New N-representability results with symmetry in molecular quantum chemistry

We prove a new type of N-representability result: given a totally symmetric density function rho, we construct a wavefunction Psi such that the totall y symmetric part of rho, (its projection over the totally symmetric functio ns) be equal to rho, and, furthermore, such that Psi belongs to a given cla ss of symmetry associated to the symmetry group of a molecule. Our proof us es deformations of density functions and which are solutions of a "Jacobian problem". This allows us to formalize rigorously an idea of A. Gorling (Ph ys. Rev. A 47 (1993) 2783), for Density-Functional Theory in molecular quan tum chemistry, by defining a density functional that takes into account the symmetry of the molecule under study.