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Pure and Applied Chemistry

Proton transfer across hydrogen bonds: From reaction path to Schrödinger's cat

F. Fillaux, Alain Cousson, Matthias Josef Gutmann

Published Jan 1, 2007• 21 citations
Publisher

Abstract

Abstract We review recent studies of the interconversion mechanism of OH···O hydrogen-bonded centrosymmetric dimers through proton transfer in the prototype crystals of potassium hydrogen carbonate (KHCO3) and benzoic acid (C6H5COOH). The point at issue is whether the proton distributions at various temperatures arise from classical statistical mixtures of tautomers or quantum mechanical superposition states. A related issue is whether it is possible to probe a quantum superposition without inducing decoherence and classicality. We show that neutron diffraction can realize decoherence-free measurements for strictly defined scattering geometries and thus evidence macroscopic quantum correlations. We present a theoretical framework for decoherence-free macroscopically entangled states of the sublattice of protons. The neutron diffraction cross-section of protons is enhanced by a factor of ~45, compared to regular Bragg diffraction, and quantum correlations are observed with remarkable contrast. At elevated temperatures, up to 300 K, quantum correlations are unaffected by proton transfer. The crystal is a coherent superposition of macroscopic tunnelling states, like Schrödinger's cat in a superposition of dead and alive states.

DOI
10.1351/pac200779061023

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Abstract We review recent studies of the interconversion mechanism of OH···O hydrogen-bonded centrosymmetric dimers through proton transfer in the prototype crystals of potassium hydrogen carbonate (KHCO3) and benzoic acid (C6H5COOH). The point at issue is whether the proton distributions at various temperatures arise from classical statistical mixtures of tautomers or quantum mechanical superposition states. A related issue is whether it is possible to probe a quantum superposition without inducing decoherence and classicality. We show that neutron diffraction can realize decoherence-free measurements for strictly defined scattering geometries and thus evidence macroscopic quantum correlations. We present a theoretical framework for decoherence-free macroscopically entangled states of the sublattice of protons. The neutron diffraction cross-section of protons is enhanced by a factor of ~45, compared to regular Bragg diffraction, and quantum correlations are observed with remarkable contrast. At elevated temperatures, up to 300 K, quantum correlations are unaffected by proton transfer. The crystal is a coherent superposition of macroscopic tunnelling states, like Schrödinger's cat in a superposition of dead and alive states.
Abstract The role of proton tunnelling in biological catalysis is investigated here within the frameworks of quantum information theory and thermodynamics. We consider the quantum correlations generated through two hydrogen bonds between a substrate and a prototypical enzyme that first catalyses the tautomerization of the substrate to move on to a subsequent catalysis, and discuss how the enzyme can derive its catalytic potency from these correlations. In particular, we show that classical changes induced in the binding site of the enzyme spreads the quantum correlations among all of the four hydrogen-bonded atoms thanks to the directionality of hydrogen bonds. If the enzyme rapidly returns to its initial state after the binding stage, the substrate ends in a new transition state corresponding to a quantum superposition. Open quantum system dynamics can then naturally drive the reaction in the forward direction from the major tautomeric form to the minor tautomeric form without needing any additional catalytic activity. We find that in this scenario the enzyme lowers the activation energy so much that there is no energy barrier left in the tautomerization, even if the quantum correlations quickly decay.
Several recent experiments have shown that protons, and to some extent also deuterons, show anomalous cross sections when the neutrons have energies in the range 10-100 eV (this results in a Compton scattering process where an essential part of the energy is transferred to one of the scattering particles). Here, an experiment on partially deuterated water, carried out by Chatzidimitriou-Dreismann et al., is analyzed in terms of a theory, which assumes that during the short duration (<10(-15) s) of this scattering process, protons are exchange correlated and cannot be considered as independent scattering objects. The quantum decoherence time for protons in liquid water is estimated from a simple model for the interaction of the water protons with hydrogen bonds.
Abstract Context Proton transfer in drug–protein cavities is central to enzymatic catalysis and pH-responsive drug delivery, yet classical models often fail to capture the quantum mechanical behavior that governs these processes. The influence of nanoscale confinement on proton dynamics through quantum effects remains poorly understood, limiting our ability to design optimized therapeutic systems. We present a quantum theoretical framework that connects cavity geometry with measurable proton transfer properties, offering new insights for biocatalysis and nanomedicine. Method We developed an analytical model for proton confinement in biological cavities by solving the Schrödinger equation for two spherically symmetric potentials: finite square wells representing hydrophobic environments and Morse potentials for hydrogen-bonded systems. Our approach systematically calculates ground-state energies, wavefunctions, tunneling probabilities, and vibrational overtones. Results show confinement geometry exponentially modulates proton behavior, with tunneling probabilities spanning > 12 orders of magnitude under physiological conditions. Kinetic isotope effects (> 10¹¹) and catalytic enhancements (10³-fold) confirm quantum tunneling dominance. While finite wells promote classical localization, Morse potentials enable efficient proton transfer through delocalization. The model incorporates environmental decoherence and establishes design rules linking cavity parameters to spectroscopic and kinetic signatures, providing a bridge between quantum theory and structural biology.
Quantum correlations are correlations that arise from a unique feature in quantum mechanics: quantum superposition. The most famous example of quantum superposition is the Schrodinger’s cat state, where a cat is in a state of neither dead nor alive before an observer determines the cat’s status. This is not what we expect. Nevertheless, quantum superposition and correlations are routinely created in the laboratories with microscopic systems involving atoms and light particles. Can this counterintuitive notion be realised in the macroscopic world? This thesis investigates this question by devising criteria that certify the existence of quantum correlations in mesoscopic/macroscopic systems. Powerful mathematical tools are used to simulate two quantum protocols in a mesoscopic system which have applications in quantum communication and computation.
We discuss the peculiarities of scattering in a three-proton system induced by the presence of an entangled proton-proton Bell-like state in the initial configuration. We formulate the problem using the standard spin formalism of nuclear physics in order to follow in detail the reaction pathways leading to the teleportation of a quantum-mechanical state within this system. By performing numerical simulations of the system and calculations based on a realistic nucleon-nucleon potential, we evaluate the relevant spin observables and search for a simple, experimentally feasible signal that could provide clear evidence of quantum teleportation. For the case in which proton 2, belonging to the entangled proton pair 23, interacts with hydrogen target 1, thereby triggering the teleportation process, we find clear evidence of teleportation through measurements of the final polarization of proton 3', even for small values of the polarization of target proton 1. The dominant component of this polarization is transferred almost entirely from target proton 1 to proton 3 in the angular region characterized by strong entanglement. For an unpolarized target proton 1, quantum teleportation is no longer possible. The only unambiguous signature of the residual quantum correlations would be provided by measurements of the spin correlations within the strongly entangled final-state proton pair 1'2'. Indirect evidence may also be obtained from measurements of the polarization of proton 2' in the final state, although the corresponding effectis relatively weak.
Abstract In this paper we re-investigate the core of Schrödinger’s “cat paradox”. We argue that one has to distinguish clearly between superpositions of macroscopic cat states |☺〉 + |☹〉 and superpositions of entangled states |☺, ↑〉 + |☹, ↓〉 which comprise both the state of the cat (☺=alive, ☹=dead) and the radioactive substance (↑=not decayed, ↓=decayed). It is shown, that in the case of the cat experiment recourse to decoherence or other mechanisms is not necessary in order to explain the absence of macroscopic superpositions. Additionally, we present modified versions of two quantum optical experiments as experimenta crucis. Applied rigorously, quantum mechanical formalism reduces the problem to a mere pseudo-paradox.