Measurement of proton tunneling in short hydrogen bonds in single crystals of 3,5 pyridinedicarboxylic acid using nuclear magnetic resonance spectroscopy.

In this Letter, we present NMR spin-lattice and relaxometry data for proton transfer in one of the shortest known N-H⋯O hydrogen bonds in a single crystal of 3,5 pyridinedicarboxylic acid (35PDCA). It is widely believed that proton transfer by quantum tunneling does not occur in short hydrogen bonds since the ground state energy level lies above the potential barrier, yet these data show a temperature independent, proton tunneling rate below 77 K and a clear deviation from classical dynamics below 91 K. This study therefore suggests that proton tunneling occurs in all hydrogen bonds at low temperature and the crossover temperature to classical hopping must be determined when evaluating whether proton tunneling persists at higher temperature, for example in enzyme catalysis under physiological conditions.

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.

Comment on "Phase diagram of a solution undergoing inverse melting".

The observation of a first order phase transition between two fluid phases, reported by R. Angelini [Phys. Rev. E 78, 020502(R) (2008)], is not supported by the measurements and is shown to be caused by the loss of solubility of alpha-cyclodextrin in the water-4-methylpyridine solvent.

Crystallization on heating and complex phase behavior of alpha-cyclodextrin solutions.

Solutions composed of alpha-cyclodextrin (alpha-CD), water, and various methylpyridines, in particular, 4-methylpyridine (4MP), undergo reversible liquid-solid transitions upon heating, the crystalline solid phases undergoing further phase transformations at higher temperatures. This unusual behavior has been characterized by an ensemble of measurements, including solubility, differential scanning calorimetry, quasielastic neutron scattering, as well as x-ray powder diffraction. For the alpha-CD/4MP system five crystalline phases have been identified. The unit cell parameters and corresponding changes with temperature indicate a scenario for the crystallization process. A simple model is proposed that mimics the observed disorder-order transition.

Freezing on heating of liquid solutions.

We report a reversible liquid-solid transition upon heating of a simple solution composed of a-cyclodextrine (alpha CD), water, and 4-methylpyridine. These solutions are homogeneous and transparent at ambient temperature and solidify when heated to temperatures between 45 degrees and 75 degrees. Quasielastic and elastic neutron scattering show that molecular motions are slowed down in the solid and that crystalline order is established. The solution "freezes on heating." This process is fully reversible, on cooling the solid melts. A rearrangement of hydrogen bonds is postulated to be responsible for the observed phenomenon.

Rotation-libration and rotor-rotor coupling in 4-methylpyridine.

The low temperature rotational dynamics of methyl groups in 4-methylpyridine is analyzed in terms of a model potential including rotation-libration and rotor-rotor coupling. The parameters of the model potential are adjusted by comparison of calculated with published and newly recorded inelastic neutron scattering spectra. Initial evaluations of the potential parameters of the model are obtained from molecular mechanics calculations. Experimental spectra are calculated from these potentials by numerical solution of Schrödinger's equation for clusters of coupled rotors embedded in a bigger ensemble of rotors treated in the mean field approximation. Adjustment of the potential parameters leads to excellent agreement with the experimental spectra of protonated 4-methylpyridine, measured at well-defined spin temperatures. At higher levels of deuteration, agreement with experiment is qualitative, only. The observed deviations are attributed to the increasing frustration of the system of coupled methyl groups and mutual localization, effects leading to a phase transition around 5.5 K in isotopic mixtures, as shown in diffraction experiments.

Isotope effects associated with tunneling and double proton transfer in the hydrogen bonds of benzoic acid.

The isotope effects associated with double proton transfer in the hydrogen bonds of benzoic acid (BA) dimers have been measured using field-cycling (1)H NMR relaxometry and quasielastic neutron scattering. By studying mixed isotope (hydrogen and deuterium) samples, the dynamics of three isotopologues, BA-HH, BA-HD, and BA-DD, have been investigated. Low temperature measurements provide accurate measurements of the incoherent tunneling rate, k(0). This parameter scales accurately with the mass number, m, according to the formula k(0)=(E/m)e(-Fm) providing conclusive evidence that the proton transfer process is a strongly correlated motion of two hydrons. Furthermore, we conclude that the tunneling pathway is the same for the three isotopologue species. Measurements at higher temperatures illuminate the through barrier processes that are mediated via intermediate or excited vibrational states. In parallel with the investigation of proton transfer dynamics, the theoretical and experimental aspects of studying spin-lattice relaxation in single crystals of mixed isotope samples are investigated in depth. Heteronuclear dipolar interactions between (1)H and (2)H isotopes contribute significantly to the overall proton spin-lattice relaxation and it is shown that these must be modeled correctly to obtain accurate values for the proton transfer rates. Since the sample used in the NMR measurements was a single crystal, full account of the orientation dependence of the spin-lattice relaxation with respect to the applied B field was incorporated into the data analysis.

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.