Self-consistent field method generalization

In the bibliography, we have tried to concentrate the interest on contributions going beyond the Hartree-Fock approximation, and papers on the self-consistent field method itself have therefore not been included, unless they have also been of value from a more general point of view. However, in our treatment of the correlation effects, the Hartree-Fock scheme represents the natural basic level for study of the further improvements, and it is therefore valuable to make references to this approximation easily available. For atoms, there has been an excellent survey given by Hartree, and, for solid-state, we would like to refer to some recent reviews. For molecules, there does not seem to exist something similar so, in a special list, we have tried to report at least the most important papers on molecular applications of the Hartree-Fock scheme, t... 

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... 

Direct ab initio methods, in which data are recomputed when required, rather than being stored and retrieved, provide an alternative that seems more useful for parallel development. The simplest level of ad initio treatment (self-consistent field methods) can be readily parallelized when direct approaches are being exploited. Experience demonstrates, however, that data replication methods will not lead to truly scalable implementations, and several distributed-data schemes (described later) have been tried. These general approaches have also been used to develop scalable parallel implementations of density functional theory (DFT) methods and the simplest conventional treatment of electron correlation (second-order perturbation theory, MP2) by several groups. 3-118... 

Harrison, et al. have reported an efficient, accurate multiresolution solver for the Kohn-Sham and Hartree-Fock self-consistent field methods for general polyatomic molecules. The Hartree-Fock exchange is a nonlocal operator, whose evaluation has been a computational bottleneck for electronic structure calculations, scaling as for small molecules... 

T. Heig, H. J. A. Jensen, J. Olsen, L. Visscher. The Generalized Active Space Concept for the Relativistic Treatment of Electron Carre- lation. Ill Large-scale configuration interaction and four-component multi-canfiguration self-consistent field methods with application to UO2. J. Chem. Phys., 124 (2006) 104106. 

But the solutions of the independent model are very far from exact solutions because the repulsion between the electrons is fer from being negligible. For this reason this interaction must be taken into account at least in part. To do so the general form of equation (7) can be kept, that is to say it is assumed that 0° is a product of mono-electronic functions variational procedure. The functions

molecular orbitals. This is the essence of the self-consistent field method. In fact it is very tedious to solve the exact equation corresponding to the self-consistent field method. A new approximation is usually made it is assumed that a molecular orbital can be expanded as a linear combination of the atomic orbitals associated with the atoms constituting the molecule this is the lcao approximation. 

The multiconfigurational self-consistent field method (MCSCF) is the generalization of the Hartree-Fock method in the sense that the wavefunction... 

Multi-configurational self-consistent field methods involving only the valence atomic orbitals, such as the generalized valence bond (GVB see Spin-coupled Theory)... 

Malmqvist P-A, Rendell A, Roos BO. The Restricted Active Space Self-Consistent-Field Method, Implemented with a Split Graph Unitary Group Approach. J Phys Chem. 1990 (4). Ma D, Li Manni G, Gagliardi L. The generalized active space concept in multiconfigurational self-consistent field methods. J Chem Phys [Internet]. 2011 Jul 28 [cited 2012 Mar 1] 135(4) 044128. Available from http //www.ncbi.nlm.nih.gov/pubmed/21806111. 

McWeeny, R., Proc. Roy. Soc. [London) A241, 239, (ii) The density matrix in self-consistent field theory. III. Generalizations of the theory/ The method of Parts I and II is generalized so as to apply to a system in which some orbitals are doubly and others singly occupied. 

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