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dc.contributor.authorSmedarchina, Zorka
dc.contributor.authorSiebrand, Willem
dc.contributor.authorFernández-Ramos, Antonio
dc.identifier.citationSmedarchina, Z., Siebrand, W., & Fernández-Ramos, A. (2018). Entanglement and co-tunneling of two equivalent protons in hydrogen bond pairs. The Journal Of Chemical Physics, 148, 102307. doi: 10.1063/1.5000681
dc.descriptionThe following article appeared in The Journal of Chemical Physics 148, 102307 (2018) and may be found at
dc.description.abstractA 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 techniques
dc.description.sponsorshipFinancial 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 acknowledged
dc.publisherAIP Publishing
dc.relationinfo:eu-repo/grantAgreement/MINECO/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/CTQ2014-58617-R/ES/IMULACION DEL PROCESO DE COMBUSTION DE BIOALCOHOLES
dc.rights© 2018 AIP Publishing LLC. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing
dc.titleEntanglement and co-tunneling of two equivalent protons in hydrogen bond pairs
dc.contributor.affiliationUniversidade de Santiago de Compostela. Centro de Investigación en Química Biolóxica e Materiais Moleculares
dc.contributor.affiliationUniversidade de Santiago de Compostela. Departamento de Química Física

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