Revisiting Artifacts of Kohn-Sham Density Functionals for Biosimulation

TL;DR

This paper investigates the unphysical charge delocalization caused by self-interaction errors in Kohn-Sham density functionals during biosimulation, revealing its causes, effects, and potential mitigation strategies with advanced functionals and solution techniques.

Contribution

It provides a detailed analysis of charge delocalization artifacts in Kohn-Sham DFT for proteins and explores solutions using range-separated hybrid functionals and specialized SCF algorithms.

Findings

Unphysical charge delocalization leads to vanishing HOMO-LUMO gaps and SCF convergence issues.

Range-separated hybrid functionals can partially reduce charge delocalization.

Stable solutions without unphysical delocalization are possible but often have non-Aufbau configurations.

Abstract

We revisit the problem of unphysical charge density delocalization/fractionalization induced by the self-interaction error of common approximate Kohn-Sham Density Functional Theory functionals on simulation of small to medium-size proteins in vacuum. Aside from producing unphysical electron densities and total energies, the vanishing of the HOMO-LUMO gap associated with the unphysical charge delocalization leads to an unphysical low-energy spectrum and catastrophic failure of most popular solvers for the Kohn-Sham (KS) self-consistent field (SCF) problem. We apply a robust quasi-Newton SCF solver [Phys. Chem. Chem. Phys. 26, 6557 (2024)] to obtain solutions for some of these difficult cases. The anatomy of the charge delocalization is revealed by the natural deformation orbitals obtained from the density matrix difference between the Hartree-Fock and KS solutions; the charge delocalization can occur not only between charged fragments (such as in zwitterionic polypeptides) but also may involve neutral fragments. The vanishing-gap phenomenon and troublesome SCF convergence are both attributed to the unphysical KS Fock operator eigenspectra of molecular fragments (e.g., amino acids or their side chains). Analysis of amino acid pairs suggests that the unphysical charge delocalization can be partially ameliorated by the use of {\em some} range-separated hybrid functionals, but not by semilocal or standard hybrid functionals. Last, we demonstrate that solutions without the unphysical charge delocalization can be located even for semilocal KS functionals highly prone to such defects, but such solutions have non-Aufbau character and are unstable with respect to mixing of the non-overlapping "frontier" orbitals.