Density matrix functional theory in average and relative coordinates

A general density matrix functional theory is formulated in terms of a basi s representation of the density matrix in average ((R) over right arrow = ( (r) over right arrow (1) + (r) over right arrow (2))/2) and relative ((r) o ver right arrow = (r) over right arrow (2) - (r) over right arrow (1)) coor dinates. This representation involves a parameter set whose dimension by co nstruction grows strictly linearly with system size. Furthermore, the two-e lectron Coulomb and exchange contributions to the Hartree-Fock and Kohn-Sha m energies factorize, and can be computed with reference only to two-index integrals. The problem of,li-representability is addressed and solutions ar e presented. Kinetic energy transpires to be the hardest term to compute ac curately, and three different approaches are discussed. The subtle relation ship between N-representability and kinetic energy is investigated. (C) 200 1 Elsevier Science B.V. All rights reserved.