URijkl: Difference between revisions
(Fix Related files → Related tags and articles; add theory page cross-link; describe format columns; fix off-centre → off-center; remove trailing ----) |
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{{Available|6.6.0}} | {{Available|6.6.0}} | ||
The {{FILE|URijkl}} file stores the effectively screened off-center Coulomb integrals | |||
::<math> | ::<math> | ||
U_{ijkl}^{\sigma\sigma'} = \int {\rm d}{\bf r}\int {\rm d}{\bf r}' | U_{ijkl}^{\sigma\sigma'} = \int {\rm d}{\bf r}\int {\rm d}{\bf r}' | ||
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w_{k}^{*\sigma'}({\bf r}'+{\bf R}) w_{l}^{\sigma'}({\bf r}'+{\bf R}) | w_{k}^{*\sigma'}({\bf r}'+{\bf R}) w_{l}^{\sigma'}({\bf r}'+{\bf R}) | ||
</math> | </math> | ||
evaluated at zero frequency (<math>\omega=0</math>) for all lattice vectors '''R''' commensurate with the selected k-point grid (see [[Constrained–random-phase–approximation formalism#Off-center interactions|off-center interactions]]). The file contains one block per lattice vector. Each block header gives the lattice vector index and its fractional coordinates. The columns I, J, K, L are the Wannier function indices; RE and IM are the real and imaginary parts. The format is as follows: | evaluated at zero frequency (<math>\omega=0</math>) for all lattice vectors '''R''' commensurate with the selected k-point grid (see [[Constrained–random-phase–approximation formalism#Off-center interactions|off-center interactions]]). The {{FILE|URijkl}} file contains one block per lattice vector. Each block header gives the lattice vector index and its fractional coordinates. The columns I, J, K, L are the Wannier function indices; RE and IM are the real and imaginary parts. The format is as follows: | ||
# U_ijkl = [ij,R|kl,0] | # U_ijkl = [ij,R|kl,0] | ||
# I J K L RE(V_IJKL) IM(V_IJKL) | # I J K L RE(V_IJKL) IM(V_IJKL) | ||
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* {{FILE|URijkl}}: Only written if all {{FILE|WFULLxxxx.tmp}} files matching the selected k-point grid are present in the working directory. | * {{FILE|URijkl}}: Only written if all {{FILE|WFULLxxxx.tmp}} files matching the selected k-point grid are present in the working directory. | ||
The basis set for these calculations can be specified using {{TAG|LOCALIZED_BASIS}}. | The basis set for these calculations can be specified using {{TAG|LOCALIZED_BASIS}} tag. | ||
Evaluating Coulomb integrals can be computationally intensive, especially when dealing with a large number of basis functions. | Evaluating Coulomb integrals can be computationally intensive, especially when dealing with a large number of basis functions. | ||
{{NB|tip|To improve performance, | {{NB|tip|To improve performance, use a coarser sub-grid of the original '''k'''-point grid by enabling {{TAG|LDOWNSAMPLE|T}}.}} | ||
== Related tags and articles == | == Related tags and articles == | ||
[[Constrained–random-phase–approximation formalism]] | [[Constrained–random-phase–approximation formalism]] | ||
{{FILE|VIJKL}}, {{FILE|UIJKL}}, {{FILE|VRijkl}} | |||
{{TAG|LTWO_CENTER}}, {{TAG|LOCALIZED_BASIS}}, {{TAG|ALGO}} | Files: {{FILE|VIJKL}}, {{FILE|UIJKL}}, {{FILE|VRijkl}} | ||
Tags: {{TAG|LTWO_CENTER}}, {{TAG|LOCALIZED_BASIS}}, {{TAG|ALGO}} | |||
[[Category:Files]][[Category:Output files]][[Category:Constrained-random-phase approximation]] | [[Category:Files]][[Category:Output files]][[Category:Constrained-random-phase approximation]] | ||
Latest revision as of 10:50, 20 March 2026
| Mind: Available as of VASP 6.6.0 |
The URijkl file stores the effectively screened off-center Coulomb integrals
- [math]\displaystyle{ U_{ijkl}^{\sigma\sigma'} = \int {\rm d}{\bf r}\int {\rm d}{\bf r}' w_{i}^{*\sigma}({\bf r}) w_{j}^{\sigma}({\bf r}) U({\bf r},{\bf r}',\omega) w_{k}^{*\sigma'}({\bf r}'+{\bf R}) w_{l}^{\sigma'}({\bf r}'+{\bf R}) }[/math]
evaluated at zero frequency ([math]\displaystyle{ \omega=0 }[/math]) for all lattice vectors R commensurate with the selected k-point grid (see off-center interactions). The URijkl file contains one block per lattice vector. Each block header gives the lattice vector index and its fractional coordinates. The columns I, J, K, L are the Wannier function indices; RE and IM are the real and imaginary parts. The format is as follows:
# U_ijkl = [ij,R|kl,0]
# I J K L RE(V_IJKL) IM(V_IJKL)
# R: 1 0.000000 0.000000 0.000000
1 1 1 1 4.3457689208 0.0000000000
2 1 1 1 0.0000021313 0.0000001349
...
# R: 2 0.000000 0.000000 1.000000
1 1 1 1 1.2535567886 0.0000000000
2 1 1 1 0.0324545667 -0.0000455665
...
The Coulomb integrals are computed and written as a post-processing step using ALGO = 2e4wa. The process differs for the two types of integrals:
- VRijkl (bare off-center Coulomb integrals): Always written when requested.
- URijkl: Only written if all WFULLxxxx.tmp files matching the selected k-point grid are present in the working directory.
The basis set for these calculations can be specified using LOCALIZED_BASIS tag.
Evaluating Coulomb integrals can be computationally intensive, especially when dealing with a large number of basis functions.
Tip: To improve performance, use a coarser sub-grid of the original k-point grid by enabling LDOWNSAMPLE = T.
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Related tags and articles
Constrained–random-phase–approximation formalism
Tags: LTWO_CENTER, LOCALIZED_BASIS, ALGO