  We present a formulation of excited state mean-field theory in which the
derivatives with respect to the wave function parameters needed for wave
function optimization (not to be confused with nuclear derivatives) are
expressed analytically in terms of a collection of Fock-like matrices. By
avoiding the use of automatic differentiation and grouping Fock builds
together, we find that the number of times we must access the memory-intensive
two-electron integrals can be greatly reduced. Furthermore, the new formulation
allows the theory to exploit existing strategies for efficient Fock matrix
construction. We demonstrate this advantage explicitly via the shell-pair
screening strategy, with which we achieve a cubic overall cost scaling. Using
this more efficient implementation, we also examine the theory's ability to
predict charge redistribution during charge transfer excitations. Using coupled
cluster as a benchmark, we find that by capturing orbital relaxation effects
and avoiding self-interaction errors, excited state mean field theory
out-performs other low-cost methods when predicting the charge density changes
of charge transfer excitations.
