New derivation and a k ‐particle generalization of SCF ‐type theories

A hierarchy of necessary conditions that an exact density matrix of a pure state or an ensemble has to satisfy is derived, namely the hermiticity of certain operators F ( k ) . For k = 1 this reduces to the well‐known Hartree‐Fock condition. It is then shown that the k th set of conditions is equivalent to stationarity of the energy with respect to unitary k ‐particle transformations. k ‐Particle generalizations of Hartree‐Fock theory are then discussed both in the spirit of k ‐particle pseudoeigenvalue equations and in the framework of a Newton–Raphson‐type constructive scheme.