  A very specific ensemble of ground and excited states is shown to yield an
exact formula for any excitation energy as a simple correction to the energy
difference between orbitals of the Kohn-Sham ground state. This alternative
scheme avoids either the need to calculate many unoccupied levels as in
time-dependent density functional theory (TDDFT) or the need for many
self-consistent ensemble calculations. The symmetry-eigenstate Hartree-exchange
(SEHX) approximation yields results comparable to standard TDDFT for atoms.
With this formalism, SEHX yields approximate double-excitations, which are
missed by adiabatic TDDFT.
