Capturing electron correlation at mean-field cost: Assessment of i-DMFT and the underlying correlation conjecture

TL;DR

This paper evaluates the i-DMFT method's ability to accurately capture strong electron correlation at mean-field computational cost, focusing on the empirical correlation-energy and entropy relation across various molecules.

Contribution

It systematically assesses the validity of Collins' conjecture in different molecular scenarios and discusses implications for entropy-based density matrix functionals.

Findings

The linear correlation-energy and entropy relation holds for bond-breaking processes involving electron redistribution.

The relation breaks down for heterolytic dissociation and excited states.

i-DMFT provides reasonable total energies in simple molecules but struggles with reduced density matrices and complex cases.

Abstract

Accurately treating strong electron correlation in quantum chemistry typically requires multireference wave-function methods with steep computational scaling. The recently proposed i-DMFT method promises near configuration-interaction accuracy at mean-field cost by invoking an empirical linear relation between correlation energy and entropy (Collins' conjecture), whose validity remains unclear. We systematically assess this relation across a range of di- and polyatomic molecules, including diverse bond types, third-row elements, different types of geometric distortions, and excited states. We find that the conjectured linearity holds for bond-breaking processes dominated by electron redistribution within orbital pairs, but breaks down for heterolytic dissociation and excited states. In simple molecules, i-DMFT provides a reasonable description of total energies, but does not reliably reproduce reduced density matrices or individual energy components. It further degrades in more complex cases such as ethylene. Based on these results, we formulate criteria for the validity of the conjecture and outline implications for entropy-based reduced density matrix functionals.