How many distinct and reliable multireference diagnostics are there?

Abstract

Economical multireference (MR) diagnostics are essential for high-throughput computational studies, enabling the rapid and accurate identification of molecules affected by nondynamic correlation within large molecular datasets. Although various MR diagnostics have been proposed, benchmarking studies that help identify the criteria for an effective diagnostic are still scarce. In this article, we examine a wide range of correlation measures to evaluate their potential as MR diagnostics. We identify a small set of valid size-intensive correlation measures based on maximum metrics, exhibiting similar predictive values. Among these, we highlight INDmax, which offers an easy interpretation: it captures the largest deviation of a natural orbital occupancy from the boundary values corresponding to a single-reference wave function. No energy-based correlation measure was found suitable for constructing MR diagnostics. Finally, we demonstrate how average correlation measures, although not suitable as MR diagnostics, can provide a more comprehensive view of electron correlation within the molecule.