DFT in a Plane Wave Basis


  • Construct the real space representation of the density, n(r) :
    • Use 3D-FFTs to convert g-space representation of each state to its r-space representation on a discrete grid of points.
    • Modulus square each state in real space and sum to obtain n(r).
  • Construct the g-space representation of the density, n(g):
    • Use a 3D-FFT of n(r) to compute n(g). This procedure is exact for a finite plane wave basis.
  • Using n(r) :
    • Compute the exchange correlation energy using trapezoidal rule integration (not exact).
    • Compute the exchange correlation potential to the r-space representation of the KS potential.
  • Using n(g) :
    • Compute the local electron-ion interaction (exact).
    • Compute the Hartree energy (exact).
    • Add the e-atom and Hartree contributions to the g-space representation of the exchange correlation potential.



  • Published by Lotus® Freelance Graphics®