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# NKRED

NKRED = [integer]

Default: **NKRED** = 1

Description: NKRED specifies an uniform reduction factor for the **q**-point grid representation of the exact exchange potential and the correlation part in GW calculations.

One may restrict the sum over **q** in the Fock exchange potential (or one of its short range counterparts) to a subset, {**q**_{k}}, of the full (*N*_{1}×*N*_{2}×*N*_{3}) **k**-point set, {**k**}, for which the following holds

where **b**_{1,2,3} are the reciprocal lattice vectors of the primitive cell,
and *C*_{i} is the integer grid reduction factor along reciprocal lattice direction
**b**_{i}. This leads to a reduction in the computational workload by a factor:

In case one sets NKRED, the grid reduction factors will be uniformly set to *C*_{1}=*C*_{2}=*C*_{3}=NKRED. If one wants to specify separate grid reduction factors for *C*_{1}, *C*_{2}, and *C*_{3} one should use *C*_{1}=NKREDX, *C*_{2}=NKREDY, and *C*_{3}=NKREDZ, respectively.

This flag also applies to GW and RPA calculations with a similar speedup. In GW and RPA type calculations,
analogously to hybrid functional calculations the outermost loop over the momentum transfer **q**
is reduced to a subgrid specified by the NKRED parameters.

**Mind**: there are circumstances under which **NKRED** and **NKREDX**,**Y**,**Z** should not be used!

## Related Tags and Sections

NKREDX, NKREDY, NKREDZ, EVENONLY, ODDONLY, downsampling, Hartree-Fock_and_HF/DFT_hybrid_functionals