Density Functional Theory (DFT) =============================== Many Body Schrödinger Equation ------------------------------ We use (Hartree) atomic units in this whole section about DFT. We use the Born-Oppenheimer approximation, which says that the nuclei of the treated atoms are seen as fixed. A stationary electronic state (for $N$ electrons) is then described by a wave function $\Psi({\bf r_1},{\bf r_2},\cdots,{\bf r}_N)$ fulfilling the many-body Schrödinger equation .. math:: \hat H\ket\Psi=(\hat T+\hat U+\hat V)\ket\Psi=E\ket\Psi where .. math:: \hat T = \sum_i^N -{1\over2}\nabla_i^2 is the kinetic term, .. math:: \hat U = \sum_{i