Density-cumulant functional theory.

Starting point is the energy expectation value as a functional of the one-particle density matrix gamma and the two-particle density cumulant lambda(2). We decompose gamma into a best idempotent approximation kappa and a correction tau, that is entirely expressible in terms of lambda(2). So we get the energy E as a functional of kappa and lambda(2), which can be varied independently. Approximate n-representability conditions, derived by perturbation theory are imposed on the variation of lambda(2). A nonlinear system of equations satisfied by lambda(2) is derived, the linearized version of which turns out to be equivalent to the coupled electron-pair approximation, variant zero. The start for kappa is Hartree-Fock, but kappa is then updated to become the best idempotent approximation of gamma. Relations to density matrix functional theory and Kohn-Sham type density functional theory are discussed.