NKREDZ: Difference between revisions
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Description: {{TAG|NKREDZ}} specifies a reduction factor for the '''q'''-point grid representation of the exact exchange potential along reciprocal space direction '''b'''<sub>3</sub>. | Description: {{TAG|NKREDZ}} specifies a reduction factor for the '''q'''-point grid representation of the exact exchange potential along reciprocal space direction '''b'''<sub>3</sub>. | ||
---- | ---- | ||
One may restrict the sum over '''q''' in the [[: | One may restrict the sum over '''q''' in the [[Hybrid functionals: formalism|Fock exchange potential]] (or one of its short range counterparts) to a subset, {'''q'''<sub>'''k'''</sub>}, of the full (''N''<sub>1</sub>×''N''<sub>2</sub>×''N''<sub>3</sub>) '''k'''-point set, {'''k'''}, for which the following holds | ||
:<math> | :<math> | ||
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In case one sets {{TAG|NKRED}}, the grid reduction factors will be uniformly set to ''C''<sub>1</sub>=''C''<sub>2</sub>=''C''<sub>3</sub>={{TAG|NKRED}}. If one wants to specify separate grid reduction factors for ''C''<sub>1</sub>, ''C''<sub>2</sub>, and ''C''<sub>3</sub> one should use ''C''<sub>1</sub>={{TAG|NKREDX}}, ''C''<sub>2</sub>={{TAG|NKREDY}}, and ''C''<sub>3</sub>={{TAG|NKREDZ}}, respectively. | In case one sets {{TAG|NKRED}}, the grid reduction factors will be uniformly set to ''C''<sub>1</sub>=''C''<sub>2</sub>=''C''<sub>3</sub>={{TAG|NKRED}}. If one wants to specify separate grid reduction factors for ''C''<sub>1</sub>, ''C''<sub>2</sub>, and ''C''<sub>3</sub> one should use ''C''<sub>1</sub>={{TAG|NKREDX}}, ''C''<sub>2</sub>={{TAG|NKREDY}}, and ''C''<sub>3</sub>={{TAG|NKREDZ}}, respectively. | ||
{{NB|warning|[[Downsampling_of_the_Hartree-Fock_operator#Caveat: when one should not use downsampling|there are circumstances under which '''NKRED''' and '''NKREDX''','''Y''','''Z''' should not be used!]]}} | |||
== Related | == Related tags and articles == | ||
{{TAG|NKRED}}, | {{TAG|NKRED}}, | ||
{{TAG|NKREDX}}, | {{TAG|NKREDX}}, | ||
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[[Category:INCAR]][[Category:Exchange-correlation functionals]][[Category: | [[Category:INCAR tag]][[Category:Exchange-correlation functionals]][[Category:Hybrid_functionals]] | ||
Latest revision as of 12:04, 18 October 2023
NKREDZ = [integer]
Default: NKREDZ = 1
Description: NKREDZ specifies a reduction factor for the q-point grid representation of the exact exchange potential along reciprocal space direction b3.
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
- [math]\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) }[/math]
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:
- [math]\displaystyle{ \frac{1}{C_1 C_2 C_3} }[/math]
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.
| Warning: there are circumstances under which NKRED and NKREDX,Y,Z should not be used! |
Related tags and articles
NKRED, NKREDX, NKREDY, EVENONLY, ODDONLY, downsampling