  The theoretical prediction of the rates of nonradiative processes in
molecules is fundamental to assess their emissive properties. In this context,
global harmonic models have been widely used to simulate vibronic spectra as
well as internal conversion rates and to predict photoluminescence quantum
yields. However, these simplified models suffer from the limitations that are
inherent to the harmonic approximation and can have a severe effect on the
calculated internal conversion rates. Therefore, the development of more
accurate semiclassical methods is highly desirable. Here, we introduce a
procedure for the calculation of nonradiative rates in the framework of the
time-dependent semi-classical Extended Thawed Gaussian Approximation (ETGA). We
systematically investigate the performance of the ETGA method by comparing it
to the the adiabatic and vertical harmonic method, which belong to the class of
widely used global harmonic models. Its performance is tested in potentials
that cannot be treated adequately by global harmonic models, beginning with
Morse potentials of varying anharmonicity followed by a double well potential.
The calculated radiative and nonradiative internal conversion rates are
compared to reference values based on exact quantum dynamics. We find that the
ETGA has the capability to predict internal conversion rates in anharmonic
systems with an appreciable energy gap, whereas the global harmonic models
prove to be insufficient.
