT procedures in the realm of biomolecules stems from the fact that the charge transfer interactions (which probably play an important role in the "function of biosystems) are mostly strongly overestimated, though the very good performance of some so-called hybrid methods provides a large improvement. For more details concerning DFT techniques see Density Functional Applications Density Functional Theory (DFT), Hartree-Fock (HF), and the Self-consistent Field and Density Functional Theory Applications to Transition Metal Problems. The application of DFT to DNA base pairs is evaluated in Section 3.2.3. 

Ab initio molecular orbital calculations. This method uses the Hartree-Fock self-consistent field (SCF) theory with one-electron molecular orbitals. It is based on the variation theorem to seek the nuclear geometry of the hydrogen bonded complex with lowest energy, and it makes use of no experimental data. Additional elaborations (electron correlation) or related approaches (density functional theory) are possible. 

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