Basis convergence of range-separated density-functional theory

TL;DR

This paper investigates the basis set convergence properties of range-separated density-functional theory, demonstrating exponential convergence of the wave function and correlation energy, and proposing an extrapolation scheme for improved accuracy.

Contribution

It provides a detailed analysis of basis convergence in range-separated DFT and introduces an exponential extrapolation method for correlation energies.

Findings

Wave function convergence is exponential with angular momentum L.

Correlation energy convergence is exponential with basis set size X.

Proposed a three-point extrapolation scheme for basis set correction.

Abstract

Range-separated density-functional theory is an alternative approach to Kohn-Sham density-functional theory. The strategy of range-separated density-functional theory consists in separating the Coulomb electron-electron interaction into long-range and short-range components, and treating the long-range part by an explicit many-body wave-function method and the short-range part by a density-functional approximation. Among the advantages of using many-body methods for the long-range part of the electron-electron interaction is that they are much less sensitive to the one-electron atomic basis compared to the case of the standard Coulomb interaction. Here, we provide a detailed study of the basis convergence of range-separated density-functional theory. We study the convergence of the partial-wave expansion of the long-range wave function near the electron-electron coalescence. We show that the rate of convergence is exponential with respect to the maximal angular momentum L for the long-range wave function, whereas it is polynomial for the case of the Coulomb interaction. We also study the convergence of the long-range second-order M{{\o}}ller-Plesset correlation energy of four systems (He, Ne, N2, and H2O) with the cardinal number X of the Dunning basis sets cc-p(C)VXZ, and find that the error in the correlation energy is best fitted by an exponential in X. This leads us to propose a three-point complete-basis-set extrapolation scheme for range-separated density-functional theory based on an exponential formula.