FOCKCORR

FOCKCORR = [integer]
Default: FOCKCORR = 1 or 2 if LMAXFOCKAE>0

Description: The tag FOCKCORR determines how the Coulomb convergence corrections are applied.

The Coulomb potential in reciprocal space

V(G)={\frac {4\pi e^{2}}{G^{2}}}

diverges for small G vectors. To alleviate this issue and improve the convergence of the exact exchange integral with respect to supercell size (or k-point mesh density) different methods have been proposed: the auxiliary function methods^[1], probe-charge Ewald ^[2] (HFALPHA), and Coulomb truncation methods^[3] (HFRCUT). These mostly involve modifying the Coulomb Kernel in a way that yields the same result as the unmodified kernel within the limit of large supercell sizes.

These corrections are implemented in VASP either by changing the $\mathbf {G} =0$ component of the Coulomb kernel when FOCKCORR=1

\Phi (\mathbf {G} )=\left\{{\begin{array}{lr}{\frac {4\pi e^{2}}{\Omega }}{\frac {1}{G^{2}}}&\mathbf {G} \neq 0\\\chi &\mathbf {G} =0\end{array}}\right.

with $\chi$ being the value of the correction and depends on whether HFALPHA or HFRCUT are set, or by including the original orbital scaled by the convergence correction when FOCKCORR=2

\langle \mathbf {k} +\mathbf {G} |V_{\text{x}}^{\text{HF}}|\mathbf {k} +\mathbf {G} '\rangle =-{\frac {4\pi e^{2}}{\Omega }}\sum _{m\mathbf {q} }f_{m\mathbf {q} }\sum _{\mathbf {G} ''}C_{m\mathbf {q} }^{*}(\mathbf {G} '-\mathbf {G} '')\Phi (\mathbf {k} -\mathbf {q} +\mathbf {G} '')C_{m\mathbf {q} }(\mathbf {G} -\mathbf {G} '')

{\begin{aligned}\langle \mathbf {k} +\mathbf {G} |{\hat {V}}_{\text{x}}^{\text{HF}}|\psi _{\mathbf {k} n}\rangle &=-{\frac {4\pi e^{2}}{\Omega }}\sum _{m\mathbf {q} }f_{m\mathbf {q} }\sum _{\mathbf {G} ''}C_{m\mathbf {q} }^{*}(\mathbf {G} '-\mathbf {G} '')\Phi (\mathbf {k} -\mathbf {q} +\mathbf {G} '')C_{m\mathbf {q} }(\mathbf {G} -\mathbf {G} '')C_{n\mathbf {k} }(\mathbf {G} )\\&=-{\frac {4\pi e^{2}}{\Omega }}\chi \sum _{m\mathbf {q} }f_{m\mathbf {q} }C_{m\mathbf {q} }(\mathbf {G} )\end{aligned}}

For Hartree-Fock or hybrid functional calculations, either FOCKCORR=1 or FOCKCORR=2 can be used and should yield the same results when LMAXFOCKAE=-1 and there are no aliasing errors in the exact exchange (see PRECFOCK for more details). For post-DFT methods such as ACDFT, GW, and BSE the FOCKCORR=2 should be used because the overlap densities are reconstructed in the plane-wave grid (see LMAXFOCKAE tag).

Note that in the case FOCKCORR=2 the corrections are only applied to orbitals in the $\mathbf {q}$ regular grid used to describe the exact exchange potential so this method cannot be used to compute band structures where this potential is applied to orbitals $n\mathbf {k}$ not in the $m\mathbf {q}$ set.

Warning: FOCKCORR set to 2 should not be used when computing the band structure along a path with the 0-weight scheme or KPOINTS_OPT

In previous versions of VASP, FOCKCORR=1 was used when ALGO=Normal; LFOCKACE=.FALSE. and FOCKCORR=2 when ALGO=All or ALGO=Normal; LFOCKACE=.TRUE. .

Mind: Only available as of VASP 6.3.1.

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