Constraining density functional approximations to yield self-interaction free potentials

Self-interactions (SIs) are a major problem in density functional approximations and the source of serious divergence from experimental results. Here, we propose to optimize density functional total energies in terms of the effective local potential, under constraints for the effective potential that guarantee it is free from SI errors and consequently asymptotically correct. More specifically, we constrain the Hartree, exchange and correlation potential to be the electrostatic potential of a non-negative effective repulsive density of N − 1 electrons. In this way, the optimal effective potentials exhibit the correct asymptotic decay, resulting in significantly improved one-electron properties

Reply to “Comment on ‘Nonanalyticity of the optimized effective potential with finite basis sets’ ”

The Comment by Friedrich et al. does not dispute the central result of our paper [Phys. Rev. A 85, 052508 (2012)] that nonanalytic behavior is present in long-established mathematical pathologies arising in the solution of finite basis optimized effective potential (OEP) equations. In the Comment, the terms “balancing of basis sets” and “basis-set convergence” imply a particular order towards the limit of a large orbital basis sets where the large-orbital-base limit is always taken first, before the large-auxiliary-base limit, until overall convergence is achieved, at a high computational cost. The authors claim that, on physical grounds, this order of limits is not only sufficient, but also necessary in order to avoid the mathematical pathologies. In response to the Comment, we remark that it is already written in our paper that the nonanalyticity trivially disappears with large orbital basis sets. We point out that the authors of the Comment give an incorrect proof of this statement. We also show that the order of limits towards convergence of the potential is immaterial. A recent paper by the authors of the Comment proposes a partial correction for the incomplete orbital basis error in the full-potential linearized augmented-plane-wave method. Similar to the correction developed in our paper, this correction also benefits from an effectively complete orbital basis, even though only a finite orbital basis is employed in the calculation. This shows that it is unnecessary to take, in practice, the limit of an infinite orbital basis in order to avoid mathematical pathologies in the OEP. Our paper is a significant contribution in that direction with general applicability to any choice of basis sets. Finally, contrary to an allusion in the abstract and assertions in the main text of the Comment that unphysical oscillations of the OEP are supposedly attributed to the common energy denominator approximation, in fact, such anomalies arise with the full treatment of the small eigenvalues of the density response function. This characteristic of the finite basis OEP is well known in the literature but also is clearly demonstrated in our paper

Orbitals from local RDMFT: Are they Kohn-Sham or Natural Orbitals?

Recently, an approximate theoretical framework was introduced, called local reduced density matrix functional theory (local-RDMFT), where functionals of the one-body reduced density matrix (1-RDM) are minimized under the additional condition that the optimal orbitals satisfy a single electron Schrödinger equation with a local potential. In the present work, we focus on the character of these optimal orbitals. In particular, we compare orbitals obtained by local-RDMFT with those obtained with the full minimization (without the extra condition) by contrasting them against the exact NOs and orbitals from a density functional calculation using the local density approximation (LDA). We find that the orbitals from local-RMDFT are very close to LDA orbitals, contrary to those of the full minimization that resemble the exact NOs. Since local RDMFT preserves the good quality of the description of strong static correlation, this finding opens the way to a mixed density/density matrix scheme, where Kohn-Sham orbitals obtain fractional occupations from a minimization of the occupation numbers using 1-RDM functionals. This will allow for a description of strong correlation at a cost only minimally higher than a density functional calculation

Testing one-body density functionals on a solvable model

There are several physically motivated density matrix functionals in the literature, built from the knowledge of the natural orbitals and the occupation numbers of the one-body reduced density matrix. With the help of the equivalent phase-space formalism, we thoroughly test some of the most popular of those functionals on a completely solvable model.Comment: Latex, 16 pages, 4 figure

Nonanalyticity of the optimized effective potential with finite basis sets

We show that the finite-basis optimized effective potential (OEP) equations exhibit previously unknown singular behavior. Imposing continuity, we derive new well-behaved finite-basis-set OEP equations that determine OEP for any orbital and any large enough potential basis sets and which adopt an analytic solution via matrix inversion

Chapter Six – Constrained Local Potentials for Self-Interaction Correction

In this chapter, we discuss a method to alleviate self-interaction (SI) errors from the approximate Kohn–Sham potential, but without altering the corresponding approximate exchange and correlation energy, which still remains contaminated with SIs. In particular, we aim to correct the asymptotic behavior—at large distances—of the potential, by enforcing two subsidiary conditions. These conditions are incorporated with the help of the optimized effective potential method. This method is applied to molecules, using LDA or approximate exchange and correlation functionals from Reduced Density Matrix Functional Theory. The resulting ionization energies of this constrained approach, as compared to LDA, are significantly improved and much closer to experiment

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

We present a method to invert a given density and find the Kohn–Sham (KS) potential in Density Functional Theory (DFT) that shares the density. Our method employs the concept of screening density, which is naturally constrained by the inversion procedure and thus ensures that the density being inverted leads to a smooth KS potential with correct asymptotic behavior. We demonstrate the applicability of our method by inverting both local and non-local (Hartree–Fock and coupled cluster) densities; we also show how the method can be used to mitigate the effects of self-interactions in common DFT potentials with appropriate constraints on the screening density

Local reduced-density-matrix-functional theory: Incorporating static correlation effects in Kohn-Sham equations

We propose a scheme to bring reduced-density-matrix-functional theory into the realm of density functional theory (DFT) that preserves the accurate density functional description at equilibrium, while incorporating accurately static and left-right correlation effects in molecules and keeping the good computational performance of DFT-based schemes. The key ingredient is to relax the requirement that the local potential is the functional derivative of the energy with respect to the density. Instead, we propose to restrict the search for the approximate natural orbitals within a domain where these orbitals are eigenfunctions of a single-particle Hamiltonian with a local effective potential. In this way, fractional natural occupation numbers are accommodated into Kohn-Sham equations allowing for the description of molecular dissociation without breaking spin symmetry. Additionally, our scheme provides a natural way to connect an energy eigenvalue spectrum to the approximate natural orbitals and this spectrum is found to represent accurately the ionization potentials of atoms and small molecules

Electronic properties of the Sn1−xPbxO alloy and band alignment of the SnO/PbO system: a DFT study

Tin monoxide (SnO) has attracted attention due to its p-type character and capability of ambipolar conductivity when properly doped, properties that are beneficial for the realization of complementary oxide thin film transistors technology, transparent flexible circuits and optoelectronic applications in general. However, its small fundamental band gap (0.7 eV) limits its applications as a solar energy material, therefore tuning its electronic properties is necessary for optimal performance. In this work, we use density functional theory (DFT) calculations to examine the electronic properties of the Sn1−xPbxO ternary oxide system. Alloying with Pb by element substitution increases the band gap of SnO without inducing defect states in the band gap retaining the anti-bonding character of the valence band maximum which is beneficial for p-type conductivity. We also examine the properties of the SnO/PbO heterojunction system in terms of band alignment and the effect of the most common intrinsic defects. A broken gap band alignment for the SnO/PbO heterojunction is calculated, which can be attractive for energy conversion in solar cells, photocatalysis and hydrogen generation. © 2020, The Author(s)