Generalized density functional theories using the k-electron densities: Development of kinetic energy functionals

Several explicit formulas for the kinetic energy of a many-electron system as a functional of the k-electron density are derived, with emphasis on the electron pair density. The emphasis is on general techniques for deriving approximate kinetic energy functionals and features generalized Weisacker bounds and methods using density-matrix reconstruction. Adapting results from statistical mechanics, a hierarchy of equations is derived that links …