We apply a Monte Carlo technique specialized for the simulation of rare events to study the activated counterions motions in the aluminosilicate Na+-mordenite. Mean activation barriers are obtained from minimum energy paths calculated on realistic potential energy surfaces by using a Metropolis algorithm. Energy barriers for Na+ hops calculated for lattices with various Si/Al ratio are found in good agreement with the Na+ detrapping energies measured by thermally stimulated current spectroscopy. One shows that the dielectric activated motions of Na+ proceed between degenerated many-body ground states with different dipolar moment by either sequential or collective hopping motions. This provides a first microscopic description of dielectric relaxation measured in zeolites.