Quantum Tunneling of Water in Ultra-Confinement

From Left to Right: (top row) Alexander I. Kolesnikov, George F. Reiter, Narayani Choudhury, Timothy R. Prisk, Eugene Mamontov; (bottom row) Andrey Podlesnyak, George Ehlers,  David J. Wesolowski, Lawrence M. Anovitz.

Authors: Alexander I. Kolesnikov¹, George F. Reiter², Narayani Choudhury³, Timothy R. Prisk⁴, Eugene Mamontov¹, Andrey Podlesnyak⁵, George Ehlers⁵, Andrew G. Seel⁶, David J. Wesolowski⁴, Lawrence M. Anovitz⁴

Affiliation:
¹Chemical and Engineering Materials Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee, USA,
²Physics Department, University of Houston, Texas, USA,
³Math and Science Division, Lake Washington Institute of Technology, Kirkland, Washington, USA; School of Science, Technology, Engineering and Math, University of Washington, Bothell, Washington, USA,
⁴Chemical Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee, USA,
⁵Quantum Condensed Matter Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee, USA,
⁶ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot, United Kingdom.

The quantum-mechanical behavior of light atoms plays an important role in shaping the physical and chemical properties of hydrogen-bonded liquids, such as water [1,2]. Tunneling is a classic quantum effect in which a particle moves through a potential barrier despite classically lacking sufficient energy to transverse it. The tunneling of hydrogen atoms in condensed matter systems has been observed for translational motions through metals, anomalous proton diffusion in water phases, and in the rotation of methyl and ammonia groups, and Gorshunov et al. inferred on the basis of terahertz spectroscopy measurements that water molecules inside the mineral beryl may undergo rotational tunneling [3, 4].

The crystal structure of beryl, shown in Figure 1, contains hexagonally shaped nanochannels just wide enough to contain single water molecules. In a recently published paper [5], we presented evidence from inelastic neutron scattering experiments and ab initio computational modeling that these water molecules do, in fact, undergo rotational tunneling at low temperatures. In their quantum-mechanical ground state, the hydrogen atoms are delocalized among the six symmetrically-equivalent positions about the channels so that the water molecule on average assumes a double-top like shape.

Figure 1: The crystal structure of beryl

The first set of inelastic neutron scattering experiments was performed using the CNCS and SEQUOIA spectrometers located at Oak Ridge National Laboratory's Spallation Neutron Source. A number of transitions are observed in the energy spectrum that can only be attributed to quantum-mechanical tunneling. Alternative origins for these transitions, such as vibrational modes or crystal field effects of magnetic impurities, are inconsistent with the temperature and wavevector dependence of the energy spectrum. However, they are consistent with an effective one-dimensional orientational potential obtained from Density Functional Theory and Path Integral Molecular Dynamics calculations.

To confirm these results we performed neutron Compton scattering of experiments on beryl single-crystals using the VESUVIO spectrometer at the Rutherford Appleton Laboratory. In this technique, a high-energy incident neutron delivers an impulsive blow to a single atom in the sample, transferring a sufficiently large amount of kinetic energy to the target atom that it recoils freely from the impact. The momentum distribution n(p) of the hydrogen atoms may then be inferred from the observed dynamic structure factor S(Q, E) in this high-energy limit, providing a direct probe of the momentum-space wavefunction of the water hydrogens in beryl.

Figure 2: the measured momentum distribution n(p) in neutron Compton scattering experiments.

The tunneling behavior of the water protons is revealed in our neutron Compton scattering experiments by the measured momentum distribution n(p), illustrated as a color contour plot in Figure 2. The variation of n(p) with angle is due to vibrations of the O—H covalent bond. If it is true that water molecules undergo rotational tunneling between the six available orientations, then n(p) will include oscillations or interference fringes as a function of angle. On the other hand, if the water molecules are incoherently and randomly arranged among the possible positions, then no such interference fringes will be observed. As marked by the yellow line in Figure 2, the interference fringes were clearly observed in our experiment! The water molecule is, therefore, in a coherent superposition of states over the six available orientational positions.

Taken together, these results show that water molecules confined in the channels in the beryl structure undergo rotational tunneling, one of the hallmark features of quantum mechanics.

References:
[1] Michele Ceriotti, Wei Fang, Peter G. Kusalik, Ross H. McKenzie, Angelos Michaelides, Miguel A. Morales, Thomas E. Markland, "Nuclear Quantum Effects in Water and Aqueous Systems: Experiment, Theory, and Current Challenges", Chemical Reviews, 116, 7529 (2016). Abstract.
[2] Xin-Zheng Li, Brent Walker, Angelos Michaelides, "Quantum nature of the hydrogen bond", Proceedings of the national Academy of Sciences of the United States of America, 108, 6369 (2011). Abstract.
[3] Boris P. Gorshunov, Elena S. Zhukova, Victor I. Torgashev, Vladimir V. Lebedev, Gil’man S. Shakurov, Reinhard K. Kremer, Efim V. Pestrjakov, Victor G. Thomas, Dimitry A. Fursenko, Martin Dressel, "Quantum Behavior of Water Molecules Confined to Nanocavities in Gemstones", The Journal of Physical Chemistry Letters, 4, 2015 (2013). Abstract.
[4] Boris P. Gorshunov, Elena S. Zhukova, Victor I. Torgashev, Elizaveta A. Motovilova, Vladimir V. Lebedev, Anatoly S. Prokhorov, Gil’man S. Shakurov, Reinhard K. Kremer, Vladimir V. Uskov, Efim V. Pestrjakov, Victor G. Thomas, Dimitri A. Fursenko, Christelle Kadlec, Filip Kadlec, Martin Dressel, "THz–IR spectroscopy of single H₂O molecules confined in nanocage of beryl crystal lattice", Phase Transitions, 87, 966 (2014). Abstract.
[5] Alexander I. Kolesnikov, George F. Reiter, Narayani Choudhury, Timothy R. Prisk, Eugene Mamontov, Andrey Podlesnyak, George Ehlers, Andrew G. Seel, David J. Wesolowski, Lawrence M. Anovitz, "Quantum Tunneling of Water in Beryl: A New State of the Water Molecule", Physical Review Letters, 116, 167802 (2016). Abstract.