# Nonanalyticity of the optimized effective potential with finite basis sets

@article{Gidopoulos2012NonanalyticityOT, title={Nonanalyticity of the optimized effective potential with finite basis sets}, author={Nikitas I. Gidopoulos and Nektarios N Lathiotakis}, journal={Physical Review A}, year={2012}, volume={85}, pages={052508} }

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.

## 18 Citations

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

- MathematicsFaraday discussions
- 2020

It is demonstrated that appropriately constraining the 'screening charge' which corresponds to the Hartree, exchange and correlation potential not only corrects its asymptotic behaviour but also allows the exchange and correlated potential to exhibit a non-zero derivative discontinuity, a feature of the exact KS potential that is necessary for the accurate prediction of band-gaps in solids but very hard to capture with semi-local density-functional approximations.

A local Fock-exchange potential in Kohn–Sham equations

- ChemistryJournal of physics. Condensed matter : an Institute of Physics journal
- 2017

A local potential is derived to represent the Fock exchange operator in electronic single-particle equations in density functional theory (DFT) and yields robust and accurate results for a variety of systems where Hartree-Fock and popular approximations of DFT typically fail.

Extension of the KLI approximation toward the exact optimized effective potential.

- MathematicsThe Journal of chemical physics
- 2013

The derived Dalgarno function is shown to be an explicit integral functional of the exact OEP Vxcσ, allowing for the reduction of the OEP equation to a self-consistent integral equation for the exact exchange-correlation potential; the exact solution to this integral equation can be determined by iteration with the natural zeroth order correction given by the KLI exchange- Correlation potential.

Constraining density functional approximations to yield self-interaction free potentials.

- PhysicsThe Journal of chemical physics
- 2012

This work constrain the Hartree, exchange and correlation potential to be the electrostatic potential of a non-negative effective repulsive density of N - 1 electrons, resulting in significantly improved one-electron properties.

Renormalized Møller–Plesset Correlation Energy Functional Used in the Optimized Effective Potential Method

- Physics
- 2018

We present the renormalized Moller–Plesset correlation energy functional that is used in the optimized effective potential (OEP) method. The correlation energy functional is developed with the aid ...

Optimal power series expansions of the Kohn–Sham potential

- PhysicsThe European Physical Journal B
- 2018

Abstract
A fundamental weakness of density functional theory (DFT) is the difficulty in making systematic improvements to approximations for the exchange and correlation functionals. In this paper,…

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

- GeologyThe Journal of chemical physics
- 2020

This work presents a method to invert a given density and find the Kohn-Sham potential in Density Functional Theory that shares the density and demonstrates the applicability of the method by inverting both local and non-local densities.

Hierarchy of model Kohn-Sham potentials for orbital-dependent functionals: a practical alternative to the optimized effective potential method.

- PhysicsThe Journal of chemical physics
- 2014

A method for constructing a hierarchy of model potentials approximating the functional derivative of a given orbital-dependent exchange-correlation functional with respect to electron density and the highest-level approximation is the density-consistent effective potential (DCEP), derived under the assumption that the KS and GKS electron densities are equal.

Approximation of Exchange-Correlation Potentials for Orbital-Dependent Functionals

- Chemistry
- 2013

Density-functional theory (DFT) is the most widely used method of modern computational chemistry. All practical implementations of DFT rely on approximations to the unknown exchange-correlation…

Accurate effective potential for density amplitude and the corresponding Kohn–Sham exchange–correlation potential calculated from approximate wavefunctions

- Physics
- 2019

Over the past few years it has been pointed out that direct inversion of accurate but approximate ground state densities leads to Kohn–Sham exchange–correlation (xc) potentials that can differ…

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