Wave function analysis with a maximum flow algorithm

Abstract

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 C₂ illustrates the method.

GRAPHICAL ABSTRACT

KEYWORDS:

• Graphically contracted function
• Shavitt graph
• arc density
• maximum-flow
• diatomic carbon

Acknowledgements

This work was supported by the Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences, U.S. Department of Energy and by the Office of Science, Office of Advanced Scientific Computing Research, Accelerated Research for Quantum Computing program and Quantum Algorithms Teams program, U.S. Department of Energy under contract DE-AC02-06CH11357. S.R.B. acknowledges the use of computational facilities at the Ohio Supercomputer Center.

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No potential conflict of interest was reported by the author(s).

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

This work was supported by U.S. Department of Energy, Office of Science, Basic Energy Sciences [contract number DE-AC02-06CH11357]; U.S. Department of Energy, Office of Science, Advanced Scientific Computing Research [contract number DE-AC02-06CH11357].