Semi-empirical Crystal Orbital Methods

The various integrals appearing in these quations are not evaluated analytically. Some of them are determined from semi-empirical expressions, which contain adjustable parameters to fit certain experimental data, others are taken directly from experiment. To be able to perform thus an MNDO calculation the following quantities have to be defined 44 

They are all determined by fitting the theoretical energies of several valence states of an atom and its ions to the corresponding spectroscopic values. 

It should be mentioned finally that the core-core repulsions appearing in equation (10) are calculated in a complicated way in the MNDO method to be consistent with other approximations.44 

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Through a short description of the semi-empirical MNDO crystal orbital method we demonstrate in Section 4 how the computational difficulties of the a priori approach can be reduced. While the procedures described in the above Sections all refer to strictly periodic polymers, we present in Section 5 three methods which also can be efficiently applied for the treatment of deviations... 

Eor transition metals the splitting of the d orbitals in a ligand field is most readily done using EHT. In all other semi-empirical methods, the orbital energies depend on the electron occupation. HyperChem s molecular orbital calculations give orbital energy spacings that differ from simple crystal field theory predictions. The total molecular wavefunction is an antisymmetrized product of the occupied molecular orbitals. The virtual set of orbitals are the residue of SCE calculations, in that they are deemed least suitable to describe the molecular wavefunction. 

Abstract. Geometrical parameters, total energy, heat of formation, energies of HOMO and LUMO orbitals, density of one-electron states (DOS) are determined by using of semi-empirical quantum chemistry PM3-method for isolated molecules Cn, dimers (Cn)2 and cuban-like clusters (Cn)8 for n = 20, 24, 28, 32. The results of calculations allow assuming the existence of polymerized cubic crystal structure on base of all considered small fullerenes. 

The problem becomes more complex when studying solid phases because the microscopic NLO responses do not provide the full information about their macroscopic coimterparts, the second- and third-order nonlinear susceptibilities, and To make the transition between the microscopic and macroscopic, it is necessary to know the structure of the condensed phases as well as the nature and the effects of the intermolecular interactions in the bulk of the material. In both the Physics and Chemistry arena, several schemes have been proposed to characterize the NLO responses of solid phases. One of the authors has recently contributed to review these approaches [3] of which one of the extremes is occupied by the oriented gas approximation that consists in performing a tensor sum of the microscopic NLO properties to obtain the macroscopic responses of the crystal. The other extreme consists in performing a complete treatment of the solid by using the supermolecule method or by taking advantage of the spatial periodicity in crystal orbital calculations. In between these techniques, one finds the interaction schemes and the semi-empirical approaches. 

Table 3 contains a list of results obtained from crystals possessing localizable orbitals built from couples of sp -hybrids, pointing in two s against each other. We give three sets of values, obtained respectively from an empirical method, a semi-empirical method, and a SCF calculation. 

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