Basis-set correction based on density-functional theory: Rigorous framework for a one-dimensional model

TL;DR

This paper revisits a basis-set correction method based on density-functional theory, applying it to a one-dimensional model to improve the understanding and development of basis-set corrections for wave-function calculations.

Contribution

It introduces a new variant of basis-set correction suited for developing an adapted local-density approximation, enhancing the theoretical foundation of the approach.

Findings

Mathematical details of the basis-set correction theory are provided.

A new local-density approximation for the correction functional is proposed.

The approach is validated on a one-dimensional model with delta-potential interactions.

Abstract

We reexamine the recently introduced basis-set correction theory based on density-functional theory consisting in correcting the basis-set incompleteness error of wave-function methods using a density functional. We use a one-dimensional model Hamiltonian with delta-potential interactions which has the advantage of making easier to perform a more systematic analysis than for three-dimensional Coulombic systems while keeping the essence of the slow basis convergence problem of wave-function methods. We provide some mathematical details about the theory and propose a new variant of basis-set correction which has the advantage of being suited to the development of an adapted local-density approximation. We show indeed how to develop a local-density approximation for the basis-set correction functional which is automatically adapted to the basis set employed, without resorting to range-separated density-functional theory as in previous works, but using instead a finite uniform electron gas whose electron-electron interaction is projected on the basis set. The work puts the basis-set correction theory on firmer grounds and provides an interesting strategy for the improvement of this approach.