Slaters Multiple Scattering Xa Method for Molecules

We ean quiekly and easily solve the HF-Xa equations for an atomie species because of the spherical symmetry. Molecules do not generally have spherical symmetry in fact, the vast majority of organie moleeules have no symmetry to speak of. The extension of HF-Xa models from atoms to molecules took many years, and most calculations in the literature relate to symmetrical inorganic species. The molecular version of the Xa model builds on a chemist s intuitive 

It was found in pilot calculations that it is necessary to enclose the molecule by an outer sphere that includes the entire molecule. I have denoted the region from the outer sphere radius to infinity as region III. The wavefunction is assumed to be of an atonnic type in region III. 

The molecular HF-Xa method has been reviewed by Connolly, and you might like to see how it works for the H2O example. 

The first step is to choose a molecular geometry, the atomic sphere radii and the exchange parameters for each atom and the outer sphere region. I have summarized these in Table 12.1. 

Orbital Touching spheres 10% overlapped spheres ESCA Conventional HF-LCAO 

The sphere radii were deduced from Slater s (1965) table based on crystal data. The basic molecular HF-Xa equations were originally derived on the basis that the spheres did not overlap (Schwarz and Connolly, 1971). But the equations remain valid when the spheres are allowed to overlap, provided that each sphere does not contain more than one nucleus and that none of the nuclei lie outside the outer sphere. A 10% overlap seems to be normal practice, and our results are given in Table 12.2. 

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