Accelerating inverse Kohn-Sham calculations using reduced density matrices

TL;DR

This paper combines the RKS and KZG methods to efficiently and accurately compute exchange-correlation potentials in density functional theory, achieving significant speedups and providing a direct comparison of their accuracy across different molecules.

Contribution

The work introduces a hybrid approach that uses RKS as an initial guess for KZG, enhancing computational efficiency and accuracy in XC potential calculations.

Findings

Achieved 3-11x speedup using RKS as initial guess for KZG.

Provided a direct comparison of RKS and KZG XC potentials.

Validated methods on weakly and strongly correlated molecules.

Abstract

The Ryabinkin-Kohut-Staroverov (RKS) and Kanungo-Zimmerman-Gavini (KZG) methods offer two approaches to find exchange-correlation (XC) potentials from ground state densities. The RKS method utilizes the one- and two-particle reduced density matrices to alleviate any numerical artifacts stemming from a finite basis (e.g., Gaussian- or Slater-type orbitals). The KZG approach relies solely on the density to find the XC potential, by combining a systematically convergent finite-element basis with appropriate asymptotic correction on the target density. The RKS method, being designed for a finite basis, offers computational efficiency. The KZG method, using a complete basis, provides higher accuracy. In this work, we combine both the methods to simultaneously afford accuracy and efficiency. In particular, we use the RKS solution as initial guess to the KZG method to attain a significant $3-11\times$ speedup. This work also presents a direct comparison of the XC potentials from the RKS and the KZG method and their relative accuracy on various weakly and strongly correlated molecules, using their ground state solutions from accurate configuration interaction calculations solved in a Slater orbital basis.