The impedance spectra are measured for protonated and deuterated clath
rates, HClO4.5.5H(2)O and DClO(4)5.5D(2)O, between 10 and 300 K. The c
onductance is investigated between 80 K and room temperature and the d
ielectric constant between 10 and 120 K. The data show deviation from
the Arrhenius behavior of conductance in the low-temperature regime. A
description of proton conductivity is developed on the basis of quant
um theory of an elementary act of proton tunneling between donor-accep
tor sites interacting with environmental fluctuations. Several models
of the elementary act are considered. The mechanism, most consistent w
ith the obtained data, incorporates-strong coupling of the proton with
local vibrational modes of the closest environment and system diabati
c transitions along these vibrational ''coordinates''-fluctuations of
the tunneling barrier for the proton. At low temperatures the motion a
long the vibrational coordinates is no longer purely classical and the
slow mode tunneling takes place. The latter gives rise to a curvature
in the Arrhenius plots apprehended as a decrease of the apparent acti
vation energy at lower temperatures. The observed isotope effect is in
line with the lower deuteron tunneling probability due to doubling th
e mass, though other parameters may also be affected by deuteration.