The Random Phase Approximation (RPA),^{Bouman:1989, Hansen:1983} also known
as time-dependent Hartree-Fock (TD-HF) theory, is an alternative to CIS for
uncorrelated calculations of excited states. It offers some advantages for
computing oscillator strengths, *e.g.*, exact satisfaction of the
Thomas-Reike-Kuhn sum rule,^{McHale:1999} and is roughly comparable in
accuracy to CIS for singlet excitation energies, but is inferior for triplet
states. RPA energies are non-variational, and in moving around on excited-state
potential energy surfaces, this method can occasionally encounter singularities
that prevent numerical solution of the underlying equations,^{Cordova:2007}
whereas such singularities are mathematically impossible in CIS calculations.