At temperatures for which there is a non-negligible rate for the
dissociation of formaldehyde 
, the dynamics takes place
on the excited potential energy surfaces, 
and 
, in
addition to the lowest lying surface 
.[21]
Since the theory outlined in Sec. ii does not account for
multiple potential energy surfaces nor for non-adiabatic effects,
here we focus on the calculation of the
reactive partition function making the non-physical assumption
that the dynamics occurs exclusively on the surface.
This should illustrate the feasibility of the method
for unimolecular dissociation.
The ``spectroscopic constants'' for the dissociation have
been determined using the derivatives of the surface calculated by
second-order Moller-Plesset perturbation theory (MP2/DZP).[1]
The reactive partition function, Eq. (2.11b), can be
readily obtained and is shown in Fig. 4.
Figure 4: The reactive partition function for the formaldehyde
dissociation for the harmonic case (solid) is compared to the
anharmonic case (dashed).
As has already been noted,[22]
the anharmonic effect on the reactive partition function is small.
Unfortunately, the anharmonicity of the reactive mode is also small and,
at temperatures below the harmonic cut-off - 
-
is not sufficient to ensure the
convergence seen in the 
reaction.
In Fig. 5, the pre-reactive partition function, and the integrand for the semiclassical rate [see, Eq. (2.11)] are shown.
Figure: SCTST results for the dissociation.
The curves are as in Fig. 3.
At the temperatures presented, the thermal rate converges although it should be clear that the tail of the integrand is rising with decreasing temperatures; at still lower temperatures, this tail is not damped and results in the diverging integral. The use of higher order perturbation theory could provide stronger damping terms, and result in convergence at these lower temperatures. This conjecture has yet to be explored.