URijkl

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.

Related tags and articles

Constrained–random-phase–approximation formalism

Files: VIJKL, UIJKL, VRijkl

Tags: LTWO_CENTER, LOCALIZED_BASIS, ALGO