Theoretical Study of Proton Tunneling in the Imidazole–Imidazolium Complex

Łukasz Boda,Marek Boczar,Takahito Nakajima,Marek J Wójcik

doi:10.1021/acs.jpca.1c02972

Abstract

Proton tunneling in the hydrogen-bonded imidazole–imidazolium complex ion has been studied theoretically. Ab initio CASSCF/6-311++G(d,p) calculations concerning geometry optimization and vibrational frequencies have been carried out for equilibrium and transition state structures of the system. Two-dimensional double-well model potentials were constructed on the basis of ab initio results and used to analyze the proton dynamics in the hydrogen bond and the influence of the excitation of low-frequency hydrogen-bond vibrations on the proton tunneling splittings. The energy of tunneling-split vibrational sublevels of the high-frequency tunneling mode have been calculated for its ground and first excited vibrational state for the series of excitations of the coupled low-frequency intramolecular hydrogen-bond modes. The promoting and suppressing effect of the low-frequency modes on the proton splittings was shown in the ground and first excited vibrational state of the tunneling mode. The vibrational sublevels form the two separate semicontinuous bands between which the absorption transitions may occur. This mechanism explains the experimentally observed splitting and doublet-component broadening of the high-frequency N–H stretching infrared (IR) absorption band.

Highlights

The tunneling process is of great importance in many areas of physics, chemistry, and biology.[1−3] The tunneling phenomenon is one of the most significant features of quantum mechanics, completely different from the classical one
There are three slightly different energy barrier values obtained by including zero-point energy (ZPE) only for vibrational degrees of freedom other than the two degrees of freedom that are treated explicitly in the model calculations based on twodimensional potentials constructed for the three pairs of modes, i.e., νs−νσ, νs−νβ[1], and νs−νβ[2]
It should be mentioned that the energy barrier strongly decreases when the ZPE correction is taken into account for all vibrational degrees of freedom and has the value 18.97 kJ/mol (1586 cm−1)

Summary

Introduction

The tunneling process is of great importance in many areas of physics, chemistry, and biology.[1−3] The tunneling phenomenon is one of the most significant features of quantum mechanics, completely different from the classical one. In a variety of tunneling processes, proton-transfer (PT) reactions are of special interest, especially in systems with hydrogen bonds. The proton tunneling in hydrogen-bonded systems is an important and fundamental process in nature, especially in the biological aspect, e.g., for DNA base pairing.[4] In the hydrogen bond, the hydrogen atom is shared between the donor and acceptor, which may result in classical proton transfer or tunneling, depending on the strength of the hydrogen bond. Infrared (IR) spectroscopy can provide key information on the tunneling dynamics and influence of vibrational couplings in a hydrogen-bonded complex on this process. In the last years there appeared several theoretical studies of proton tunneling in different systems,[5−19] as well as experimental ones.[20−24]

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Conclusion