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Register a new userMarcus Electron Transfer Reactions with Bulk Metallic Catalysis
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Electron transfer organic reaction rates are considered employing the classic physical picture of Marcus wherein the heats of reaction are deposited as the energy of low frequency mechanical oscillations of reconfigured molecular positions. If such electron transfer chemical reaction events occur in the neighborhood of metallic plates, then electrodynamic interface fields must also be considered in addition to mechanical oscillations. Such electrodynamic interfacial electric fields in principle strongly effect the chemical reaction rates. The thermodynamic states of the metal are unchanged by the reaction which implies that metallic plates are purely catalytic chemical agents.
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In the pioneering work by R. A. Marcus, the solvation effect on electron transfer (ET) processes was investigated, giving rise to the celebrated nonadiabatic ET rate formula. In this work, on the basis of the thermodynamic solvation potentials analysis, we reexamine Marcus formula with respect to the Rice-Ramsperger-Kassel-Marcus (RRKM) theory. Interestingly, the obtained RRKM analogue, which recovers the original Marcus rate that is in a linear solvation scenario, is also applicable to the nonlinear solvation scenarios, where the multiple curve{crossing of solvation potentials exists. Parallelly, we revisit the corresponding Fermis golden rule results, with some critical comments against the RRKM analogue proposed in this work. For illustration, we consider the quadratic solvation scenarios, on the basis of physically well-supported descriptors.
We examine electron transfer between two quantum states in the presence of a dissipative environment represented as a set of independent harmonic oscillators. For this simple model, the Marcus transfer rates can be derived and we show that these rates are associated to an explicit expression for the environment correlation time. We demonstrate that as a manifestation of the Goldilocks principle, the optimal transfer is governed by a single parameter which is equal to just the inverse root square of two.
Marcus-Levich-Jortner (MLJ) theory is one of the most commonly used methods for including nuclear quantum effects into the calculation of electron-transfer rates and for interpreting experimental data. It divides the molecular problem into a subsystem treated quantum-mechanically by Fermis golden rule and a solvent bath treated by classical Marcus theory. As an extension of this idea, we here present a reduced semiclassical instanton theory, which is a multiscale method for simulating quantum tunnelling of the subsystem in molecular detail in the presence of a harmonic bath. We demonstrate that instanton theory is typically significantly more accurate than the cumulant expansion or the semiclassical Franck-Condon sum, which can give orders-of-magnitude errors and in general do not obey detailed balance. As opposed to MLJ theory, which is based on wavefunctions, instanton theory is based on path integrals and thus does not require solutions of the Schrodinger equation, nor even global knowledge of the ground- and excited-state potentials within the subsystem. It can thus be efficiently applied to complex, anharmonic multidimensional subsystems without making further approximations. In addition to predicting accurate rates, instanton theory gives a high level of insight into the reaction mechanism by locating the dominant tunnelling pathway as well as providing information on the reactant and product vibrational states involved in the reaction and the activation energy in the bath similarly to what would be found with MLJ theory.
A comprehensive description of molecular electron transfer reactions is essential for our understanding of fundamental phenomena in bio-energetics and molecular electronics. Experimental studies of molecular systems in condensed-phase environments, however, face difficulties to independently control the parameters that govern the transfer mechanism with high precision. We show that trapped-ion experiments instead allow to reproduce and continuously connect vastly different regimes of molecular charge transfer through precise tuning of, e.g., phonon temperature, electron-phonon interactions, and electronic couplings. Such a setting allows not only to reproduce widely-used transport models, such as Marcus theory. It also provides access to transfer regimes that are unattainable for molecular experiments, while controlling and measuring the relevant observables on the level of individual quanta. Our numerical simulations predict an unconventional quantum transfer regime, featuring a transition from quantum adiabatic- to resonance-assisted transfer as a function of the donor-acceptor energy gap, that can be reached by increasing the electronic coupling at low temperatures. Trapped ion-based quantum simulations thus promise to enhance our microscopic understanding of molecular electron transfer processes, and may help to reveal efficient design principles for synthetic devices.
Fermis golden rule defines the transition rate between weakly coupled states and can thus be used to describe a multitude of molecular processes including electron-transfer reactions and light-matter interaction. However, it can only be calculated if the wave functions of all internal states are known, which is typically not the case in molecular systems. Marcus theory provides a closed-form expression for the rate constant, which is a classical limit of the golden rule, and indicates the existence of a normal regime and an inverted regime. Semiclassical instanton theory presents a more accurate approximation to the golden-rule rate including nuclear quantum effects such as tunnelling, which has so far been applicable to complex anharmonic systems in the normal regime only. In this paper we extend the instanton method to the inverted regime and study the properties of the periodic orbit, which describes the tunnelling mechanism via two imaginary-time trajectories, one of which now travels in negative imaginary time. It is known that tunnelling is particularly prevalent in the inverted regime, even at room temperature, and thus this method is expected to be useful in studying a wide range of molecular transitions occurring in this regime.
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