Self-consistent field molecular orbital treatment

Scattering, Reactive, in Molecular Beams (Herschbach). Self-Consistent Field Molecular-Orbital Treatment of 10 319... 

A SELF-CONSISTENT FIELD MOLECULAR ORBITAL TREATMENT OF CARBONYL BASE STRENGTH... 

Although the MEG model is essentially ionic in nature, it may also be used to evaluate interactions in partially covalent compounds by appropriate choices of the wave functions representing interacting species. This has been exemplified by Tossell (1985) in a comparative study in which MEG treatment was coupled with an ab initio Self Consistent Field-Molecular Orbital procedure. In this way, Tossell (1985) evaluated the interaction of C03 with Mg in magnesite (MgC03). Representing the ion by a 4-31G wave function, holding its... 

Many approximate self-consistent field molecular orbital schemes have been proposed, and the complete or partial neglect of differential overlap simplification has become widely accepted as a useful, but not too severe approximation to full ab initio methods. The advantages and justifications of the basic approximations in the CNDO and INDO method have been detailed by Pople ). Of course other considerations of time necessitate the use of empirical type calculations rather than full ab initio treatments when large numbers of calculations are required for series of molecules. 

A question of philosophy arises concerning the molecular properties to be predicted by semiempirical treatments. On the one hand, the molecular orbital NDO methods were designed to mimic minimum basis set ab initio self-consistent field (SCF) property calculations parameters were chosen accordingly. Although internally consistent, this procedure is limited in accuracy by the minimum basis ab initio SCF results themselves. An alternative approach is to fit, and predia, measured physical properties. This is not internally consistent because experimental values cannot, in principle, be obtained from self-consistent field molecular orbital theory, regardless of basis set, because of the lack of elearon correlation. Furthermore, experimental values of properties obtained at room temperature cannot be equated to those calculated for 0° K. Nonetheless, the relatively high level of accuracy that can be achieved makes such an approach useful, and that is why it has been pursued by Dewar and co-workers in their series of M(odified)NDO methods. 

The most useful method for background studies is based on the MNDO model [18], which is a valence-electron self-consistent-field (SCF) MO treatment. It takes up a minimal basis of atomic orbitals (AOs) and the NDDO integral estimation. The molecular orbitals, ([), , and the corresponding orbital energies, s , are obtained from the linear combination of the AO base functions, cjaM, and the solution of the secular equations with Suv ... 

SCF, see Self-consistent field treatment (SCF) Schroedinger equation, 2,4,74 Secular equations, 6,10, 52 solution by matrix diagonalization, 11 computer program for, 31-33 Self-consistent field treatment (SCF), of molecular orbitals, 28 Serine, structure of, 110 Serine proteases, 170-188. See also Subtilisin Trypsin enzyme family comparison of mechanisms for, 182-184, 183... 

However, despite their proven explanatory and predictive capabilities, all well-known MO models for the mechanisms of pericyclic reactions, including the Woodward-Hoffmann rules [1,2], Fukui s frontier orbital theory [3] and the Dewar-Zimmerman treatment [4-6] share an inherent limitation They are based on nothing more than the simplest MO wavefunction, in the form of a single Slater determinant, often under the additional oversimplifying assumptions characteristic of the Hiickel molecular orbital (HMO) approach. It is now well established that the accurate description of the potential surface for a pericyclic reaction requires a much more complicated ab initio wavefunction, of a quality comparable to, or even better than, that of an appropriate complete-active-space self-consistent field (CASSCF) expansion. A wavefunction of this type typically involves a large number of configurations built from orthogonal orbitals, the most important of which i.e. those in the active space) have fractional occupation numbers. Its complexity renders the re-introduction of qualitative ideas similar to the Woodward-Hoffmann rules virtually impossible. 

In the hands of Lipscomb and others 76,143, 145a, 153,189, 190), such localized bond schemes, particularly when obtained via self-consistent field (SCF) molecular orbital (MO) treatments, have proved particularly valuable for rationalizing the shapes and interatomic distances and estimating the charge distribution in many higher boranes. 

The Hartree-Fock or self-consistent-field approximation is a simplification useful in the treatment of systems containing more than one electron. It is motivated partly by the fact that the results of Hartree-Fock calculations are the most precise that still allow the notion of an orbital, or a state of a single electron. The results of a Hartree-Fock calculation are interpretable in terms of individual probability distributions for each electron, distinguished by characteristic sizes, shapes and symmetry properties. This pictorial analysis of atomic and molecular wave functions makes possible the understanding and prediction of structures, spectra and reactivities. 

By virtue of the results obtained for BaF, these error margins appear to be somewhat too narrow. With empirical data extracted from molecular beam experiments, Kozlov [149] obtained in 1985 a value for the parity violating effective constant Wpy of 212 Hz and a value of 180 Hz with data derived from electron paramagnetic resonance (EPR) spectra of the matrix-isolated molecule. With a different method for the treatment of the spin-orbit interaction, Kozlov and Labzowsky [32] obtained in 1995 Wpy = 240 Hz and 210 Hz, respectively. The ab initio calculations performed by Kozlov, Titov, Mosyagin and Souchko [171] with RECPs, however, resulted in Wpv = 111 Hz on the self-consistent field (SCF) level and Wpy = 181 Hz on the SCF level with an effective operator technique designed to take... 

Considering the crystal as a giant molecule, one could suppose that after having performed an self-consistent field (SCF) treatment, which yields delocalized molecular orbitals belonging to the group of lattice symmetry and therefore possessing translational network symmetry, one can then localize these orbitals by suitable unitary transformation. As with the molecules of finite size, one would obtain (1) localized orbitals around diverse nuclei, identifying themselves with the inner atomic orbitals of isolated atoms,... 

The site-site RISM/HNC theory has been coupled with the ab initio molecular orbital (MO) theory in a self-consistent field (SCF) calculation of the electronic and solvation structure of a solute molecule immersed in molecular solvent, referred to as the RISM-SCF method [59, 60, 61]. Since the site-site treatment of the solute-solvent correlations involves the approximation of radial averaging, it constitutes a bottleneck of the RISM-SCF method. Although this approach yields reasonable results for the thermodynamics of solvation for many solute species and solvents [62], it lacks a 3D picture of the solvation structure for complex solutes and oversimplifies the contribution to the solvation properties from highly directed electron orbitals of the solute molecule. 

The solids with weak and with strong correlations require different methods of treatment. For example, when the correlations are weak, a wavefunction of independent electrons, i.e. a self-consistent field (SCF) or Hartree-Fock (HF) wavefunction seems a good starting point for the implementation of correlation corrections. In a solid, the molecular orbitals are replaced by crystalline (Bloch) orbitals. The latter are solutions of the SCP(HF) equations (4.57). 

There are some fundamental approximations in the simple LCAO method that are harder to evaluate. One is the validity of the linear combination of atomic orbitals as an approximation to molecular orbitals. Another is the assumption of localized o bonds. A proper treatment probably should take account of the so-called cr—ir interactions. Beyond these rather basic assumptions is the bothersome business of dealing explicitly with interelectronic repulsions. These repulsions are expected to be functions of molecular geometry as well as the degree of self-consistency of the molecular field. Thus, cyclobutadiene must have considerably greater interelectronic repulsion than butadiene, with the same number of tr electrons. 

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