Occupation function in extended systems

Abstract

The occupation function in the sense of occupation numbers for the natural spin orbitals for a solid is analyzed from several points of view. The connection with the generalized overlap amplitudes is pointed out and the theory is developed for general spin orbitals both in position and momentum space. The symmetry properties of the occupation function and its Fourier coefficients are analyzed. General expressions for the gradient of the occupation function are derived. The special restricted Hartree-Fock case, where the occupation function is a step function is described as an illustration.