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Multiconfiguration VB theory. Non-orthogonal orbitals

The difficulties of dealing with non-orthogonal orbitals are once again of practice rather than principle. With the same notation as in the last section, we now need overlap and matrix-element formulae for two functions of type (7.5.1). As in (7.5.3), we start from [Pg.239]

In this somewhat unsatisfactory situation, there are two main ways of proceeding. In the first, every function is expressed as a linear combination of Slater determinants (by expanding each 0. in terms of elementary spin products, attaching the spatial factor Qk and anti-symmetrizing) the matrix elements then become sums of contributions from, all pairs of determinants, and these may be evaluated, even with non-orthogonal spin-orbitals, by using (3.3.11), (3.3.17) and (3.3.18). This method has been developed into a useful tool by Simonetta et al. [Pg.239]

The second method, which we now develop, is due mainly to Gallup and coworkers (for a review see Gallup et al., 1982), and may be regarded as another application (cf. p. 226) of the spin-free approach (Matsen, 1964) it leads to rather efficient procedures, and also involves ideas needed in Chapter 10 that are conveniently introduced at this point. [Pg.240]

Since the matrix elements of H between different terms in (7.6.4) vanish, through spin orthogonality, while the fs diagonal terms must be identical by symmetry (Appendix 3), the energy becomes (for a normalized i ) [Pg.240]

The spatial function (7.6.6) transforms under permutations like the first basis vector of the irrep with matrices V(P) but the choice p = K = l is purely conventional. [Pg.241]


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