Models and corrections: range separation for electronic interaction -- lessons from density functional theory

TL;DR

This paper explores the use of range separation in density functional theory to improve the calculation of electronic interactions, providing a foundation for more accurate modeling of Coulomb systems without relying solely on traditional theorems.

Contribution

It introduces a method combining density functionals with range separation that can calculate electronic states without the Hohenberg-Kohn theorem, with error estimation and basis set correction considerations.

Findings

Allows calculation of ground and excited states without Hohenberg-Kohn theorem

Provides error estimates for validation of results

Offers approaches for correcting finite basis set errors

Abstract

Model Hamiltonians with long-range interaction yield energies that are corrected taking into account the universal behavior of the electron-electron interaction at short range. Although the intention of the paper is to explore the foundations of using density functionals combined with range separation, the approximations presented can be used without them, as illustrated by a calculation on Harmonium. In the regime when the model system approaches the Coulomb system, they allow the calculation of ground states, excited states, and properties, without making use of the Hohenberg-Kohn theorem. Asymptotically, the technique is improvable, allows for error estimates that can validate the results. Some considerations for correcting the errors of finite basis sets in this spirit are also presented. Being related to the present understanding of density functional approximations, the results are comparable to those obtained with the latter, as long as these are accurate.