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The charge density of equation (6) is a quantity that extends over the entire simulation cell. The individual contributions to the charge density, i.e., the
of equation (7), however, are localised in real space and may thus be calculated using the FFT box with a cost that is independent of systemsize. For a given pair of overlapping NGWFs,
and
, we project them from the simulation cell into their FFT box. Both are then interpolated onto the fine grid of the FFT box using fast Fourier transforms and zeropadding in reciprocal space. The cost associated with this procedure is systemsize independent as it is done over the grid points of the FFT box only. The interpolated NGWFs are multiplied together on the fine grid points of the FFT box and the result projected back onto the fine grid of the simulation cell. In terms of our projection operators, this becomes

(32) 
The total charge density is then built up by summing all the contributions from the FFT boxes of pairs of overlapping NGWFs according to

(33) 
Next: Hartree, local pseudopotential, and
Up: Total energy using the
Previous: Nonlocal pseudopotential energy
Peter D. Haynes
20021029