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

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{ø}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.

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• A basis-set error correction based on density-functional theory for strongly correlated molecular systems
• Self-consistent double-hybrid density-functional theory using the optimized-effective-potential method
• Self-consistent range-separated density-functional theory with second-order perturbative correction via the optimized-effective-potential method
• A new form of transcorrelated Hamiltonian inspired by range-separated DFT
• Four-component relativistic range-separated density-functional theory: Short-range exchange local-density approximation
• Variations of the Hartree-Fock fractional-spin error for one electron
• Random Phase Approximation in Projected Oscillator Orbitals