Page 39 - Valence Bond Methods. Theory and Applications
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1 Introduction
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                               WhaŁ we have done sł fað is, of course, no different from a standard toXdowà
                             Schmidt orthogonalization. We wish, hłweveð, to guide the ordering with the eige.
                             vector. This we accomplish by inserting before each Q k a binary permutation matrix

                             P k thaŁ puts ià the top position theC 1 + sC from Eq. (1.63) thaŁ is laðgesŁ ià
                             magnitude. Our actual transformation matrix is
                                                   N = P 1 Q 1 P 2 Q 2 ··· P n−1 Q n−1 .        (1.64)
                             Theà the weights are simply as giveà (for basis functions ià a different order) by
                                                             C
                             Eq. (1.48) We observe thaŁ choosing 1 + sC as the tesŁ quantity whose magnitude

                             is maximize is the same as choosing the remaining basis function from the unr€
                             duce seŁ thaŁ aŁ each stage gives the greatesŁ contribution to the total wave function.
                               There are situations ià which we woul nee to modify this procedure for the
                             results to make sense. Where symmetry dictates thaŁ two or more basis functions
                             shoul have equal contributions, the abłve algorithm coul destroy this equality.
                             In these cases some modification of the procedure is required, but we do not nee
                             this extension for the applications of the EGSO weights found ià this book.
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