NKRED: Difference between revisions
No edit summary |
No edit summary |
||
| Line 3: | Line 3: | ||
Description: {{TAG|NKRED}} specifies an uniform reduction factor for the '''q'''-point grid representation of the exact exchange potential. | Description: {{TAG|NKRED}} specifies an uniform reduction factor for the '''q'''-point grid representation of the exact exchange potential. | ||
---- | ---- | ||
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> | ||
| Line 11: | Line 11: | ||
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> | ||
| Line 18: | Line 18: | ||
</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 11:27, 16 February 2011
NKRED = [integer]
Default: NKRED = 1
Description: NKRED specifies an uniform reduction factor for the q-point grid representation of the exact exchange potential.
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.
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