Self-consistent field method computational chemistry

The equation is used to describe the behaviour of an atom or molecule in terms of its wave-like (or quantum) nature. By trying to solve the equation the energy levels of the system are calculated. However, the complex nature of multielectron/nuclei systems is simplified using the Born-Oppenheimer approximation. Unfortunately it is not possible to obtain an exact solution of the Schrddinger wave equation except for the simplest case, i.e. hydrogen. Theoretical chemists have therefore established approaches to find approximate solutions to the wave equation. One such approach uses the Hartree-Fock self-consistent field method, although other approaches are possible. Two important classes of calculation are based on ab initio or semi-empirical methods. Ah initio literally means from the beginning . The term is used in computational chemistry to describe computations which are not based upon any experimental data, but based purely on theoretical principles. This is not to say that this approach has no scientific basis - indeed the approach uses mathematical approximations to simplify, for example, a differential equation. In contrast, semi-empirical methods utilize some experimental data to simplify the calculations. As a consequence semi-empirical methods are more rapid than ab initio. 

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. 

The Section on More Quantitive Aspects of Electronic Structure Calculations introduces many of the computational chemistry methods that are used to quantitatively evaluate molecular orbital and configuration mixing amplitudes. The Hartree-Fock self-consistent field (SCF), configuration interaction (Cl), multiconfigurational SCF (MCSCF), many-body and Mpller-Plesset perturbation theories,... 

The computationally viable description of electron correlation for stationary state molecular systems has been the subject of considerable research in the past two decades. A recent review1 gives a historical perspective on the developments in the field of quantum chemistry. The predominant methods for the description of electron correlation have been configuration interactions (Cl) and perturbation theory (PT) more recently, the variant of Cl involving reoptimization of the molecular orbitals [i.e., multiconfiguration self-consistent field (MCSCF)] has received much attention.1 As is reasonable to expect, neither Cl nor PT is wholly satisfactory a possible alternative is the use of cluster operators, in the electron excitations, to describe the correlation.2-3... 

The self-consistent field approach in relativistic quantum chemistry provides one of the most convenient and useful computational tools for the study of the electronic structure and properties of atoms, molecules and solids just as it does in nonrelativistic quantum chemistry. This chapter describes only methods in which the motion of electrons is described by the Dirac operator, namely... 

Over the past decades the semiempirical molecular orbital (MO) methods of quantum chemistry have been used widely in computational studies. Self-consistent-field (SCF) tr-electron calculations have been carried out since the 1950s and valence-electron calculations since the 1960s. Several books [1-8] and reviews [9-15] describe the underlying theory, the variants of semiempirical methods, and the numerical results in much... 

Abstract. The title paper is reviewed in perspective of the later development of computational methods in quantum chemistry. The importance of the concept of natural spin orbitals is discussed and its implication for the future development of multiconfigurational self-consistent-field theories is illustrated. 

Abstract. The direct self-consistent-field (SCF) method recalculates all two-electron integrals each time they are needed in an SCF calculation. This perspective article discusses how the original paper on direct SCF by Almlof et al. developed the principles by which this could be made efficient and thereby provided an example of the semantic approach to computational chemistry in which algorithm development and coding are not compartmentalized. 

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