Performance of the Constrained Minimization of the Total Energy in Density Functional Approximations: the Electron Repulsion Density and Potential

TL;DR

This paper details a constrained minimization approach to improve density functional approximations by reducing self-interaction errors, leading to more accurate ionization energies and correct HOMO energies for anions.

Contribution

It introduces a refined constrained minimization method that effectively removes self-interaction errors across various density functional approximations.

Findings

Significantly reduces errors in ionization energy predictions.

Correctly predicts negative HOMO energies for several anions.

Performance is consistent across different density functional approximations.

Abstract

In the constrained minimization method of Gidopoulos and Lathiotakis (J. Chem. Phys. 136, 224109), the Hartree exchange and correlation Kohn-Sham potential of a finite $N$-electron system is replaced by the electrostatic potential of an effective charge density that is everywhere positive and integrates to a charge of $N-1$ electrons. The optimal effective charge density (electron repulsion density, $\rho_{\rm rep}$) and the corresponding optimal effective potential (electron repulsion potential $v_{\rm rep}$) are obtained by minimizing the electronic total energy in any density functional approximation. The two constraints are sufficient to remove the self-interaction errors from $v_{\rm rep}$, correcting its asymptotic behavior at large distances from the system. In the present work, we describe, in complete detail, the constrained minimization method, including recent refinements. We also assess its performance in removing the self-interaction errors for three popular density functional approximations, namely LDA, PBE, and B3LYP, by comparing the obtained ionization energies to their experimental values for an extended set of molecules. We show that the results of the constrained minimizations are almost independent of the specific approximation with average percentage errors 15%, 14%, 13% for the above DFAs respectively. These errors are substantially smaller than the corresponding errors of the plain (unconstrained) Kohn-Sham calculations at 38%, 39%, and 27% respectively. Finally, we showed that this method correctly predicts negative values for the HOMO energies of several anions.