(3.7.11) Gao : I would like to add an alternative formulation of the density functional of an ensemble energy in multistate DFT (MSDFT). We have been experimenting with this approach in the past few years, with excellent results in a variety of applications -including applications to singlet fission, 456 proton-coupled electron transfer, conical intersections, 454 local-valence and charge-transfer excited states, and core-level excitation energies. Recently, my coworker Dr. Yangyi Lu and I proved that MS-DFT is an exact DFT in the subspace V N spanned by the lowest N eigenstates of the Hamiltonian. It is proved (1) that the Hamiltonian projected onto V N is a matrix functional H[D(r)] of the multistate matrix density D(r) and ( ) that variational minimization of the multistate ensemble energy,