Density matrix functional theory in average and relative coordinates

A general density matrix functional theory is formulated in terms of a basis representation of the density matrix in average (R→=(r→1+r→2)/2) and relative (r→=r→2−r→1) coordinates. This representation involves a parameter set whose dimension by construction grows strictly linearly with system size. Furthermore, the two-electron Coulomb and exchange contributions to the Hartree–Fock and Kohn–Sham energies factorize, and can be computed with reference only to two-index integrals. The problem of N-representability is addressed and solutions are presented. Kinetic energy transpires to be the hardest term to compute accurately, and three different approaches are discussed. The subtle relationship between N-representability and kinetic energy is investigated.