DFT in a Plane Wave Basis (con't)


  • Compute the total KS potential in real space.
    • Use a 3D-FFT to put the reciprocal portion (from Hartree and local external) into real space on the discrete grid.
    • Add the two contributions to the KS potential.
  • Compute the derivative of the three terms with respect to the Fourier coefficients of the states:
    • Use 3D-FFTs to compute the real space rep. of each state.
    • Multiply the state by the KS potential
    • 3D-FFT the product back to real space to produce the exact derivative of the energy expression evaluated.
  • Compute the non-local energy and kinetic energy of non-interacting electrons and the derivatives.
  • Evolve the Fourier coefficients of states towards the minima using a solver (e.g. constrained conjugate gradient).
  • Enforce Orthonormality : Fix finite step size errors in the solver.



  • Published by Lotus® Freelance Graphics®