Restricted Open-shell cluster Mean-Field theory for Strongly Correlated Systems

TL;DR

This paper introduces the Restricted Open-shell cluster Mean-Field (RO-cMF) method, extending previous cluster mean-field approaches to better handle open-shell systems without spin polarization, providing a more suitable reference for post-cMF correlation methods.

Contribution

The paper develops the RO-cMF method for open-shell systems, addressing spin contamination issues and enabling more accurate post-cMF correlation calculations.

Findings

RO-cMF provides a spin-pure reference state for open-shell systems.

Demonstrated accurate exchange coupling constants for transition metal complexes.

First perturbative corrections (RO-cMF-PT2) applied to the new method.

Abstract

The cluster-based Mean Field method (cMF) and it's second order perturbative correction[1], was introduced by Jim\'enez-Hoyos and Scuseria to reduce the cost of modeling strongly correlated systems by dividing an active space up into small clusters, which are individually solved in the mean-field presence of each other. In that work, clusters with unpaired electrons are treated naturally, by allowing the $\alpha$ and $\beta$ orbitals to spin polarize. While that provided significant energetic stabilization, the resulting cMF wavefunction was spin-contaminated, making it difficult to use as a reference state for spin-pure post-cMF methods. In this work, we propose the Restricted Open-shell cMF (RO-cMF) method, extending the cMF approach to systems with open-shell clusters, while not permitting spin-polarization. While the resulting RO-cMF energies are necessarily higher in energy than the unrestricted orbital cMF, the new RO-cMF provides a simple reference state for post-cMF methods that recover the missing inter-cluster correlations. We provide a detailed explanation of the method, and report demonstrative calculations of exchange coupling constants for three systems: a di-iron complex, a di-chromium complex, and a dimerized organic radical. We also report the first perturbatively corrected RO-cMF-PT2 results as well.