Entanglement and co-tunneling of two equivalent protons in hydrogen bond pairs

The following article appeared in The Journal of Chemical Physics 148, 102307 (2018) and may be found at https://doi.org/10.1063/1.5000681A theoretical study is reported of a system of two identical symmetric hydrogen bonds, weakly coupled such that the two mobile protons can move either separately (stepwise) or together (concerted). It is modeled by two equivalent quartic potentials interacting through dipolar and quadrupolar coupling terms. The tunneling Hamiltonian has two imaginary modes (reaction coordinates) and a potential with a single maximum that may turn into a saddle-point of second order and two sets of (inequivalent) minima. Diagonalization is achieved via a modified Jacobi-Davidson algorithm. From this Hamiltonian the mechanism of proton transfer is derived. To find out whether the two protons move stepwise or concerted, a new tool is introduced, based on the distribution of the probability flux in the dividing plane of the transfer mode. While stepwise transfer dominates for very weak coupling, it is found that concerted transfer (co-tunneling) always occurs, even when the coupling vanishes since the symmetry of the Hamiltonian imposes permanent entanglement on the motions of the two protons. We quantify this entanglement and show that, for a wide range of parameters of interest, the lowest pair of states of the Hamiltonian represents a perfect example of highly entangled quantum states in continuous variables. The method is applied to the molecule porphycene for which the observed tunneling splitting is calculated in satisfactory agreement with experiment, and the mechanism of double-proton tunneling is found to be predominantly concerted. We show that, under normal conditions, when they are in the ground state, the two porphycene protons are highly entangled, which may have interesting applications. The treatment also identifies the conditions under which such a system can be handled by conventional one-instanton techniquesFinancial support from Ministerio de Economia y Competitividad of Spain (Research Grant No. CTQ2014-58617-R), the Consellería de Cultura, Educación e Ordenación Universitaria (Centro singular de investigacion de Galicia acreditación 2016-2019, No. ED431G/09), and the European Regional Development Fund (ERDF) is gratefully acknowledgedS

Competing tunneling trajectories in a 2D potential with variable topology as a model for quantum bifurcations

We present a path - integral approach to treat a 2D 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. 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 multi-stability and tunneling phenomena.Comment: 11 pages, 8 eps figures, Revtex-

Conditional Born–Oppenheimer Dynamics: Quantum Dynamics Simulations for the Model Porphine

We report a new theoretical approach to solve adiabatic quantum molecular dynamics halfway between wave function and trajectory-based methods. The evolution of a N-body nuclear wave function moving on a 3N-dimensional Born–Oppenheimer potential-energy hyper-surface is rewritten in terms of single-nuclei wave functions evolving nonunitarily on a 3-dimensional potential-energy surface that depends parametrically on the configuration of an ensemble of generally defined trajectories. The scheme is exact and, together with the use of trajectory-based statistical techniques, can be exploited to circumvent the calculation and storage of many-body quantities (e.g., wave function and potential-energy surface) whose size scales exponentially with the number of nuclear degrees of freedom. As a proof of concept, we present numerical simulations of a 2-dimensional model porphine where switching from concerted to sequential double proton transfer (and back) is induced quantum mechanically

Investigation of Terahertz Vibration–Rotation Tunneling Spectra for the Water Octamer

We report a combined theoretical and experimental study of the water octamer-h16. The calculations used the ring-polymer instanton method to compute tunnelling paths and splittings in full dimensionality. The experiments measured extensive high resolution spectra near 1.4 THz, for which isotope dilution experiments and group theoretical analysis support assignment to the octamer. Transitions appear as singlets, consistent with the instanton paths, which involve the breakage of two hydrogen-bonds and thus give tunneling splittings below experimental resolution

Model, First-Principle Calculation of Ammonia Dissociation on Si(100) Surface. Importance of Proton Tunneling

Abstract: The dissociation of an ammonia molecule on a cluster of Si atoms simulating the 100 silicon crystal structure with two Si dimers has been investigated by means of the DFT and an approximate instanton methods. The model corresponds to the low coverage limit of the surface. Absolute rate constants of two different dissociation paths are evaluated together with deuterium isotope effects. It is demonstrated that, even at room temperatures, the process is dominated by tunneling and that dissociation to a silicon atom of the adjacent dimer, rather than a silicon within the same dimer, is the prevailing mechanism. This leads to creation of a metastable structure which will slowly decay through a two-step hydrogen atom migration towards the absolute minimum on the potential energy surface corresponding to the NH2 group and the hydrogen atom residing in the same dimer

Zero-point tunneling splittings in compounds with multiple hydrogen bonds calculated by the rainbow instanton method

Zero-point tunneling splittings are calculated, and the values are compared with the experimentally observed values for four compounds in which the splittings are due to multiple-proton transfer along hydrogen bonds. These compounds are three binary complexes, namely, the formic acid and benzoic acid dimer and the 2-pyridone-2-hydroxypyridine complex, in which the protons move in pairs, and the calix[4]arene molecule, in which they move as a quartet. The calculations make use of and provide a test for the newly developed rainbow approximation for the zero-temperature instanton action which governs the tunneling splitting (as well as the transfer rate). This approximation proved to be much less drastic than the conventional adiabatic and sudden approximations, leading to a new general approach to approximate the instanton action directly. As input parameters the method requires standard electronic-structure data and the Hessians of the molecule or complex at the stationary configurations only; the same parameters also yield isotope effects. Compared to our earlier approximate instanton method, the rainbow approximation offers an improved treatment of the coupling of the tunneling mode to the other vibrations. Contrary to the conventional instanton approach based on explicit evaluation of the instanton trajectory, both methods bypass this laborious procedure, which renders them very efficient and capable of handling systems that thus far have not been handled by other theoretical methods. Past results for model systems have shown that the method should be valid for a wide range of couplings. The present results for real compounds show that it gives a satisfactory account of tunneling splittings and isotope effects in systems with strong coupling that enhances tunneling, thus demonstrating its applicability to low-temperature proton dynamics in systems with multiple hydrogen bonds.Peer reviewed: YesNRC publication: Ye

Model, First-Principle Calculation of Ammonia Dissociation on Si(100) Surface. Importance of Proton Tunneling

Abstract: The dissociation of an ammonia molecule on a cluster of Si atoms simulating the 100 silicon crystal structure with two Si dimers has been investigated by means of the DFT and an approximate instanton methods. The model corresponds to the low coverage limit of the surface. Absolute rate constants of two different dissociation paths are evaluated together with deuterium isotope effects. It is demonstrated that, even at room temperatures, the process is dominated by tunneling and that dissociation to a silicon atom of the adjacent dimer, rather than a silicon within the same dimer, is the prevailing mechanism. This leads to creation of a metastable structure which will slowly decay through a two-step hydrogen atom migration towards the absolute minimum on the potential energy surface corresponding to the NH2 group and the hydrogen atom residing in the same dimer