LMODELHF: Difference between revisions

Revision as of 09:26, 8 May 2020

LMODELHF = .TRUE. | .FALSE.
Default: LMODELHF = .FALSE.

Description: LMODELHF selects a decomposition of the exchange functional with full exchange in the short range, and AEXX in the long range.

LMODELHF=.TRUE. selects the range separated hybrid functional suggested in Ref.^[1] and Ref. ^[2] under the name dielectric-dependent hybrid functionals (DDH) and doubly screened hybrid (DSH), respectively. These two functionals are completely identical, but for the way the amount of exact exchange is determined in the long range limit (short wave length limit).

The corresponding functional has been available in VASP since VASP.5.2 released in 2009 (so way before the two publications), although the gradient contribution had been erroneously implemented in all VASP.5 releases and is only correct in VASP.6. The corresponding bug fix has been made available by the authors of Ref. ^[2]. The non-local exchange part of the functional has also been used and documented in Ref. ^[3], and is covered in Improving the dielectric function.

Typically the INCAR file will show the following tags for a calculation selecting dielectric-dependent hybrid functionals:

LHFCALC = .TRUE.
LMODELHF = .TRUE.
HFSCREEN = 1.26
AEXX = 0.1

In this case, AEXX specifies the amount of exact exchange in the long range, that is for short wave vectors ( $\mathbf{G} \to 0$ ). In the short range, that is for large wave vectors, always the full non-local exchange is used. The HFSCREEN determines how quickly the non-local exchange changes from AEXX to 1.

Specifically, in VASP, the Coulomb kernel $4 \pi e^2 / (\mathbf{q}+\mathbf{G})^2$ in the exact exchange is multiplied by a model for the dielectric function $\epsilon^{-1} (\mathbf{q}+\mathbf{G})$ :

\epsilon^{-1} (\mathbf{q}+\mathbf{G})=1-(1-{{\varepsilon}_{\infty}^{-1}})\text{exp}(-\frac{|\mathbf{q+G}|^2}{4{\mu}^2})

.

where $\mu$ corresponds to HFSCREEN, and ${{\varepsilon}_{\infty}^{-1}}$ is specified by AEXX. In real space this correspond to a Coulomb kernel

V(r) =(1-(1-{{\varepsilon}_{\infty}^{-1}})\text{erf}( {\mu} r)) \frac{e^2}{r}

.

The remaining part of the exchange is handled by an appropriate semi-local exchange correlation functional. For further detail we refer to the literature listed below.

Related Tags and Sections

LHFCALC, HFSCREEN, AEXX, hybrid functionals, Thomas-Fermi screening, settings for specific hybrid functionals

References

[chen2018nonempirical-1] W. Chen, G. Miceli, G.M. Rignanese, A. Pasquarello Physical Review Materials 2, 073803 (2018).

[cui2018doubly-2] Z.H. Cui, Y.C. Wang, M.Y. Zhang, X. Xu, H. Jiang, J. Phys. Chem. Lett., 9, 2338-2345 (2018).

[bokdam:scr:6-3] M. Bokdam, T. Sander, A. Stroppa, S. Picozzi, D. D. Sarma, C. Franchini, G. Kresse, Scientific Reports 6, 28618 (2016).

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[2]

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 Specifically, in VASP, the  Coulomb kernel <math> 4 \pi e^2 / (\mathbf{q}+\mathbf{G})^2</math> in the exact exchange is multiplied by a model for the dielectric function <math> \epsilon^{-1} (\mathbf{q}+\mathbf{G})</math>:
-:<math> \epsilon^{-1} (\mathbf{q}+\mathbf{G})=1-(1-{{\varepsilon}_{\infty}^{-1}})\text{exp}(-\frac{|\mathbf{q+G}|^2}{4{\sigma}^2})</math>.
+:<math> \epsilon^{-1} (\mathbf{q}+\mathbf{G})=1-(1-{{\varepsilon}_{\infty}^{-1}})\text{exp}(-\frac{|\mathbf{q+G}|^2}{4{\mu}^2})</math>.
-where <math> \sigma  </math> corresponds to {{TAG|HFSCREEN}}, and  <math> {{\varepsilon}_{\infty}^{-1}} </math> is specified by {{TAG|AEXX}}. The remaining part of the exchange is handled by an appropriate
+where <math> \mu  </math> corresponds to {{TAG|HFSCREEN}}, and  <math> {{\varepsilon}_{\infty}^{-1}} </math> is specified by {{TAG|AEXX}}. In real space this correspond to a Coulomb kernel
-semi-local exchange correlation functional.
+:<math> V(r) =(1-(1-{{\varepsilon}_{\infty}^{-1}})\text{erf}( {\mu} r)) \frac{e^2}{r} </math>.
+The remaining part of the exchange is handled by an appropriate
+semi-local exchange correlation functional. For further detail we refer to the literature listed below.