Self-consistent field method correlation interactions

In this paper a method [11], which allows for an a priori BSSE removal at the SCF level, is for the first time applied to interaction densities studies. This computational protocol which has been called SCF-MI (Self-Consistent Field for Molecular Interactions) to highlight its relationship to the standard Roothaan equations and its special usefulness in the evaluation of molecular interactions, has recently been successfully used [11-13] for evaluating Eint in a number of intermolecular complexes. Comparison of standard SCF interaction densities with those obtained from the SCF-MI approach should shed light on the effects of BSSE removal. Such effects may then be compared with those deriving from the introduction of Coulomb correlation corrections. To this aim, we adopt a variational perturbative valence bond (VB) approach that uses orbitals derived from the SCF-MI step and thus maintains a BSSE-free picture. Finally, no bias should be introduced in our study by the particular approach chosen to analyze the observed charge density rearrangements. Therefore, not a model but a theory which is firmly rooted in Quantum Mechanics, applied directly to the electron density p and giving quantitative answers, is to be adopted. Bader s Quantum Theory of Atoms in Molecules (QTAM) [14, 15] meets nicely all these requirements. Such a theory has also been recently applied to molecular crystals as a valid tool to rationalize and quantitatively detect crystal field effects on the molecular densities [16-18]. 

This expression excludes self-interaction. There have been a number of attempts to include into the Hartree-Fock equations the main terms of relativistic and correlation effects, however without great success, because the appropriate equations become much more complex. For a large variety of atoms and ions both these effects are fairly small. Therefore, they can be easily accounted for as corrections in the framework of first-order perturbation theory. Having in mind the constantly growing possibilities of computers, the Hartree-Fock self-consistent field method in various... 

Many of the principles and techniques for calculations on atoms, described in section 6.2 of this chapter, can be applied to molecules. In atoms the electronic wave function was written as a determinant of one-electron atomic orbitals which contain the electrons these atomic orbitals could be represented by a range of different analytical expressions. We showed how the Hartree-Fock self-consistent-field methods could be applied to calculate the single determinantal best energy, and how configuration interaction calculations of the mixing of different determinantal wave functions could be performed to calculate the correlation energy. We will now see that these technques can be applied to the calculation of molecular wave functions, the atomic orbitals of section 6.2 being replaced by one-electron molecular orbitals, constructed as linear combinations of atomic orbitals (l.c.a.o. method). 

Looking at the history of correlation from the fifties to the seventies, one may be led to ask whether correlation has been a scientific fashion or a real problem. Twenty years ago, almost everybody seemed to accept the idea that the simple molecular orbital method (MO) must be completed by configuration interaction (Cl), in order to obtain reliable prediction for the physical properties of atoms and molecules. Ten years ago, electron correlation was considered as the central problem of Quantum Chemistry (7). Nowadays, about 90% of the quantum-mechanical calculations on molecules are performed by the self-consistent-field method (SCF) using more or less extended sets of basis functions, without any consideration of the possible effects of correlation. 

W. Kutzelnigg, Theor. Chim. Acta, 80, 349 (1991). Error Analysis and Improvements of Coupled-Cluster Theory. W. Kutzelnigg, in Modern Theoretical Chemistry, Vol. Ill, Methods of Electronic Structure Theory H. F. Schaefer 111, Ed., Plenum, New York, 1977, pp. 129-188. Pair Correlation Theories. A. C. Wahl and G. Das, in Modem Theoretical Chemistry, Vol. Ill, Methods of Electronic Structure Theory, H. F. Schaefer 111, Ed., Plenum, New York, 1977, pp. 51-78. The Multiconfiguration Self-Consistent Field Method. 1. Shavitt, in Modem Theoretical Chemistry Vbl. Ill, Methods of Electronic Structure Theory, H. F. Schaefer III, Ed., Plenum, New York, 1977, pp. 189-276. The Method of Configuration Interaction. 

A number of types of calculations begin with a HF calculation and then correct for correlation. Some of these methods are Moller-Plesset perturbation theory (MPn, where n is the order of correction), the generalized valence bond (GVB) method, multi-configurational self-consistent field (MCSCF), configuration interaction (Cl), and coupled cluster theory (CC). As a group, these methods are referred to as correlated calculations. 

MRCI (multireference configuration interaction) a correlated ah initio method multiconfigurational self-consistent field (MCSCF) a correlated ah initio method... 

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. 

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