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 Møller-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.arXiv:1607.03621v1 [physics.chem-ph]

Range‐separated multiconfigurational density functional theory methods

“…Gradient corrections substantially increased the accuracy of RS MC‐DFT, which also manifested in much lower sensitivity to changes of the range‐separated parameter compared to the local functionals 18,21 . Unfortunately, short‐range GGA exchange‐correlation functionals still suffer from fractional charge and fractional spin errors, although to a lesser extent than the full‐range approximations 39 . Consequently, potential energy surfaces modeled with range‐separated multiconfigurational methods will be inaccurate in the stretched‐bond regions, even if the wavefunction part accounts for the multireference effects.…”

A general range-separated double-hybrid density-functional theory

“…W sr,µ ee = 1 2 w sr,µ ee (r 12 )n 2 (r 1 , r 2 )dr 1 dr 2 , (9) wheren 2 (r 1 , r 2 ) =n(r 1 )n(r 2 ) − δ(r 1 − r 2 )n(r 1 ) is the pair-density operator, written with the density operatorn(r). Equation (6)…”

Range-separated multideterminant density-functional theory with a short-range correlation functional of the on-top pair density

“…As regards the short-range density functional, it is usually decomposed into three contribu-tionsĒ [n] = ē sr,µ,pbe x/c (n(r), ∇n(r)) dr. (15) It has been shown that such semi-local densityfunctional approximations become more accurate as the range of the electron-electron interaction is reduced [2]. Nevertheless, for the values of the range-separation parameter commonly used, the short-range PBE exchange and correlation density functionals still contain substantial self-interaction and static-correlation errors [22]. In lieu of the standard expression of the groundstate energy in the context of RS-DFT using only the long-range electron-electron interaction in the expectation value over the wave function Ψ µ as described by Eq.…”