There is no long-range HF exchange in HSE, only short-range HF.įor w=0 HSE reduces to the hybrid functional PBEh, andįor w- $\infty$ ω → ∞, HSE becomes identical with PBE.Ģ1 HSE with a finite value of w can be regarded as an interpolation between these two limits. Where xx is the short-range HF exchange【短程作用HF交换项】, E PBE, SR x and xxx and xxx E PBE, LR x are the short-range and long-range components of the PBE exchange functional obtained by integration of the model PBE exchange hole, 13,17 and xxxx E PBE c is the PBE correlation energy.ġ8 Note that HSE may be viewed as an adiabatic【绝热的】 connection functional, 18 but only in the short-range portion of the potential. The HSE functional partitions 【分开/分割】the Coulomb potential for exchange into short-range (SR) and long-range (LR) components:Į HSE xc = a E HF, SR x ( ω ) + ( 1 − a ) E PBE, SR x ( ω ) + E PBE, LR x ( ω ) + E PBE c, (2) This enables a substantial lowering of the computational cost for calculations in extended systems【与Roald的观点一致，extended systems】.
THOMAS FERMI SCREENING PARAMETER FULL
In HSE, the spatial decay of the HF exchange interaction 【HF交换项空间衰变】is accelerated by substitution of the full 1 / r Coulomb potential with a screened one【全库伦势】. However, HF exchange drastically increases the computational demand for calculations in periodic systems【HF非常耗时】.Īn efficient alternative to conventional hybrids is the screened hybrid functional【屏蔽杂化泛函】 of Heyd, Scuseria, and Ernzerhof (HSE). Recent studies have shown that hybrid density functionals, which include a portion of Hartree-Fock (HF) exchange, partially solve these problems. (2) Also, semilocal functionals overestimate electron delocalization effects 【高估电子局域作用】and therefore fail for many d - and f -element compounds. (1) they systematically underestimate band gaps with respect to experiment. However, semi-local functionals have some important shortcomings.【半局域函数】
Where the screening parameter w defines the separation range. Such as the functional of Perdew, Burke, and Ernzerhof (PBE). ( 6.59 ), one straightforwardly obtains:Īpplications of KohnSham density functional theory to solids mostly employ semilocal approximations to the exchange-correlation energy, Using the decomposed Coulomb kernel and Equ. To conform with the HSE06 functional you need to select ( HFSCREEN =0.2). Note: It has been shown that the optimum, controlling the range separation is approximately Å. Is the parameter that defines the range-separation, and is related to a characteristic distance, ( ), at which the short-range interactions become negligible. The parameter a=1/4 is the HF mixing constant derived from perturbation theory. Finally, a rigorous version of screening is introduced to account for thermodynamic stability.The Heyd-Scuseria-Ernzerhof (HSE) screened hybrid functional Thomas-Fermi theory is developed in some detail because, as is also pointed out, it is the asymptotically correct picture of heavy atoms and molecules (in the Z→ limit). Next the Pauli principle, together with some facts about Thomas-Fermi theory, is shown, to account for the stability (i.e., saturation) of bulk matter. First, the stability of atom is demonstrated, in the framework of nonrelativistic quantum mechanics. The resolution is given here in three steps. Finally, a rigorous version of screening is introduced to account for thermodynamic stability.ĪB - A fundamental paradox of classical physics is why matter, which is held together by Coulomb forces, does not collapse. N2 - A fundamental paradox of classical physics is why matter, which is held together by Coulomb forces, does not collapse.
National Science Foundation grant MCS 75-21684.
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