Joshua Jortner

In this paper we present a unified treatment of non-radiative decay processes in large molecules which involve either electronic relaxation between two electronic states or unimolecular rearrangement reactions in excited electronic states. The present treatment is analogous to the formalism previously applied for the line shape problem in nuclear recoil and in the optical spectra of solids. We were able to derive theoretical expressions for the non-radiative decay probability so that an arbitrary number of different molecular vibrations can be incorporated in the vibrational overlap factors. The general expressions obtained herein can be reduced to analytical form for two limiting cases, which we call the strong coupling case (which corresponds to a substantial horizontal displacement of the potential energy surfaces of the two electronic states) and the weak coupling limit (whereupon the relative horizontal displacement of the two potential energy surfaces is small). Quantitative criteria for the applicability of these two coupling limits are provided. In the strong coupling limit the transition probability is determined by a gaussian function of the energy parameter (ΔE - EM ), where ΔE is the energy gap between the origins of the two electronic states and 2EM is the Stokes shift. This limit exhibits a generalized Arrhenius type temperature behaviour whereupon the transition probability depends exponentially on the energy barrier for the intersection of the two potential surfaces. At low temperatures the transition probability is determined by the mean vibrational frequency and is thus expected to reveal only a moderately weak deuterium isotope effect. The weak coupling limit reveals an exponential (or rather superexponential) dependence of the transition probability on the energy gap ΔE. In this limit the transition probability is dominated by the highest vibrational frequency (e.g. the C-H or C-D vibrations) and thus will reveal a marked isotope effect. When semi-empirical estimates of the pre-exponential factors are provided, the approximate theoretical expression for the weak coupling limit is found to be consistent with the available experimental data on electronic relaxation in large organic molecules.

This paper considers electron transfer between biological molecules in terms of a nonadiabatic multiphonon nonradiative decay process in a dense medium. This theoretical approach is analogous to an extended quantum mechanical theory of outer sphere electron transfer processes, incorporating the effects of both low-frequency medium phonon modes and the high-frequency molecular modes. An explicit, compact and useful expression for the electron transfer probability is derived, which is valid throughout the entire temperature range, exhibiting a continuous transition from temperature independent tunneling between nuclear potential surfaces at low temperatures to an activated rate expression at high temperatures. This result drastically differs at low temperatures from the common, semiclassical, Gaussian approximation for the transition probability. The experimental data of De Vault and Chance [Biophys. J. 6, 825 (1966)] on the temperature dependence of the rate of electron transfer from cytochrome to the chlorophyll reaction center in the photosynthetic bacterium Chromatium are properly accounted for in terms of the present theory.

In this paper we consider a theory for intramolecular radiationless transitions in an isolated molecule. The Born–Oppenheimer zero-order excited states are not pure in view of configuration interaction between nearly degenerate zero-order states, leading to the broadening of the excited state, the line shape being Lorentzian. The optically excited state can be described in terms of a superposition of molecular eigenstates, and the resulting wavefunction exhibits an exponential nonradiative decay. The linewidth and the radiationless lifetime are expressed in terms of a single molecular parameter, that is the square of the interaction energy between the zero-order state and the manifold of all vibronic states located within one energy unit around that state. The validity criteria for the occurrence of an unimolecular radiationless transition and for exponential decay in an isolated molecule are derived. Provided that the density of vibrational states is large enough (i.e., exceeds the reciprocal of the interaction matrix element) radiationless transitions are expected to take place. The gross effects of molecular structure on the relevant molecular parameters are discussed.

Electron Transfer Past and Future (R. Marcus). Electron Transfer Reactions in Solution: A Historical Perspective (N. Sutin). Electron Transfer--From Isolated Molecules to Biomolecules (M. Bixon & J. Jortner). Charge Transfer in Bichromophoric Molecules in the Gas Phase (D. Levy). Long--Range Charge Separation in Solvent--Free Donor--Bridge--Acceptor Systems (B. Wegewijs & J. Verhoeven). Electron Transfer and Charge Separation in Clusters (C. Dessent, et al.). Control of Electron Transfer Kinetics: Models for Medium Reorganization and Donor--Acceptor Coupling (M. Newton). Theories of Structure--Function Relationships for Bridge--Mediated Electron Transfer Reactions (S. Skourtis & D. Beratan). Fluctuations and Coherence in Long--Range and Multicenter Electron Transfer (G. Iversen, et al.). Lanczos Algorithm for Electron Transfer Rates in Solvents with Complex Spectral Densities (A. Okada, et al.). Spectroscopic Determination of Electron Transfer Barriers and Rate Constants (K. Omberg, et al.). Photoinduced Electron Transfer Within Donor--Spacer--Acceptor Molecular Assemblies Studied by Time--Resolved Microwave Conductivity (J. Warman, et al.). From Close Contact to Long--Range Intramolecular Electron Transfer (J. Verhoeven). Photoinduced Electron Transfers Through sigma Bonds in Solution (N.--C. Yang, et al.). Indexes.

A general quantum mechanical description of exothermic electron transfer reactions is formulated by treating such reactions as the nonradiative decay of a ’’supermolecule’’ consisting of the electron donor, the electron acceptor, and the polar solvent. In particular, the role of the high-frequency intramolecular degrees of feedom on the free energy relationship for series of closely related reactions was investigated for various model systems involving displacement of potential energy surfaces, frequency shift, and anharmonicity effects. The free energy plots are generally found to pass through a maximum and to be asymmetric with a slower decrease in the transition probability with increasing energy of reaction. For high-frequency intramolecular modes this provides a rationalization of the experimental observation of ’’activationless’’ regions. Isotope effects are discussed as also are the oscillatory free energy relationships, predicted for low temperatures and high frequencies, and which are analogous to the vibrational structure in optical transitions.