Electron transfer in the nonadiabatic regime: Crossover from quantum-mechanical to classical behaviour (original) (raw)
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Electron transfer reactions: generalized spin-boson approach
Journal of Mathematical Chemistry, 2012
We introduce a mathematically rigorous analysis of a generalized spinboson system for the treatment of a donor-acceptor (reactant-product) quantum system coupled to a thermal quantum noise. The donor/acceptor probability dynamics describes transport reactions in chemical processes in presence of a noisy environment-such as the electron transfer in a photosynthetic reaction center. Besides being rigorous, our analysis has the advantages over previous ones that (1) we include a general, non energyconserving system-environment interaction, and that (2) we allow for the donor or acceptor to consist of multiple energy levels lying closely together. We establish explicit expressions for the rates and the efficiency (final donor-acceptor population difference) of the reaction. In particular, we show that the rate increases for a multi-level acceptor, but the efficiency does not.
A nonadiabatic and nonlinear theory for electron transfer
2008
We propose a new and general formalism for elementary chemical reactions where quantum electronic variables are used as reaction coordinates. This formalism is in principle applicable to all kinds of chemical reactions ionic or covalent. Our theory reveals the existence of an intermediate situation between ionic and covalent which may be almost barrierless and isoenegetic and which should be of high interest for understanding biochemistry. PACS numbers: 82.20.Gk ,82.20.Ln,82.30.Fi,82.39.Rt Chemical reactions are primarly changes of electronic states (associated with molecular and environmental reorganization) which appears either in radical ionization (redox) or in the forming/breaking of chemical bonds. They can be generally decomposed into sequences of elementary reactions corresponding to single transitions between two different electronic states for example an electron transfer (ET) between a Donor and an Acceptor.The rate of chemical reactions often obeys the Arrhenius law which manifest the existence of an energy barrier between the reactants and the products which has to be overcome by the thermal fluctuations. This energy barrier is usually quite large compared to the ambient temperature energy (≈ 0.026eV at 300K). There are also chemical reactions which do not obey the Arrhenius law (with a positive energy barrier). This is the situation for free radicals with unpaired electrons which are generally highly reactive [2] and generate covalent bonds.
Quantum effects on the rates of electron-transfer reactions
The Journal of Physical Chemistry, 1981
In this paper we compare the quantum-mechanical and classical theories of electron transfer in polar media, which involve large inner-shell reorganization energy. For symmetrical electron-transfer reactions, quantum corrections result from nuclear tunneling effects. These quantum effects increase the absolute value of the rate of the electron-transfer process for the Co(NH3):+-Co(NH3)2+ exchange at room temperature by less than 1 order of magnitude.
Quantum effects in electron transfer reactions with strong electronic coupling
The Journal of Chemical Physics, 1994
A new complex centroid reaction coordinate method is used to study electron transfer systems with strong electronic coupling. Formal analogy between current problem and the Ising model of one-dimensional spin system is used to develop a useful approximation for the partition function of electron transfer system in all orders of perturbation theory and when quantum effects are present. The reactions in the inverted region are discussed. The range of applicability of the usual nonadiabatic theory is reexamined. It is concluded that quantum solvent modes can effectively reduce electronic coupling in such a way that a nonadiabatic behavior can sometimes be induced in conventionally strongly coupled systems. Such an induced quantum nonadiabaticity is demonstrated in a numerical calculation.
2005
We investigate electron transfer processes in donor-acceptor systems with a coupling of the electronic degrees of freedom to a common bosonic bath. The model allows to study many-particle effects and the influence of the local Coulomb interaction U between electrons on donor and acceptor sites. Using the non-perturbative numerical renormalization group approach we find distinct differences between the electron transfer characteristics in the single- and two-particle subspaces. We calculate the critical electron-boson coupling alpha_c as a function of U and show results for density-density correlation functions in the whole parameter space. The possibility of many-particle (bipolaronic) and Coulomb-assisted transfer is discussed.
