Range-Separated Local Hybrid Functionals with Small Fractional-Charge and Fractional-Spin Errors: Escaping the Zero-Sum Game of DFT Functionals

Abstract

Extending recent developments on strong-correlation (sc) corrections to local hybrid functionals to the recent accurate ωLH22t range-separated local hybrid, a series of highly flexible strong-correlation-corrected range-separated local hybrids (scRSLHs) has been constructed and evaluated. This has required the position-dependent reduction of both short- and long-range exact-exchange admixtures in regions of space characterized by strong static correlations. Using damping procedures provides scRSLHs that retain largely the excellent performance of ωLH22t for weakly correlated situations and, in particular, for accurate quasiparticle energies of a wide variety of systems while reducing dramatically static-correlation errors, e.g., in stretched-bond situations. An additional correction to the local mixing function to reduce delocalization errors in abnormal open-shell situations provides further improvements in thermochemical and kinetic parameters, making scRSLH functionals such as ωLH23tdE or ωLH23tdP promising tools for complex molecular or condensed-phase systems, where low fractional-charge and fractional-spin errors are simultaneously important. The proposed rung 4 functionals thereby largely escape the usual zero-sum game between these two quantities and are expected to open new areas of accurate computations by Kohn–Sham DFT. At the same time, they require essentially no extra computational effort over the underlying ωLH22t functional, which means that their use is only moderately more demanding than that of global, local, or range-separated hybrid functionals.

Spin-Symmetry Breaking and Hyperfine Couplings in Transition-Metal Complexes Revisited Using Density Functionals Based on the Exact-Exchange Energy Density

“…This construction indeed reduces dramatically FSEs. Due to the inclusion of damping factors in q AC ( r ) and f FR ( r ), the correct LR asymptotic potential is largely retained in weakly correlated situations E XC scRSLH = E normalX ex + prefix∫ 2 q AC ( r ) [ false( 1 − g ( r ) false) ∑ σ false( normalΔ e SR , σ ( r ) + f FR ( r ) normalΔ e LR, σ ( r ) false) + e C B95c false( boldr false) ] .25em normald boldr with normalΔ e SR , σ ( r ) = e normalX , σ PBE,SR, ω ( r ) + G σ pig2 ( r ) − e normalX , σ <...…”

“…ωLH23tE and ωLH23tP are constructed more analogously to scLH23t-mBR and scLH23t-mBR-P, respectively, by using a simple ratio between semilocal (mBR) and EXX energy densities. They differ in the form of the local AC interpolation: while ωLH23tE uses a simple error function, ωLH23tP uses a more flexible Padé function to reduce local maxima in spin-restricted dimer dissociation curves …”

“…As the present work concentrates on spin-polarized open-shell systems, the recently introduced additional DE correction (DEC) to the LMF becomes relevant. It was found that the performance of ωLH22t and the derived scRSLHs for specific open-shell systems could be improved by enhancing EXX admixture locally by an additional DEC term in the LMF, that is also constructed from z ( r ) . In contrast to the sc-corrections, it aims to reduce the DE locally, in analogy to the second part of the LMF of the PSTS functional .…”

“…In contrast to the sc-corrections, it aims to reduce the DE locally, in analogy to the second part of the LMF of the PSTS functional . The resulting modified LMF can be written as g td‐LMF ( r ) = 1 − ( 1 − g t‐LMF false( boldr false) ) ( 1 − a d false( boldr false) ) with a normald ( r ) = ( ζ 2 false( boldr false) + δ − δ ) .25em erf ( h max false( z ( r ) , 0 false) ) where ζ is the spin polarization, δ = 0.00001, and h is an adjustable parameter …”

“…We have recently introduced density functionals depending on the EXX energy density, which include corrections for sc. − More specifically, we have applied sc factors in the spirit of the B13 and KP16/B13 coordinate-space models for nondynamic and strong correlations to local hybrid functionals (scLHs) − and to range-separated local hybrids (RSLHs), generating many scLHs and strong-correlation range-separated local hybrids (scRSLHs). These show substantial improvements over the underlying LHs and RSLHs regarding spin-restricted bond-disssociation curves and the closely related FSEs of open-shell atoms.…”