Work

A Graph-Based Algorithm for Computing Matrix Elements of Arbitrary Operators between Configuration State Functions

Year: 2026

Type: article

Abstract: We present a graph-based algorithm for computing matrix elements of arbitrary second-quantized operators between configuration state functions (CSFs) defined in a genealogical scheme. Unlike Slater determinants, CSFs are spin-adapted and offer a more compact representation of many-electron wave functions, but their use in quantum chemical methods is often hindered by the complexity of evaluating matrix elements. Our approach leverages a graphical representation to efficiently encode the expansion of CSFs in terms of Slater determinants without explicitly constructing the full expansion. The algorithm applies operator sequences directly to the graph and computes overlaps via graph traversal, yielding matrix elements, and is completely general for any operator sequence. Numerical tests demonstrate that the method achieves machine-level precision and outperforms explicit determinant expansion by several orders of magnitude. This framework opens new possibilities for CSF-based implementations in selected and stochastic configuration interaction methods.

Source: The Journal of Physical Chemistry A

DOI: 10.1021/acs.jpca.5c08310

Authors: Ignacio Fdez. Galván, Mitra Rooein, Roland Lindh

Institution: Uppsala University

Language: English

Topic: Advanced Chemical Physics Studies

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Funder: Carl Tryggers Stiftelse för Vetenskaplig Forskning

Award: G4805466759