Density matrix of crystalline systems. I. Long‐range behavior and related computational problems

Abstract

AbstractThe one‐electron density matrix (DM) of crystalline systems is discussed, especially concerning its longrange behavior; reference is made throughout to systems treated at a Hartree–Fock–LCAO–SCF level of approximation. The analysis is performed on the assumption of generally smooth behavior of eigenvalues and eigenvectors in k (reciprocal) space, so that they can be expressed by means of a truncated Fourier expansion. This assumption allows us to obtain analytic approximations for the DM, on the basis of the information collected at a few, suitably selected sampling k points. It is therefore possible at the same time to discuss the influence of structural parameters (dimensionality of the system, existence and shape of the Fermi surface, structure of the chemical bonds) and to set up a computational scheme that is general and simple enough.