Improving the Accuracy of Density Functional Approximations: Self-Interaction Correction and Random Phase Approximation

Abstract

Complexes containing a transition metal atom with a 3d^4 - 3d^7 electron configuration typically have two low-lying, high spin (HS) and low spin (LS) states. The adiabatic energy difference between these states, known as the spin-crossover energy, is small enough to pose a challenge even for electronic structure methods that are well known for their accuracy and reliability. In this work we analyze the quality of electronic structure approximations for spin-crossover energies of iron complexes with four different ligands by comparing energies from self-consistent and post-self-consistent calculations for methods based on the random phase approximation and the Fermi-L\"{o}wdin self-interaction correction. Considering that Hartree-Fock densities were found by Song et al. J. Chem. Theory Comput. 14,2304 (2018) to eliminate the density error to a large extent, and that the Hartree-Fock method and the Perdew-Zunger-type self-interaction correction share some physics, we compare the densities obtained with these methods to learn about their resemblance. We find that evaluating non-empirical exchange-correlation energy functionals on the corresponding self-interaction-corrected densities can mitigate the strong density errors and improves the accuracy of the adiabatic energy differences between HS and LS states.