Performance of the constrained minimization of the total energy in density functional approximations: the electron repulsion density and potential

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, 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.

Density-inversion method for the Kohn–Sham potential: Role of the screening density

“…However, the flexibility we have in choosing the screening charge can be used to our advantage, to remove the effects of self-interactions (SIs) from LDA and other SI contaminated densities by setting Q scr = N − 1. The success of this 'constrained DFT' approach has been already demonstrated 6,19 , but using a different method in which the energy is minimized under the following constraints:…”

Improving the exchange and correlation potential in density-functional approximations through constraints

“…In the constrained minimisation method, [8][9][10] we employ the standard total energy expression in DFT, using a density-functional approximation for the xc energy density-functional, E DFA xc […”

“…[4][5][6][7] The advantage of this approach is that the energy difference is bound from below, even in approximations from nite-order (second) perturbation theory; the latter can then be employed directly to derive accurate exchange-correlation (xc) potentials without the risk of variational collapse. 4,6 In this paper, we review briey and expand on our work [8][9][10] to improve the performance of local and semi-local density-functional approximations (DFAs), by imposing physical constraints on the single-particle, local, effective (KS) potential, whose orbitals minimise the total energy functional. In ref.…”

“…In ref. [8][9][10] we argued that these constraints improve the asymptotic behaviour and overall quality of the KS potential by removing the erroneous effects of self-interactions (SIs). As evidence, we demonstrated that, compared with the results from the unconstrained minimisation, the ionisation potentials (IPs) 51 of a large number of atoms, molecules and even anions obtained from our constrained minimisation improved signicantly, while the calculated total energies increased only minimally.…”

Special issue in honor of Eberhard K.U. Gross for his 65th birthday

“…Callow and Gidopoulos discuss the optimal power series expansions of the Kohn-Sham potential, and in particular the different choices for the zeroth-order Hamiltonian in such expansions [12]. An interesting alternative to the evaluation of the Hartree and exchange-correlation potential of a finite N -electron system is to replaced it by the electrostatic potential of an effective charge density, a method whose performance is analyzed in [13]. Gómez Pueyo and Castro discuss the relation of electron-electron interaction potentials with exchange and correlation functionals [14], while Takada looks at the on-top density in the nonlinear metallic screening and its implication on the correlation functional [15].…”