  The mean-field solutions of electronic excited states are much less
accessible than ground state (e.g.\ Hartree-Fock) solutions. Energy-based
optimization methods for excited states, like $\Delta$-scf, tend to fall into
the lowest solution consistent with a given symmetry -- a problem known as
"variational collapse". In this work, we combine the ideas of direct
energy-targeting and variance-based optimization in order to describe excited
states at the mean-field level. The resulting method, $\sigma$-scf, has several
advantages. First, it allows one to target any desired excited state by
specifying a single parameter: a guess of the energy of that state. It can
therefore, in principle, find \emph{all} excited states. Second, it avoids
variational collapse by using a variance-based, unconstrained local
minimization. As a consequence, all states -- ground or excited -- are treated
on an equal footing. Third, it provides an alternate approach to locate
$\Delta$-scf solutions that are otherwise inaccessible by the usual non-aufbau
configuration initial guess. We present results for this new method for small
atoms (He, Be) and molecules (H2, HF).
