Empirical Functionals for Reduced Density Matrix Functional Theory

TL;DR

This paper develops empirical exchange-correlation functionals for reduced density matrix functional theory using Pade approximants, optimized on molecular datasets, and demonstrates improved correlation energy predictions over existing functionals.

Contribution

Introduces new empirical RDMFT functionals with minimal parameters, optimized via Pade approximants, outperforming previous RDMFT functionals and rivaling MP2 accuracy.

Findings

Functionals outperform existing RDMFT methods.

Correlation energies are comparable or better than MP2.

Few-parameter functionals achieve high accuracy.

Abstract

We present fully empirical exchange-correlation functionals to be used within reduced density matrix functional theory (RDMFT). These are of the popular J-K form, where the function of the occupation numbers that multiplies the Fock orbital term is written as a Pade approximant. The coefficients of the Pade are optimized for a testset of eight molecules, and then refined for a larger set of 35 molecules. Two different approaches were tried, either keeping the self-interaction terms, or by removing them explicitly from the functional. The functionals thus obtained involve very few parameters, but are able to outperform other RDMFT functionals, yielding correlation energies that are, on average, even slightly better than Moeller-Plesset MP2 theory.