Essentials of Computational Chemistry

14.2 SINGLY EXCITED STATES 493
and the orbital into which it is excited on the right. Finding wave functions for these states
is sometimes facilitated by this relative simplicity of their character.
14.2.1 SCF Applicability
Ideally, one would like to study excited states and ground states using wave functions of
equivalent quality. Ground-state wave functions can very often be expressed in terms of a
single Slater determinant formed from variationally optimized MOs, with possible accounting
for electron correlation effects taken thereafter (or, in the case of DFT, the optimized orbitals
that intrinsically include electron correlation effects are use in the energy functional). Such
orbitals are determined in the SCF procedure.
However, the problem of variational collapse typically prevents an equivalent SCF description
for excited states. That is, any attempt to optimize the occupied MOs with respect to
the energy will necessarily return the wave function to that of the ground state. Variational
collapse can sometimes be avoided, however, when the nature of the ground and excited
states prevents their mixing within the SCF formalism. This situation occurs most commonly
in symmetric molecules, where electronic states belonging to different irreducible representations
do not mix in the SCF, and also in any situation where the ground and excited states
have different spin.
As an example of the former, consider the electronic states of fluorovinylidene illustrated
in Figure 14.4. There are two different low lying triplet states, one having A ′ electronic state
symmetry and the other A ′′ . Furthermore, within each respective irreducible representation,
the states indicated are the lowest energy triplets. Thus, wave functions for each may be
determined via an SCF approach. In this case, HF theory is not particularly attractive as an
H
F
H
F
3 A ′′
H
F
p CC
Figure 14.4 Valence MO occupations for three different electronic states of fluorovinylidene. The
triplet states belong to different irreducible representations of the molecular point group because the
singly occupied orbitals in which they differ belong alternatively to either the a ′ or a ′′ irreps
1 A ′
H
F
3 A ′
p C
n C