Efficient algorithm for the spin-free valence bond theory. I. New strategy and primary expressions

A new algorithm for nonorthogonal valence bond (VB) method is presented by using symmetric group approach. In the present algorithm, a new function, called paired-permanent-determinant (PPD), is defined, which is an algebrant and has the same symmetry of a corresponding VB structure. The evaluation of a PPD is carried out by using a recursion formula similar to the Laplace expansion method for determinants. An overlap matrix element in the spin-free VB method may be obtained by evaluating a corresponding PPD, while the Hamiltonian matrix element is expressed in terms of the products of electronic integrals and sub-PPDs. In the present work, some important properties of PPDs are discussed, and the primary procedure for the evaluation of PPD is deduced. Furthermore, the expressions for evaluating both the overlap and Hamiltonian matrix elements are also given in details, which are essential to develop an efficient algorithm for nonorthogonal VB calculations. In the present study, some further effective technical considerations will be adopted, and a new ab initio VB program will be introduced. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 67: 287–297, 1998

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