Proton tunneling assisted by the intermolecular vibration excitation. Temperature dependence of the proton spin-lattice relaxation time in benzoic acid powder

Abstract

Temperature dependence of the proton spin-lattice relaxation time (T1) in powdered benzoic acid dimer and in its deuterated analog is calculated. The model assumes that two protons (deuterons) synchronously move in the double-minimum potential of the dimer. The two-dimensional potential energy surface was constructed previously, which adequately describes the static properties of the hydrogen-bonded complex. The important characteristics of this potential are a very strong mode coupling and a very high proton potential barrier (≳25 kcal/mol), whereas the experimental activation energy for the proton transfer is known to be on the order of 1 kcal/mol only. This apparent discrepancy is removed by our suggestion that the proton transfer is driven by the transitions between OHO fragment vibrational levels under the action of random forces of the surrounding. The excitation of the low-frequency intermolecular vibrations assists such transfer mechanism strongly. Using four fitting parameters to allow for the medium repolarization, the calculated T1 temperature dependence is found to be in good agreement with the experiments in the natural and deuterated benzoic acid dimer. The agreement is best at high temperature where the apparent activation energy for proton transfer was found to be 2.3 kcal/mol.

Proton transfer in benzoic acid crystals: Another look using quantum operator theory

“…24 and set ⍀ϭ120 cm Ϫ1 , which is a typical value for an intramolecular oscillation of heavy atoms. We should mention that the results depend only on the ratio c 2 /(M ⍀ 2 ), therefore there is effectively only one fitting parameter, the coupling c ͑assuming that the frequency ⍀ is smaller than k B T so that the mode is thermally excited͒.…”

“…The mass of the Q vibration is not known ͑since the heavy atoms are coupled to the rest of the crystal͒, so we follow Ref. 24 and set M Q ϭ100m H which is a reasonable value since it is equal to the mass of several C atoms. The coupling c of the reaction coordinate to the Q vibration is not known.…”

“…24. However, some oversimplifications were made in that work: The quantum solution was obtained in an adiabatic approximation and the effect of the environment was modeled as a random force.…”

Coherent Proton Tunneling in Hydrogen Bonds of Isolated Molecules: Carboxylic Dimers

“…These studies have investigated the temperature dependence of the transfer process: They included a density matrix model for hydrogen transfer in the benzoic acid dimer, where bath induced vibrational relaxation and dephasing processes are taken into account [25]. Sakun et al [26] have calculated the temperature dependence of the spin-lattice relaxation time in powdered benzoic acid dimer and shown that low frequency modes assist the proton transfer. At high temperatures the activation energy was found to be 2.3 kcal mol -1 .…”

Quantum Tunneling of Ions through the Closed Voltage-Gated Channels of the Biological Membrane: A Mathematical Model and Implications

“…Tunneling calculations become more complicated when moving to two-well potentials. In this case, it is necessary to apply numerical methods to solve the corresponding Schrodinger equation [8,9]. Moreover, by applying the idea of quantum tunneling on the ions, quantum conductance can be calculated and, consequently, the role of closed voltage-gated channels at resting state would be better investigated.…”