Graphic Characterization and Clustering Configuration Descriptors of Determinant Space for Molecules

Quantum Monte Carlo approaches based on stochastic sampling of 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 provide insightful information on the electronic structures of computed states, for example, the population, connection, and clustering of determinants, which have not been fully explored. In this work, we devise a configuration graph for visualizing 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 multideterminant wave functions. The graph and descriptors provide us with a fresh perspective of the electronic structures of molecules and can assist with further development of configuration interaction-based electronic structure methods.