The efficient conversion between linear wave function expansions and nonlinear graphically contracted function expansions

Abstract

Several algorithms are examined for the transformation of a graphically contracted function (GCF) to a configuration state function (CSF) vector, denoted , and for the reverse transformation from CSF vector to GCF, denoted . The initial implementation of these algorithms is applied to a sequence of full-CI wave functions of similar molecules. The most efficient transformation is based on a depth-first search (DFS) and scales as where is an average facet count for the GCF wave function, is the dimension of the vector x, and is the dimension of the GCF basis. Two different transformations are proposed, one based on a pairwise recursive merge algorithm and the other based on a least-squares fitting algorithm. The recursive merge is a reliable algorithm, but our initial implementation does not display the expected scaling behaviour with respect to . The iterative least-squares fitting algorithm is based on an efficient DFS procedure to compute the error ε and its gradient g. However, the resulting iterative least-squares optimisation is slowly convergent, requiring excessive iterations to converge to a target error tolerance. For most of the calculations in this case study, the recursive merge procedure is found to be more efficient than the least-squares optimisation procedure.