R. A. Marcus

Electron transfers in chemistry and biology

Electron-transfer reactions between ions and molecules in solution have been the subject of considerable experimental study during the past three decades. Experimental results have also been obtained on related phenomena, such as reactions between ions or molecules and electrodes, charge-transfer spectra, photoelectric emission spectra of ionic solutions, chemiluminescent electron transfers, electron transfer through frozen media, and electron transfer through thin hydrocarbon-like films on electrodes.

Dynamical effects in electron transfer reactions

A theoretical treatment is given for the effect of intramolecular vibrational and diffusive solvent orientational motions on the rate of electron transfer reactions. Four limiting cases are considered for the two‐electronic state problem: slow reaction, wide and narrow reaction window, and nondiffusing limits. With the aid of a decoupling approximation, an expression is derived for the reaction rate which reduces to the appropriate expression for each limiting case when the latter is approached. Under certain conditions the time dependence of the survival probability is multiexponential rather than single exponential. Because of this behavior two average survival times are defined and expressions for each are obtained. Experimental data are considered with the present treatment in mind. One feature of the present work is a more general analysis for the case that both vibrational and solvent diffusive motion contribute to the activation process. The relation to previous works in the literature is described.

Electrostatic Free Energy and Other Properties of States Having Nonequilibrium Polarization. I

Various processes such as electron transferreactions, redox reactions at electrodes, and electronic excitation of dissolved ions may proceed by way of intermediate states whose electrical polarization is not in equilibrium with the field arising from the charges present. The usual expressions for the electrostatic-free energy and for the differential equation satisfied by the potential assume that the polarization and the field are in equilibrium. Accordingly, these equations are of but limited applicability to these processes. In the present paper equations are derived for various properties of systems having such nonequilibrium electrostatic configurations. These properties include the free energy, energy, and entropy of the nonequilibrium system, and the spacial dependence of the electrostatic potential. The free energy, for example, will be used to calculate the probability of formation of nonequilibrium states in certain problems of physical interest.

Unimolecular Dissociations and Free Radical Recombination Reactions

The steric and pressure effects associated with the recombination of free radicals both depend on the nature of the activated complex, and are therefore intimately related. From a consideration of the reverse process of unimolecular dissociation, some equations are derived for these properties using an extension of earlier transition state and quasi‐unimolecular theories. The present formalism differs from previous formulations of the latter in a number of ways, particularly in the expression used for the density of quantum states of the high energy molecules. Subsequent applications of the theory tentatively suggest that essentially all vibrational degrees of freedom of these molecules can contribute their energy to the vibrationally excited molecules. Consequently, vibrational anharmonicity would appear to be an important factor in intramolecular energy transfer. The present paper is an extension of a previously developed theory for the recombination of methyl radicals and iodine atoms.

Universal emission intermittency in quantum dots, nanorods and nanowires

Virtually all known fluorophores exhibit mysterious episodes of emission intermittency. A remarkable feature of the phenomenon is a power-law distribution of on- and off-times observed in colloidal semiconductor quantum dots, nanorods, nanowires and some organic dyes. For nanoparticles, the resulting power law extends over an extraordinarily wide dynamic range: nine orders of magnitude in probability density and five to six orders of magnitude in time. Exponents hover about the ubiquitous value of -3/2. Dark states routinely last for tens of seconds—practically forever on quantum mechanical timescales. Despite such infinite states of darkness, the dots miraculously recover and start emitting again. Although the underlying mechanism responsible for this phenomenon remains a mystery and many questions persist, we argue that substantial theoretical progress has been made.

On the Theory of Oxidation‐Reduction Reactions Involving Electron Transfer. II. Applications to Data on the Rates of Isotopic Exchange Reactions

The rates of some homogeneous isotopic exchange reactions in solution are considered in the light of a recently developed quantitative theory of redox processes (Part I). The relative importance of several factors influencing the rates of these reactions is discussed. These factors include the Coulombic repulsion between the ionic reactants and the extent of solvation of the ions. Free energies and entropies of activation of various reactions are calculated from the theory without the use of any adjustable parameters. The agreement with the experimental data is considered to be satisfactory. On the basis of the theory and of earlier experiments in heavy water an experimental method is tentatively suggested for distinguishing electron and atom transfer mechanisms. This method applies to halide‐catalyzed exchange reactions of metal aquo-ions, and to other anion‐catalyzed reactions of this type not involving breakable OH bonds.

A new tunneling path for reactions such as H+H2→H2+H

The standard tunneling path in transition state theory for reactions such as H+H2→H2+H has been the so‐called reaction path, namely the path of steepest ascent to the saddle point. This path is now known to give numerical results for the reaction probability which are in disagreement with the exact quantum mechanical ones by an order of magnitude at low tunneling energies. A new tunneling path corresponding to a line of vibrational endpoints is proposed. It is much shorter and is shown to give results in agreement with the quantum ones to within about a factor of two. A semiclassical basis for choosing this new path is given.

Dynamical effects in electron transfer reactions. II. Numerical solution

In part I a reaction–diffusion equation was introduced for the description of electron transfer reactions which are induced by fluctuations in both the solvent polarization and in the intramolecular vibrational coordinates. We analyze the model employing a generalized moment expansion for the time behavior of the survival probability Q(t), i.e., for the fraction of molecules that have not transferred their electron at time t. Numerical and, in the narrow reaction window limit, analytical solutions are given for the average survival times τ. When the contribution of the intramolecular coordinates is appreciable an approximate power‐law behavior τ∝τ^α_L, with 0<α≤1, is found for the dependence of τ on the solvent dielectric relaxation time τ_L, in the large τ_L regime. Within the framework of the generalized moment description Q(t) is approximated as a superposition of several optimized exponential functions. In the small and intermediate τ_L regimes it is found that a single‐ or bi‐exponential description, respectively, is sufficient. Simple formulas for such approximations in terms of the average survival times are given. Furthermore it is demonstrated that in the large τ_L regime a truly multiexponential time behavior for the survival probability is encountered which, over a certain range of time, can appear to be algebraic, i.e., Q(t) ∝t^(−γ). The relation of these results to experimental data is discussed.

Analytical Mechanics of Chemical Reactions. III. Natural Collision Coordinates

The coordinates of earlier papers of this series are extended from linear collisions to reactions in three dimensions. Termed “natural collision coordinates,” they have a unique property of passing smoothly from those suited to reactants to those suited to products. Potential applications to bimolecular reactions are described.

On the relation of protein dynamics and exciton relaxation in pigment–protein complexes: An estimation of the spectral density and a theory for the calculation of optical spectra

A theory for calculating time– and frequency–domain optical spectra of pigment–protein complexes is presented using a density matrix approach. Non-Markovian effects in the exciton–vibrational coupling are included. A correlation function is deduced from the simulation of 1.6 K fluorescence line narrowing spectra of a monomer pigment–protein complex (B777), and then used to calculate fluorescence line narrowing spectra of a dimer complex (B820). A vibrational sideband of an excitonic transition is obtained, a distinct non-Markovian feature, and agrees well with experiment on B820 complexes. The theory and the above correlation function are used elsewhere to make predictions and compare with data on time–domain pump–probe spectra and frequency–domain linear absorption, circular dichroism and fluorescence spectra of Photosystem II reaction centers.