Two different AO bases

Examination of the coefficients shows that, although the numbers are not greatly different, there are some significant equalities and differences between the two sets. Considering the equalities first, we note thatthis occurs for functions 7 and 13. These contribute to angular correlation around the internuclear axis and are completely orthogonal to all of the other functions. This is the reason that the coefficients are the same for the two bases. 

At any internuclear separation, the overlap of the raw 5-type orbitals at the same center is 

This is measured by the determinant of 14 x 14 MCVB overlap matrix. The smaller this is, the larger are all of die coefficients of the VB fimctions. 

When we make these same comparisons for an internuclear separation of 20 bohr, we obtain the coefficients shown in Table 2.5 and the weights shown in Table 2.6. Now the orthogonalized AOs give the asymptotic ffinction with one configuration, while it requires three for the raw AOs. The energies are the same, of course. The EGSO weights imply the same situation. A little reflection will show that the three terms in the raw VB function are just those required to reconstruct the proper HI5 orbital. 

It should be clear that coefficients and weights in such calculations as these depend on the exact arrangement of the basis, and that their interpretations also depend upon how much physical or chemical significance can be associated with individual basis functions. 

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