VIJKL: Difference between revisions
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(Fix Related files → Related tags and articles; add theory page cross-link; describe R=0 context and format columns; remove trailing ----) |
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This file stores the bare Coulomb integrals | This file stores the bare Coulomb integrals at the unit-cell origin ('''R''' = 0): | ||
::<math> | ::<math> | ||
V_{ijkl}^{\sigma\sigma'} = \int {\rm d}{\bf r}\int {\rm d}{\bf r}' | V_{ijkl}^{\sigma\sigma'} = \int {\rm d}{\bf r}\int {\rm d}{\bf r}' | ||
\frac{ w_{i}^{*\sigma}({\bf r}) w_{j}^{\sigma}({\bf r}) w_{k}^{*\sigma'}({\bf r}') w_{l}^{\sigma'}({\bf r}')}{|{\bf r}-{\bf r}'|} | \frac{ w_{i}^{*\sigma}({\bf r}) w_{j}^{\sigma}({\bf r}) w_{k}^{*\sigma'}({\bf r}') w_{l}^{\sigma'}({\bf r}')}{|{\bf r}-{\bf r}'|} | ||
</math> | </math> | ||
The format is as follows: | 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: | ||
# V_ijkl = [ij,R|kl,0] | |||
# I J K L RE(V_IJKL) IM(V_IJKL) | |||
1 1 1 1 14.4576272582 0.0000000000 | |||
2 1 1 1 0.0000010313 0.0000031049 | |||
... | |||
== Related | |||
{{FILE|UIJKL}},{{FILE|URijkl}},{{FILE|VRijkl}} | == Related tags and articles == | ||
[[Constrained–random-phase–approximation formalism]], | |||
{{FILE|UIJKL}}, {{FILE|URijkl}}, {{FILE|VRijkl}}, | |||
{{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]] | ||
Revision as of 10:19, 20 March 2026
This file stores the bare Coulomb integrals at the unit-cell origin (R = 0):
- [math]\displaystyle{ V_{ijkl}^{\sigma\sigma'} = \int {\rm d}{\bf r}\int {\rm d}{\bf r}' \frac{ w_{i}^{*\sigma}({\bf r}) w_{j}^{\sigma}({\bf r}) w_{k}^{*\sigma'}({\bf r}') w_{l}^{\sigma'}({\bf r}')}{|{\bf r}-{\bf r}'|} }[/math]
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:
# V_ijkl = [ij,R|kl,0]
# I J K L RE(V_IJKL) IM(V_IJKL)
1 1 1 1 14.4576272582 0.0000000000
2 1 1 1 0.0000010313 0.0000031049
...
Related tags and articles
Constrained–random-phase–approximation formalism, UIJKL, URijkl, VRijkl, LOCALIZED_BASIS, ALGO