Geometrical perturbation

As shown in Section 3.2, the first-order mixing coefficient and the first- and second-order energy terms are given by 

The first-order energy correction, is related to changes between atomic orbital overlap integrals when the geometry is modified. In general, e is stabilizing (i.e., 0) ifthe value of S is positive, but destabilizing (i.e. 0) ifthe value of 

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The first-order MCSCF response equations were first derived by Dalgaard and Jdrgensen (1978). For geometrical perturbations these equations were derived by Osamura et al. (1982a) using a Fock-operator approach. 

The excited state behaviors of chroir ium(IIl)(N4)X2 (N4 = macrocycHc tetraamine, X = NH3 or CN ) complexes have been studied by Lessard et al. Allinger s MM2/MMP2>5 program was used to model the effects of geometric perturbations on associative or dissociative relaxation coordinates. Stereochemical perturbations were introduced by methyl substituents on the tetraamine ligands. The substituents assume positions near the Cr—X coordination sites. 

The Gaussian model was found to describe the photophysical behavior of both pyrene and 9,10-dipheny-lanthracene adsorbed on silica gel well. The physical interpretation of the Gaussian model in these systems would be that each probe experiences slightly different geometric perturbations due to surface irregularities on the scale of the probe s cross-sectional area or various surface-bound strengths. The Gaussian model permits the removal of the constraint of a very limited number of types of adsorption sites found in the biexponential model and leaves only two variable parameters, obs and y, in the mathematical simulation of the decay profile. 

Molecular Orbitals of AH2,87 Geometrical Perturbation, 91 Walsh Diagrams, 93 Jahn-Teller Distortions, 95... 

S. M. Omohundro, Geometric Perturbation Theory in Physics (World Scientific, Singapore, 1986), p. 29. 

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