Tunneling splittings in vibrational spectra of non-rigid molecules

Proton tunnelling in the hydrogen bonds of the benzoic acid dimer: (18)O substitution and isotope effects of the heavy atom framework

Field-cycling (1)H NMR relaxometry has been used to measure the rate of concerted double proton transfer in the hydrogen bonds of (16)O and (18)O isotopologues of benzoic acid dimers. The experiments have been conducted in the solid state at low temperature 13.3 ≤ T ≤ 80 K where the dynamics are dominated by incoherent proton tunnelling. The low temperature tunnelling rate in the (16)O isotopologue is observed to be approximately 15% faster than in the (18)O isotopologue. The difference is attributed to an isotope effect of the heavy atom framework of the benzoic acid dimer resulting from displacements of the oxygen atoms that accompany the proton transfer. Sources of systematic uncertainty have been minimized in the design of the experimental protocols and the experiments are critically appraised in formally assigning the measured differences to an effect of mass on the tunnelling dynamics.

Ground-state and vibrationally assisted tunneling in the formic acid dimer

The previously developed instanton theory [G. V. Mil'nikov and H. Nakamura, J. Chem. Phys. 122, 124311 (2005)] is applied to the calculation of vibrationally assisted tunneling splitting of the deuterated formic acid dimer (DCOOH)2 with all the degrees of freedom taken into account. The ground-state tunnel splitting is determined by the density-functional theory combined with coupled cluster level of quantum chemistry to be 0.0038 cm(-1) which is comparable to the experimental value of 0.0029 cm(-1). Further, the tunnel splittings of fundamental excitations are estimated for frequencies below 300 cm(-1). In this energy range it is found that the excitation modes may either enhance or suppress tunneling as compared to the ground state. For the higher-frequency modes a rapid growth of the tunnel splitting is observed. At frequencies above 1000 cm(-1) the semiclassical solution becomes unstable and no reliable tunneling splittings can be obtained. This is in vast contrast to the adiabatic approximation to the instanton theory in which the tunnel splittings can be retrieved up to 3000 cm(-1). We discuss this disparity from the viewpoint of the multidimensional character of tunneling in hydrogen bonds and the adiabatic approximation is concluded to be inaccurate.

Instanton theory for the tunneling splitting of low vibrationally excited states

We develop the instanton theory for calculating the tunneling splitting of excited states. For the case of low vibrational quantum states we derive a canonically invariant formula which is applicable to a multidimensional system of arbitrary Riemannian metric. The effect of multidimensionality in relation to the vibrational excitation is explained in terms of the effective frequencies along the instanton trajectory. The theory is demonstrated to work well by taking HO2 molecule as an example.

Competing tunneling trajectories in a two-dimensional potential with variable topology as a model for quantum bifurcations

We present a path-integral approach to treat a two-dimensional model of a quantum bifurcation. The model potential has two equivalent minima separated by one or two saddle points, depending on the value of a continuous parameter. Tunneling is, therefore, realized either along one trajectory or along two equivalent paths. The zero-point fluctuations smear out the sharp transition between these two regimes and lead to a certain crossover behavior. When the two saddle points are inequivalent one can also have a first order transition related to the fact that one of the two trajectories becomes unstable. We illustrate these results by numerical investigations. Even though a specific model is investigated here, the approach is quite general and has potential applicability for various systems in physics and chemistry exhibiting multistability and tunneling phenomena.