Graphic characterization and clustering configuration descriptors of determinant space for molecules

TL;DR

This paper introduces a novel visualization and analytical framework for the determinant space in quantum Monte Carlo methods, enhancing understanding of molecular electronic structures and aiding method development.

Contribution

It proposes a configuration graph and two descriptors to characterize and quantify determinant clustering in multi-determinant wave functions, offering new insights.

Findings

Configuration graph visualizes electronic structure.

Descriptors quantify the extent of determinant clustering.

Framework aids development of electronic structure methods.

Abstract

Quantum Monte Carlo approaches based on the stochastic sampling of the determinant space have evolved to be powerful methods to compute the electronic states of molecules. These methods not only calculate the correlation energy at an unprecedented accuracy but also provides insightful information on the electronic structure of computed states, e.g. the population, connection, and clustering of determinants, which have not been fully explored. In this work, we devise a configuration graph for visualizing the determinant space, revealing the nature of the molecule's electronic structure. In addition, we propose two analytical descriptors to quantify the extent of configuration clustering of multi-determinant wave functions. The graph and descriptors provide us with a fresh perspective of the electronic structure of molecules and can assist the further development of configuration interaction based electronic structure methods.