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The passage of proton through conjugated aromatic and non-aromatic ring systems by considering the one-dimensional motion of proton along a line perpendicular to the plane of the ring in a pi complex was studied. The potential for the motion of proton from one side of the ring to the other through the center of the rings is symmetric double-well and such complexes are suggested as molecular rattles that can exhibit a ring umbrella-like inversion. We also studied the effect of substitution as well as the effect of size on different rings in order to lower the potential barrier for tunneling motion of proton through these rings and calculate the energy levels of the complex in the symmetric double-well potential using computational chemistry software.