  We show that, as in Hartree Fock theory, the orbitals for excited state mean
field theory can be optimized via a self-consistent one-electron equation in
which electron-electron repulsion is accounted for through mean field
operators. In addition to showing that this excited state ansatz is
sufficiently close to a mean field product state to admit a one-electron
formulation, this approach brings the orbital optimization speed to within
roughly a factor of two of ground state mean field theory. The approach
parallels Hartree Fock theory in multiple ways, including the presence of a
commutator condition, a one-electron mean-field working equation, and
acceleration via direct inversion in the iterative subspace. When combined with
a configuration interaction singles Davidson solver for the excitation
coefficients, the self consistent field formulation dramatically reduces the
cost of the theory compared to previous approaches based on quasi-Newton
descent.
