Wave function analysis with a maximum flow algorithm
An efficient algorithm for computing the maximum-flow path in a network is applied to the identification of the dominant configuration state functions (CSFs) in a graphically contracted function (GCF), configuration interaction, wave function. The flow network is a space of spin-adapted CSFs represented by a Shavitt graph, wherein the nodes correspond to orbital occupations and spin quantum numbers. The graph nodes are connected by arcs, and an arc density is defined as sums of the associated squared CSF coefficients. A max-min approach determines an upper bound to the maximum possible incoming flow for each graph node. A backtracking step generates a candidate walk and is followed by a limited search of alternative branching paths for the dominant CSF. The arc density contributions are removed from the graph, and the algorithm is reapplied to the updated graph. This list of generated walks can be partitioned in order to guarantee that the dominant CSFs have been identified. All of the steps in this algorithm are computationally efficient and do not depend on the potentially large dimension of the underlying linear CSF expansion space. An analysis of low-lying valence states of C-2 illustrates the method.