Self-consistent field , evaluation methods

Like their related methods such as the Intermediate Neglect of Differential Overlap (INDO) [2] and Modified Intermediate Neglect of Differential Overlap (MINDO) [6] the methods already mentioned have a number of features in common. They are all self-consistent field (SCF) methods that take into account electrostatic repulsion and exchange stabilization and where all integrals are evaluated by approximate means. They are further characterized by the fact that they all use a restricted basis set, that is, one s oibital and three p orbitals per atom, except for the hydrogen atom, which is represented by an s orbital. 

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]. 

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,... 

Hiickel and extended Huckel methods are termed semi-empirical because they rely on experimental data for the quantification of parameters. There are other semi-empirical methods, such as CNDO, MINDO, INDO, in which experimental data are still used, but more care is taken in evaluating the Htj. These methods are self-consistent field procedures based on 3 SCF. They are discussed in various works on molecular orbital theory.4... 

The scientific interests of Huzinaga are numerous. He initially worked in the area of solid-state theory. Soon, however, he became interested in the electronic structure of molecules. He studied the one-center expansion of the molecular wavefunction, developed a formalism for the evaluation of atomic and molecular electron repulsion integrals, expanded Roothaan s self-consistent field theory for open-shell systems, and, building on his own work on the separability of many-electron systems, designed a valence electron method for computational studies on large molecules. 

Julg et al.24 employed an approximation based on the self consistent field molecular orbital method to evaluate the average energy per atom for various structures. They calculate that whereas the normal b.c.c. structure is more stable for clusters containing more than 106 atoms, smaller clusters prefer to take up pentagonal symmetry. However, these authors make an important point, namely, that the calculated energies for different structures are very similar. Interconversion of different structures will be facile, and external factors such as the method of deposition, level of impurities, support effects, etc., may cause the less stable structure to grow. For example, impurities on... 

The self-consistent-field (SCF) ab initio Hartree-Fock crystal orbital method is applied with success to polysulfur nitride (SN)X, chains using non-local exchange and evaluating all integrals over atomic orbitals within 5 atomic neighbours accurately. 

Highly-ionized atoms DHF calculations on isoelectronic sequences of few-electron ions serve as the starting point of fundamental studies of physical phenomena, though many-body corrections are now applied routinely using relativistic many-body theory. Relativistic self-consistent field studies are used as the basis of investigations of systematic trends in ionization energies [137-144], radiative transition probabilities [145-148], and quantum electrodynamic corrections [149-151] in few-electron systems. Increased experimental precision in these areas has driven the development of many-body methods to model the electron correlation effects, and the inclusion of Breit interaction in the evaluation of both one-body and many-body corrections. 

The self-consistent field procedure in Kohn-Sham DFT is very similar to that of the conventional Hartree-Fock method [269]. The main difference is that the functional Exc[p] and matrix elements of Vxc(r) have to be evaluated in Kohn-Sham DFT numerically, whereas the Hartree-Fock method is entirely analytic. Efficient formulas for computing matrix elements of Vxc(r) in finite basis sets have been developed [270, 271], along with accurate numerical integration grids [272-277] and techniques for real-space grid integration [278,279]. 

D11.8 In ab initio methods an attempt is made to evaluate all integrals that appear in the secular determinant. Approximations are still employed, but these are mainly associated with the construction of the wavefunctions involved in the integrals. In semi-empirical methods, many of the integrals are expressed in terms of spectroscopic data or physical properties. Semi-empirical methods exist at several levels. At some levels, in order to simplify the calculations, many of the integrals are set equal to zero. Density functional theory (DFT) is considered an ab initio method, but it is different from the Hartree-Fock (HF) or self-consistent field (SCF) approach in that DFT focuses on the electron density while HF/SCF methods focus on the wavefunction. They are both iterative self consistent methods in that the calculations are repeated until the energy and wavefunctions (HF) or energy and electron density (DFT) are unchanged to within some acceptable tolerance. 

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