Orthonormal orbitals for the representation of an arbitrary density

Abstract

An alternative to the Gilbert construction is presented. It is shown that for any nonnegative, normalized density an arbitrary number of orthonormal orbitals can be constructed with squares which sum, with minimal restrictions on the occupation numbers, to the given density. In three dimensions substantial freedom remains in the choice of orbitals within the basic scheme. The kinetic-energy density obtained includes the Weizs\"acker term and another term which, in simple cases, is proportional to the cube of the density.