Quantum Tunneling in the Quadruple Proton Rearrangement on a Hydroxyl Hydrogen Bond Ring in Calix[4]arene

Proton rearrangement rates in hydrogen bond networks are dominated by classical activation and quantum tunneling at higher and lower temperatures, respectively. Calix[4]arene (C4A) has a square-ring network composed of four hydroxyl groups with the O···O length of ∼0.265 nm. Calorimetry and dielectric relaxation measurements were applied to determination of the rates in the crystals of C4A and its deuteron analogue (C4A-d). The rearrangement rates in C4A-d exhibited Arrhenius dependence in the measured temperature range. On the other hand, the rates in C4A showed the same dependence as those in C4A-d above 200 K, deviated from this dependence at around 180 K, and became independent of temperature at around 10–4 s–1 below 100 K. This evidenced that the tunneling in the quadruple proton rearrangement proceeds at a very slow rate of 10–4 s–1. This is the first determination by calorimetry of the proton tunneling rate.