A harmonic quantum transition slate theory, suggested recently by Pollak and Gershinsky [in Lectures an Stochastic Dynamics, edited by W. Lutz and T. Poeschel, Lecture Notes in Physics (Springer Verlag, New York, 1997)], is applied for the first time to a realistic reacting system. The isomerization of trans-stilbene in the gas phase and in the presence of dense liquid ethane solvent is investigated. We find that the overall quantum effect at room temperature is rather small. The quantum correction to the classical reaction rate estimate is approximately 23% for gas phase stilbene at room temperature. The addition of the dense solvent lowers the correction down to 13%, thus making the reacting system even more "classical," justifying the extensive use of classical molecular dynamics in investigating this reaction.