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# NKRED

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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, {qk}, of the full (N1×N2×N3) k-point set, {k}, for which the following holds

${\displaystyle {\mathbf {q_{k}} }={\mathbf {b} }_{1}{\frac {n_{1}C_{1}}{N_{1}}}+{\mathbf {b} }_{2}{\frac {n_{2}C_{2}}{N_{2}}}+{\mathbf {b} }_{3}{\frac {n_{3}C_{3}}{N_{3}}},\quad (n_{i}=0,..,N_{i}-1)}$

where b1,2,3 are the reciprocal lattice vectors of the primitive cell, and Ci is the integer grid reduction factor along reciprocal lattice direction bi. This leads to a reduction in the computational workload by a factor:

${\displaystyle {\frac {1}{C_{1}C_{2}C_{3}}}}$

In case one sets NKRED, the grid reduction factors will be uniformly set to C1=C2=C3=NKRED. If one wants to specify separate grid reduction factors for C1, C2, and C3 one should use C1=NKREDX, C2=NKREDY, and C3=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.