By the Jahn-Teller theorem, systems with orbital degeneracy will distort so as
to remove the degeneracy. However, many dynamic Jahn-Teller systems are known
in which the time-average geometry is of the higher point-group. These systems
are the kind that will be addressed here.

The analytical RHF configuration interaction first derivative calculation
developed by Liotard [43] has been modified to allow systems with
degenerate states to be run.

Each of the degenerate states is a linear combination of microstates. Each
microstate can be described by a Slater
determinant [66,67], which represents a specific pattern
of occupancy of molecular orbitals. Each M.O. is a linear combination of
Slater atomic orbitals.

The whole state is best described by an equal
mixture of the degenerate states of which it is composed. Note that this is
NOT a combination of states, rather it is a mixture. An example of a
combination of states is a state function, composed of a linear combination of
microstates. In such a combination the phase-factor between microstates is
significant, thus state(1)=
(1/ 2)^{1/2}(Microstate(a) + Microstate(b)) is
different from state(2)
(1/ 2)^{1/2}(Microstate(a) - Microstate(b)). An
example of a mixture of states is the ^{2}T_{2g} state of TiF_{6}^{3-}, a
d^{1} system, in which the best description of the state is an equal mixture of
the three degenerate space components of T_{2g}, and an equal mixture of the
two spin components of the Kramer's doublet. The overall state is thus
1/6((T_{2g}(x)+T_{2g}(y)+T_{2g}(z))+
(T_{2g}(x)+T_{2g}(y)+T_{2g}(z)).

If equimixtures are not used, then the Jahn-Teller theorem applies, and the
system would immediately distort so as to remove the degeneracy. In the case
of TiF_{6}^{3-}, this would result in distortion from O_{h} to D_{4h}symmetry.