Fractional-charge and fractional-spin errors in range-separated density-functional theory

TL;DR

This paper analyzes how range-separated density-functional theory reduces fractional-charge errors compared to traditional methods, but still faces challenges with fractional-spin errors, especially when long-range correlation is included.

Contribution

It provides a detailed comparison of fractional-charge and fractional-spin errors in RSH and RSH+MP2 methods, highlighting their strengths and limitations.

Findings

RSH significantly reduces fractional-charge errors compared to KS and HF.

RSH+MP2 lowers fractional-charge errors for diffuse systems but increases errors for compact systems.

Long-range MP2 correlation causes infinite fractional-spin errors.

Abstract

We investigate fractional-charge and fractional-spin errors in range-separated density-functional theory. Specifically, we consider the range-separated hybrid (RSH) method which combines long-range Hartree-Fock (HF) exchange with a short-range semilocal exchange-correlation density functional, and the RSH+MP2 method which adds long-range second-order M{{\o}}ller-Plesset (MP2) correlation. Results on atoms and molecules show that the fractional-charge errors obtained in RSH are much smaller than in the standard Kohn-Sham (KS) scheme applied with semilocal or hybrid approximations, and also generally smaller than in the standard HF method. The RSH+MP2 method tends to have smaller fractional-charge errors than standard MP2 for the most diffuse systems, but larger fractional-charge errors for the more compact systems. Even though the individual contributions to the fractional-spin errors in the H atom coming from the short-range exchange and correlation density-functional approximations are smaller than the corresponding contributions for the full-range exchange and correlation density-functional approximations, RSH gives fractional-spin errors that are larger than in the standard KS scheme and only slightly smaller than in standard HF. Adding long-range MP2 correlation only leads to infinite fractional-spin errors. This work clarifies the successes and limitations of range-separated density-functional theory approaches for eliminating self-interaction and static-correlation errors.