Generalized density-functional theory: Conquering the e?‘?-representability problem with exact functionals for the electron pair density and the second-order reduced density matrix

摘要

Using the constrained search and Legendre-transform formalisms, one can derive ``generalizeda€? density-functional theories, in which the fundamental variable is either the electron pair density or the second-order reduced density matrix. In both approaches, the e?‘?-representability problem is solved by the functional, and the variational principle is with respect to all pair densities (density matrices) that are nonnegative and appropriately normalized. The Legendre-transform formulation provides a lower bound on the constrained-search functional. Noting that experience in density-functional and density-matrix theories suggests that it is easier to approximate functionals than it is to approximate the set of e?‘?-representable densities sheds some light on the significance of this work.