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

Pitts, Tom; Gidopoulos, Nikitas; Lathiotakis, N.

Abstract

In the constrained minimization method of Gidopoulos and Lathiotakis [N.I. Gidopoulos, N.N. Lathiotakis, J. Chem. Phys. 136, 224109 (2012)], 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, ρrep) and the corresponding optimal effective potential (electron repulsion potential vrep) 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 vrep, 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.

Citation

Pitts, T., Gidopoulos, N., & Lathiotakis, N. (2018). Performance of the Constrained Minimization of the Total Energy in Density Functional Approximations: the Electron Repulsion Density and Potential. The European Physical Journal B, 91(6), Article 130. https://doi.org/10.1140/epjb/e2018-90123-8

• Journal Article Type: Article
• Acceptance Date: Apr 30, 2018
• Online Publication Date: Jun 22, 2018
• Publication Date: Jun 22, 2018
• Deposit Date: May 31, 2018
• Publicly Available Date: Jun 22, 2019
• Journal: The European Physical Journal B
• Print ISSN: 1434-6028
• Electronic ISSN: 1434-6036
• Publisher: SpringerOpen
• Peer Reviewed: Peer Reviewed
• Volume: 91
• Issue: 6
• Article Number: 130
• DOI: https://doi.org/10.1140/epjb/e2018-90123-8
• Public URL: https://durham-repository.worktribe.com/output/1329687
• Related Public URLs: https://arxiv.org/abs/1806.00092