FOCKCORR
FOCKCORR = 1 | 2
| Default: FOCKCORR | = 2 | if LMAXFOCKAE>0 |
| = 1 | else |
Description: The tag FOCKCORR determines how the Coulomb convergence corrections are applied.
The Coulomb potential in reciprocal space
- [math]\displaystyle{ V(G)=\frac{4\pi e^2}{G^2} }[/math]
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 [math]\displaystyle{ \mathbf{G}=0 }[/math] component of the Coulomb kernel when FOCKCORR=1
- [math]\displaystyle{ \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. }[/math]
with [math]\displaystyle{ \chi }[/math] 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
- [math]\displaystyle{ \langle \mathbf{k}+\mathbf{G}' | V^\text{HF}_\text{x} | \mathbf{k}+\mathbf{G} \rangle = - \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}'') }[/math]
- [math]\displaystyle{ \begin{aligned} \langle \mathbf{k}+\mathbf{G}' |\hat{V}^\text{HF}_{\text{x}} | \psi_{\mathbf{k}n} \rangle &= - \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})\\ &= - \chi\sum_{m\mathbf{q}}f_{m\mathbf{q}} C_{m\mathbf{q}}(\mathbf{G}) \end{aligned} }[/math]
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 [math]\displaystyle{ \mathbf{q} }[/math] 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 [math]\displaystyle{ n\mathbf{k} }[/math] not in the [math]\displaystyle{ m\mathbf{q} }[/math] set.
| Warning: FOCKCORR=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. |