NKREDX: Difference between revisions

Latest revision as of 12:03, 18 October 2023

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, {q_k}, 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 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:

[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!

@@ Line 1: / Line 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>&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 [[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>&times;''N''<sub>2</sub>&times;''N''<sub>3</sub>)  '''k'''-point set, {'''k'''}, for which the following holds
 :<math>
@@ Line 11: / Line 11: @@
 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>
@@ Line 18: / Line 18: @@
 </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 {{TAG|NKREDX}}, {{TAG|NKREDY}}, and {{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.
-== Related Tags and Sections ==
+{{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!]]}}
-{{TAG|NKREDX}},
+== Related tags and articles ==
+{{TAG|NKRED}},
 {{TAG|NKREDY}},
 {{TAG|NKREDZ}},
 {{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|NKREDX|Examples|Examples that use this tag}}
 ----
-[[The_VASP_Manual|Contents]]
-[[Category:INCAR]][[Category:Hybrids]]
+[[Category:INCAR tag]][[Category:Exchange-correlation functionals]][[Category:Hybrid_functionals]]