Electron Correlation Considerations

It is observed empirically that atoms with two or more p electrons (four or more s-p electrons) in outer, unfilled shells tend to form homopolar bonds with one another, thus giving the (8 — N) rule, and to form covalent or ionic bonds with other atoms, the degree of covalence depending upon the electronegativity difference. 

In the MO approach appropriate to outer s and p electrons, the simple formalism does not distinguish between a covalent-ionic band and a metallic band. The use of determinantal (antisymmetrized) wave functions automatically introduces correlations between electrons of parallel spin. Traditionally the many-electron wave function has, at best, been represented by a single Slater determinant of one-electron wave functions (Hartree-Fock approximation), whereas the true wave function would be given by a series of such determi- 

Given a two-sublattice structure with near-neighbor-overlapping atomic orbitals that are more than half filled, it is no longer possible 

If the two-sublattice condition does not exist, there can be no electron correlations that avoid exclusion of electron charge from the region between positive atomic cores. Therefore the bottom of the valence-electron band should be less stable than that of a corresponding bonding band, the top more stable than that of a corresponding antibonding band. Such a band is called metallic as it is characteristic of the close-packed metals. 

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The structure planarity is broken with the inclusion of polarization functions into the basis set and electron correlation consideration. The semi-empirical calculation forecasts the planarity disturbance of the atom group considered. The hydrogen bond for j -naphthol complexes is longer than one for a-naphthol. These values are 0.1812 nm for cw-yff-naphthol and 0.1819 nm for trara-yS-naphthol calculated at HF/6-31G level. The values obtained at MP2/6-31G level oftheory are 0.1861 nm and 0.1862 nm. They are in accordance with the results of more accurate calculations 0.1849 nm and 0.1850 run [9]. 

Although NBOs are most commonly used to analyze a given wavefunction, they may also be used to improve the computation of wavefunctions, particularly with respect to inclusion of electron correlation. Considerable evidence suggests that correlation effects are most efficiently described in terms of localized orbitals. ... 

Another approach is spin-coupled valence bond theory, which divides the electrons into two sets core electrons, which are described by doubly occupied orthogonal orbitals, and active electrons, which occupy singly occupied non-orthogonal orbitals. Both types of orbital are expressed in the usual way as a linear combination of basis functions. The overall wavefunction is completed by two spin fimctions one that describes the coupling of the spins of the core electrons and one that deals with the active electrons. The choice of spin function for these active electrons is a key component of the theory [Gerratt ef al. 1997]. One of the distinctive features of this theory is that a considerable amount of chemically significant electronic correlation is incorporated into the wavefunction, giving an accuracy comparable to CASSCF. An additional benefit is that the orbitals tend to be... 

Azulene does have an appreciable dipole moment (0.8 The essentially single-bond nature of the shared bond indicates, however, that the conjugation is principally around the periphery of the molecule. Several MO calculations have been applied to azulene. At the MNDO and STO-3G levels, structures with considerable bond alternation are found as the minimum-energy structures. Calculations which include electron correlation effects give a delocalized n system as the minimum-energy structure. ... 

In conclusion, we note that there has recently been considerable interest in including intrasolute electron correlation energy in SCRF theory [77, 92-106], Further progress in this area will be very important in improving the reliability of the predictions, at least for small solutes. 

The problem of the sign of AR/R for the divalent tin compounds was investigated by Lees and Flinn (16). In the relationship between the quadrupole splitting and chemical shift for the stannous compounds, two distinct correlations became apparent—compounds with a linear covalent bond, and compounds with a predominantly planar bond. Furthermore, there exists a linear relationship between the number of 5 p electrons and the chemical shift and hence the total 5 electron density. Using free tin ion wave functions in a self-consistent field calculation, they showed that the direct eflEect of adding 5 electrons is considerably... 

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