https://doi.org/10.1140/epjb/e2018-90123-8
Regular Article
Performance of the constrained minimization of the total energy in density functional approximations: the electron repulsion density and potential★
1
Department of Physics, Durham University,
South Road,
Durham
DH1 3LE, UK
2
Theoretical and Physical Chemistry Institute, National Hellenic Research Foundation,
Vass. Constantinou 48,
116 35
Athens, Greece
a e-mail: lathiot@eie.gr
Received:
2
March
2018
Received in final form:
28
April
2018
Published online: 22
June
2018
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.
© EDP Sciences / Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 2018