We provide {\it a priori} error estimates for the spectral and pseudospectral
Fourier (also called planewave) discretizations of the periodic
Thomas-Fermi-von Weizs\"acker (TFW) model and of the Kohn-Sham model, within
the local density approximation (LDA). These models allow to compute
approximations of the ground state energy and density of molecular systems in
the condensed phase. The TFW model is stricly convex with respect to the
electronic density, and allows for a comprehensive analysis (Part I).