The MP2 energy as a functional of the Hartree–Fock density matrix

The explicit E[2][P] functional is presented, where E[2] is the second order Møller–Plesset correlation energy and P is the standard Hartree–Fock density matrix. The ideas leading to this functional are implicit in previous studies, but the significance of its existence has not yet been sufficiently emphasized and its simple explicit form has not been presented. With the proposed functional one may obtain the correlation energy in the absence of molecular orbitals, knowing merely the density matrix. This may further facilitate linear scaling computation of the correlation energy.