Rattling motion of proton through five membered aromatic ring systems

We study the passage of proton (H$^{+}$) through different five membered aromatic ring systems by considering one dimensional motion of the proton along a line perpendicular to the plane of the ring. The potential for the motion of (H$^{+}$) from one side of the ring to the other through the center of the ring is found to be a symmetric double well and such complexes are suggested as molecular rattles which can exhibit a ring umbrella like inversion. Our study reveals C$_{2}$H$_{2}$P$_{3}^{-}$ - H$^{+}$ to be a molecular rattle with a barrier height of 44.277 kcal mol$^{-1}$ and exciting it to the third vibrational level makes easy for the proton to go through the ring.