NKREDZ: Difference between revisions

Revision as of 20:03, 14 March 2022

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 [[[:Category:Hybrids|short range counterparts]]) to a subset, {q_k}, 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 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:

{\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.

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

Related Tags and Sections

NKRED, NKREDX, NKREDY, EVENONLY, ODDONLY, downsampling

Examples that use this tag

@@ Line 3: / Line 3: @@
 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 [[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>&times;''N''<sub>2</sub>&times;''N''<sub>3</sub>)  '''k'''-point set, {'''k'''}, for which the following holds
+One may restrict the sum over '''q''' in the [[:Category:Hybrids|Fock exchange potential]] (or one of its [[[:Category:Hybrids|short range counterparts]]) to a subset, {'''q'''<sub>'''k'''</sub>}, of the full (''N''<sub>1</sub>&times;''N''<sub>2</sub>&times;''N''<sub>3</sub>)  '''k'''-point set, {'''k'''}, for which the following holds
 :<math>
@@ Line 20: / Line 20: @@
 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''': [[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 Tags and Sections ==
@@ Line 28: / Line 28: @@
 {{TAG|EVENONLY}},
 {{TAG|ODDONLY}},
-[[Hartree-Fock_and_HF/DFT_hybrid_functionals#downsampling|downsampling]],
+[[Downsampling of the Hartree-Fock operator|downsampling]]
-[[Hartree-Fock_and_HF/DFT_hybrid_functionals]]
 {{sc|NKREDZ|Examples|Examples that use this tag}}