Quantum effects on the activation free energy for the transfer of a qu
antum particle between two ions immersed in a classical dipolar solven
t are investigated. The bare potential for the quantum particle-ion co
mplex has an intrinsic barrier that is negligible compared to k(B)T an
d corresponds to a strongly hydrogen bonded system if the quantum part
icle is a proton. In this circumstance the activation free energy is d
ominated by solvent contributions. We compare the solvent free energie
s along the reaction coordinate for a classical particle with charge 1, a proton and a muon. The quantum calculations are carried out using
Feynman's path integral methods. The smaller mass of the muon gives r
ise to enhanced quantum effects and allows one to probe the effects of
the dispersion of the charge density of the particle undergoing trans
fer on the solvent contribution to the free energy.