NKREDX: Difference between revisions
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{{TAGDEF|NKREDX|[integer]|1}} | {{TAGDEF|NKREDX|[integer]|1}} | ||
Description: {{TAG|NKREDX}} specifies a reduction factor for the '''q'''-point grid representation of the exact exchange potential along reciprocal space direction '''b'''<sub> 1</sub>. | Description: {{TAG|NKREDX}} specifies a reduction factor for the '''q'''-point grid representation of the exact exchange potential along reciprocal space direction '''b'''<sub>1</sub>. | ||
---- | ---- | ||
One may restrict the sum over '''q''' in the [[Hartree-Fock_and_HF/DFT_hybrid_functionals#VxFock|Fock exchange potential]] (or one of its [[Hartree-Fock_and_HF/DFT_hybrid_functionals#VxFockSR|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 | One may restrict the sum over '''q''' in the [[Hartree-Fock_and_HF/DFT_hybrid_functionals#VxFock|Fock exchange potential]] (or one of its [[Hartree-Fock_and_HF/DFT_hybrid_functionals#VxFockSR|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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where '''b'''<sub>1,2,3</sub> are the reciprocal lattice vectors of the primitive cell, | where '''b'''<sub>1,2,3</sub> are the reciprocal lattice vectors of the primitive cell, | ||
and ''C''<sub> i</sub> is the integer grid reduction factor along reciprocal lattice direction | and ''C''<sub>i</sub> is the integer grid reduction factor along reciprocal lattice direction | ||
'''b'''<sub> i</sub>. This leads to a reduction in the computational workload by a factor: | '''b'''<sub>i</sub>. This leads to a reduction in the computational workload by a factor: | ||
:<math> | :<math> | ||
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</math> | </math> | ||
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. | ||
'''Mind''': [[Hartree-Fock_and_HF/DFT_hybrid_functionals#downsamplingCaveat|there are circumstances under which '''NKRED''' and '''NKREDX''','''Y''','''Z''' should not be used!]] | '''Mind''': [[Hartree-Fock_and_HF/DFT_hybrid_functionals#downsamplingCaveat|there are circumstances under which '''NKRED''' and '''NKREDX''','''Y''','''Z''' should not be used!]] | ||
Revision as of 11:28, 16 February 2011
NKREDX = [integer]
Default: NKREDX = 1
Description: NKREDX specifies a reduction factor for the q-point grid representation of the exact exchange potential along reciprocal space direction b1.
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
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:
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.
Mind: there are circumstances under which NKRED and NKREDX,Y,Z should not be used!
Related Tags and Sections
NKRED, NKREDY, NKREDZ, EVENONLY, ODDONLY, downsampling, Hartree-Fock_and_HF/DFT_hybrid_functionals