An explicit density matrix functional of the (N – 1)-particle system when the N-particle system is known

An explicit 1-particle density matrix functional is derived for the ground state of an (N – 1)-particle system when the ground state wavefunction of the N-particle system is known. The extended Koopmans' theorem is used to express the (N – 1)-particle wavefunction in terms of the N-particle wavefunction. The electron repulsion part of the energy expression is an integral of a product of the 1-particle density matrix of the (N – 1)-particle system and an explicit function that contains correlation and exchange information from the N-particle system.