Predicting fundamental gaps accurately from density functional theory with non-empirical local range separation

Abstract

We present an exchange–correlation approximation in which the Coulomb interaction is split into long- and short-range components and the range separation is determined by a non-empirical density functional. The functional respects important constraints, such as the homogeneous and slowly varying density limits, leads to the correct long-range potential, and eliminates one-electron self-interaction. Our approach is designed for spectroscopic purposes and closely approximates the piecewise linearity of the energy as a function of the particle number. The functional’s accuracy for predicting the fundamental gap in generalized Kohn–Sham theory is demonstrated for a large number of systems, including organic semiconductors with a notoriously difficult electronic structure.

Combining Local Range Separation and Local Hybrids: A Step in the Quest for Obtaining Good Energies and Eigenvalues from One Functional

“…Table confirms these trends for a larger database of molecules. This finding is in line with the findings of ref , which showed that local range separation even in a completely nonempirical form can reach higher accuracy than optimal tuning.…”

“…In line with the reasoning that motivated the ln-term, its influence on binding energies is relatively small. 76 Therefore, the construction of ωBT21a takes a different approach at the high-density limit. The local hybrid term of eq 12 exploits that t 2 scales like λ.…”

“…The long-range (lr) and short-range (sr) superscripts refer to the usual range-separation splitting of eq . For E c sl , we combine the LDA correlation energy density ϵ c LDA [ n ↑ , n ↓ ] in the parametrization of ref with an iso-orbital indicator-based one-electron self-interaction correction ,, E c normals normall = ∫ ( 1 − z ζ 2 ) ϵ c normalL normalD normalA .25em d 3 r Here z = τ normalW τ = ℏ 2 8 m false| ∇ n false| 2 n τ ζ = ( n ↑ – n ↓ )/ n and τ denotes the (generalized) Kohn–Sham kinetic energy density. For ϵ x,σ sr,LDA , we use the short-range LDA energy density as parametrized in ref .…”

Toward the Next Generation of Density Functionals: Escaping the Zero-Sum Game by Using the Exact-Exchange Energy Density

“…85 Using an advanced range-separation function and a self-interaction-corrected correlation functional, 89 improved ground-state computations compared to regular RSHs could be demonstrated, 90 and most recently, an LRSH with excellent performance for band gaps has been reported. 92 Another way to combine the LH and RSH ideas is the position-dependent mixing of SR and LR exchange-energy densities by an LMF, leading to range-separated local hybrids (RSLHs), see Figure 1, bottom right. 93,94 We need to distinguish this concept from the use of range separation in the correlation functional of LHs, which we have also employed elsewhere.…”

“…Apart from using RSHs with some SR EXX admixture, one remedy can be to replace the constant ω by a range-separation function depending on position in space. This leads to the concept of locally range-separated hybrids (LRSH). ,− Initially, outer-valence spectra with comparable accuracy as for OT-RSHs could indeed be obtained . Using an advanced range-separation function and a self-interaction-corrected correlation functional, improved ground-state computations compared to regular RSHs could be demonstrated, and most recently, an LRSH with excellent performance for band gaps has been reported …”