A theoretical study of hydrogen bond dynamics in carboxylic acids

This study is concerned with theoretical calculations of the rate of proton transfer in carboxylic acids with a focus on the effect of anharmonic coupling between the characteristic vibrational modes of the hydrogen bond.; The method of calculation involves quantum mechanical transition state theory to evaluate the partition function of the transition state by path integration. The path integral is constrained by a centroid, which represents the location of the transition state, and is introduced as the time average of all quantum paths of the path integral (Voth, et al. [1989]).; The potential function has been adjusted to reproduce the vibrational frequencies as well as the geometry of the hydrogen bond. The hydrogen bond dynamics are described by a double minimum hydroxyl bond stretching vibration coupled by an anharmonic term with a harmonic hydrogen bond stretching vibration. The results of the calculations show that vibrational coupling reduces the rate of proton transfer.; The temperature dependence of the rate constant indicates high values at low and high temperatures, which are attributed to tunneling and Arrhenius type thermal activation.; Proton transfer in solid carboxylic acids is related to NMR spin-lattice relaxation by a similar phonon assisted processes of absorption and emission of lattice energy. The rate of proton transfer is simulated by employing asymmetric double minimum potentials for the crystalline state.; The asymmetric potential accounts for the breakdown of the symmetry of the potential, due to the effect of neighboring dimers in the solid, which leads to wells with unequal depths. This effect is described by a statistical factor, which tends to lengthen the spin-lattice relaxation time at low temperatures.; Calculations in this study have been carried out for protonated and deuterated benzoic acid using a common potential and the results are in good agreement with experiment. The calculated values of the rate constant and the spin lattice relaxation time show similar temperature profiles. It was found that the rate constant of the deuterated species has a minimum at a higher temperature than the rate constant of the protonated acid. This is attributed to the slower rate of tunneling of the deuteron.