VRijkl

Mind: Available as of VASP 6.6.0

The VRijkl file is written for ALGO = 2e4wa and stores all bare off-center Coulomb integrals commensurate with the selected k-point grid (see off-center interactions):

[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}'+{\bf R}) w_{l}^{\sigma'}({\bf r}'+{\bf R})}{|{\bf r}-{\bf r}'|} }[/math]

The file contains one block per lattice vector R. 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:

 # V_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       14.4576272582        0.0000000000
    2   1   1   1        0.0000010313        0.0000031049
  ... 
 # R:    2  0.000000  0.000000  1.000000
    1   1   1   1        4.6546536926        0.0000000000
    2   1   1   1        0.0617934919       -0.0000371600
  ...

A proper WAVECAR file must be present in the working directory. The basis can be specified using LOCALIZED_BASIS tag.

Evaluation of Coulomb integrals can be computationally demanding if the number of basis functions becomes large.

Tip: To improve performance, use a coarser sub-grid of the original k-point grid by enabling LDOWNSAMPLE = T.

Related tags and articles

Constrained–random-phase–approximation formalism

Files: VIJKL, UIJKL, URijkl

Tags: LTWO_CENTER, LOCALIZED_BASIS, ALGO