State-specific electronic
structure theory provides a
route toward
balanced excited-state wave functions by exploiting higher-energy
stationary points of the electronic energy. Multiconfigurational wave
function approximations can describe both closed- and open-shell excited
states and avoid the issues associated with state-averaged approaches.
We investigate the existence of higher-energy solutions in complete
active space self-consistent field (CASSCF) theory and characterize
their topological properties. We demonstrate that state-specific approximations
can provide accurate higher-energy excited states in H2(6-31G) with more compact active spaces than would be required in
a state-averaged formalism. We then elucidate the unphysical stationary
points, demonstrating that they arise from redundant orbitals when
the active space is too large or symmetry breaking when the active
space is too small. Furthermore, we investigate the singlet–triplet
crossing in CH2(6-31G) and the avoided crossing in LiF
(6-31G), revealing the severity of root flipping and demonstrating
that state-specific solutions can behave quasi-diabatically or adiabatically.
These results elucidate the complexity of the CASSCF energy landscape,
highlighting the advantages and challenges of practical state-specific
calculations.