  The vibrational theory of olfaction was posited to explain subtle effects in
the sense of smell inexplicable by models in which molecular structure alone
determines an odorant's smell. Amazingly, behavioral and neurophysiological
evidence suggests that humans and some insects can be trained to distinguish
isotopologue molecules which are related by the substitution of isotopes for
certain atoms, such as a hydrogen-to-deuterium substitution. How is it possible
to smell a neutron? The physics of olfaction may explain this isotopomer
effect. Inelastic electron transfer spectroscopy (IETS) has been proposed as a
candidate mechanism for such subtle olfactory effects: the vibrational spectrum
of an appropriately-quantized odorant molecule may enhance a transfer rate in a
discriminating electron transfer (ET) process. In contrast to other
semi-classical or quantum-master-equation-based models of olfactory IETS, the
model presented here explicitly treats the dynamics of a dominant odorant
vibrational mode, which provides an indirect dissipative path from the electron
to the thermal environment. A direct dissipative path to the environment also
is included. Within this model, a calculation of ET rate is developed, along
with a calculation of power dissipation to the thermal environment. Under very
weak direct dissipative coupling, spectroscopic behaviors of the indirect path
are revealed, and the resulting ET rate exhibits resonant peaks at certain
odorant frequencies. Resonant peaks in ET rate also correlate to peaks in power
dissipation. Spectroscopic behaviors are masked by strong direct dissipative
coupling. Results support a rate-based discrimination between a preferred
ligand and an isotopomer if indirect dissipative coupling dominates.
