Overlap Weighting Factors

The developers of ZINDO found that the parameters required to reproduce orbital energy orderings and UV spectra are different from those required to reproduce accurate structures by geometry optimization. They introduced anew pair of parameters, called the overlap weighting factors, to account for this. These parameters are provided in HyperChem in the Semi-empirical Options dialog box. Their effect is to modify the resonance integrals for the off-diagonal elements of the Fock matrix. 

For geometry optimizations and comparison of total energies (which should be carried out with ZINDO/1, not ZINDO/S), both overlap weighting factors (Sigma-Sigma and Pi-Pi) should be set to 1 in the Semi-empirical Options dialog box. 

The mixed model used in ZINDO/1 is identical to that used in CNDO and INDO if there is no d-orbital involved in the quantum 

Slater exponent for the 5 type Slater orbitals on atom A and 5 orbital Slater exponent for the s type Slater orbitals on atom B. 

ZINDO/S is an modified INDO method parameterized to reproduce UV visible spectroscopic transitions when used with the Cl singles methods. It was developed in the research group of Michael Zerner of the Quantum Theory Project at the University of Florida. As with the other semi-empirical methods, HyperChem s implementation of ZINDO/S is restricted to spin multiplicities of up to a quartet state. Higher spin systems may not be done using HyperChem. 

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A theoretical approach in molecular orbital studies to formulate an expression for the wave function of a molecular orbital (both for bonding and antibonding orbitals) by linear combinations of the overlapping atomic orbitals with appropriate weighting factors. 

W [(Vy n Vy) - Mo i,j)] + (1 - w) Mp i,j) where Mo(i, /) and Mp(i, j) are the common overlap steric volume and the integrated spatial difference in field potential, and w is a weighting factor between zero and one. The two descriptors are considered complementary in the sense that the overlap volume measures the shape within the van der Waals surface formed by superimposition of i and j, while ISDFP measures the shape outside the van der Waals surface. 

This equation indicates that the energy of an extended Huckel MO is equal to its net contributions to AO populations times AO energy weighting factors plus its contributions to overlap populations times overlap energy weighting factors. 

This means that particle configurations where at least two particles overlap, i.e., have a distance r smaller than the diameter cr, are forbidden. They are forbidden because the Boltzmann factor contains a term, exp(—oo) 0, that leads to a vanishing statistical weight. Hence we have an ensemble of... 

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