Accurate singlet-triplet gaps in biradicals via the spin averaged anti-Hermitian contracted Schr\"odinger equation

TL;DR

This paper introduces a spin-averaged anti-Hermitian contracted Schrödinger equation (ACSE) method that accurately predicts singlet-triplet gaps in biradicals, overcoming limitations of traditional single-reference approaches.

Contribution

The authors develop a spin-averaged ACSE approach that handles higher multiplicity states from CAS input without extra state preparation, improving biradical gap predictions.

Findings

Accurately predicts singlet-triplet gaps in small biradicals.

Outperforms some existing methods in benchmark tests.

Effective for complex organic biradicals.

Abstract

The accurate description of biradical systems, and in particular the resolution of their singlet-triplet gaps, has long posed a major challenge to the development of electronic structure theories. Biradicaloid singlet ground states are often marked by strong correlation and, hence, may not be accurately treated by mainstream, single-reference methods such as density functional theory or coupled cluster theory. The anti-Hermitian contracted Schr\"odinger equation (ACSE), whose fundamental quantity is the two-electron reduced density matrix rather than the N-electron wave function, has previously been shown to account for both dynamic and strong correlations when seeded with a strongly correlated guess from a complete active space (CAS) calculation. Here, we develop a spin-averaged implementation of the ACSE, allowing it to treat higher multiplicity states from the CAS input without additional state preparation. We apply the spin-averaged ACSE to calculate the singlet-triplet gaps in a set of small main group biradicaloids, as well as the organic four-electron biradicals trimethylenemethane and cyclobutadiene, and naphthalene, benchmarking the results against other state-of-the-art methods reported in the literature.