KLI with k-points.

Description

Implementation of the KLI approximation with k-points. This does not include the spinor case.

The implementation is tested against the results of [PRB 93, 205205 (2016)] for the SCAN XC functional, for Si, GaAs, and C:

• gKS bandgap (eV)

  • BAND: 0.97 0.8 4.58
  • Octopus: 0.95 0.92 4.78

• KLI bandgap for Si (eV)

  • BAND: 0.78 0.45 4.26
  • Octopus: 0.76 0.62 4.56

• Derivative discontinuity (eV)

  • BAND: 0.19 0.34 0.32
  • Octopus: 0.19 0.29 0.22

Octopus calculations are done with SCAN, and are not fully converged with the grid spacing. Also, it is not s clear which lattice parameter and pseudopotentials are used in [PRB 93, 205205 (2016)], and the ZORA effect in this work are not considered here.

News snippet

Implementation of the KLI approximation with k-points.

Checklist

• I have checked that my code follows the Octopus coding standards
• I have added tests for all the new features added in this request.