Kinetics of non-thermal electron transfer controlled by the dynamical solvent effect
Chemical Physics Letters, 2008
Recombination of ion pairs created by photoexcitation of viologen complexes is studied by a theory accounting for diffusion along the reaction coordinate to the crossing points of the electronic terms. The kinetics of recombination convoluted with the instrument response function are shown to differ qualitatively from the simplest exponential decay in both the normal and inverted Marcus regions. The deviations of the exponentiality are minimal only in the case of activationless recombination and are reduced even more by taking into consideration a single quantum mode assisting the electron transfer.
Dissipative Two-Electron Transfer
2008
We investigate non-equilibrium two-electron transfer in a model redox system represented by a two-site extended Hubbard model and embedded in a dissipative environment. The influence of the electron-electron interactions and the coupling to a dissipative bosonic bath on the electron transfer is studied in different temperature regimes. At high temperatures Marcus transfer rates are evaluated and at low temperatures, we calculate equilibrium and non-equilibrium population probabilities of the donor and acceptor with the non-perturbative Numerical Renormalization Group approach. We obtain the non-equilibrium dynamics of the system prepared in an initial state of two electrons at the donor site and identify conditions under which the electron transfer involves one concerted two-electron step or two sequential single-electron steps. The rates of the sequential transfer depend non-monotonically on the difference between the inter-site and on-site Coulomb interaction which become renormalized in the presence of the bosonic bath. If this difference is much larger than the hopping matrix element, the temperature as well as the reorganization energy, simultaneous transfer of both electrons between donor and acceptor can be observed.
Spontaneous Emission and Nonadiabatic Electron Transfer Rates in Condensed Phases
The Journal of Physical Chemistry A, 1998
In this paper we explore the non-Condon effect of fluctuations of the tunneling matrix element caused by a condensed medium on the rates of nonadiabatic electron transfer (ET) and spontaneous emission from an excited electronic state. For a charge-transfer complex immersed in a polar polarizable liquid, the solvent effect renormalizes the ET matrix element due to (i) the instantaneous field of the solvent nuclear polarization and (ii) equilibrium solvation by the electronic solvent polarization. Fluctuations of the classical electric field of the solvent affect the form of the preexponential factor in the ET rate constant. In the new expression for the rate preexponent the vacuum ET matrix element is multiplied by the factor θ forming an effective ET matrix element in condensed phases. The parameter θ is controlled by the magnitude and orientation (relative to the differential solute dipole) of the diabatic transition dipole of the charge-transfer complex. The theory predicts a possibility of localization of the transferred electron when θ becomes equal to zero. The same treatment is applied to the rate of spontaneous radiative electronic transitions. We find that the product of the transition frequency and the adiabatic transition dipole is invariant in all solvents when (i) the diabatic transition dipole is collinear to the differential solute dipole moment and (ii) the spectral shift due to dispersion solvation is small. Under the same conditions, the adiabatic transition dipole in condensed phases and the effective ET matrix element are related by the Mulliken-Hush equation that becomes exact in our treatment. † From
Journal of Physical Chemistry A, 2005
Two competing theories are used for bridging the gap between the nonadiabatic and the deeply adiabatic electron transfer between symmetric parabolic wells. For the high friction limit, a simple analytic interpolation is proposed as a reasonable alternative to them, well-fitted to the results of numerical simulations. It provides a continuous description of the electron transfer rate in the whole range of variation of the nonadiabatic coupling between the diabatic states. For lower friction, the original theories are used for the same goal. With an increase in coupling, the cusped barrier transforms into the parabolic one. Correspondingly, the pre-exponent of the Arrhenius transfer rate first increases with coupling, then levels off approaching the "dynamic solvent effect" plateau but finally reduces reaching the limit of the adiabatic Kramers theory for the parabolic barrier. These changes proceeding with a reduction in the particle separation affect significantly the spatial dependence of the total transfer rate. When approaching the contact distance, the exact rate becomes smaller than in the theory of dynamical solvent effects and much smaller than predicted by perturbation theory (golden rule), conventionally used in photochemistry and electrochemistry.