Temperature dependent activation energy for electron transfer between biological molecules
15 Jun 1976-Journal of Chemical Physics (American Institute of Physics)-Vol. 64, Iss: 12, pp 4860-4867
TL;DR: In this paper, the authors considered electron transfer between biological molecules in terms of a nonadiabatic multiphonon nonradiative decay process in a dense medium and derived an explicit, compact and useful expression for the electron transfer probability.
Abstract: 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.
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TL;DR: In this paper, the electron transfer reactions between ions and molecules in solution have been the subject of considerable experimental study during the past three decades, including charge transfer, photoelectric emission spectra, chemiluminescent electron transfer, and electron transfer through frozen media.
7,155 citations
TL;DR: Proton-coupled electron transfer is an important mechanism for charge transfer in a wide variety of systems including biology- and materials-oriented venues and several are reviewed.
Abstract: ▪ Abstract Proton-coupled electron transfer (PCET) is an important mechanism for charge transfer in a wide variety of systems including biology- and materials-oriented venues. We review several are...
2,182 citations
TL;DR: This review considers only polynuclear transition metal complexes that can be defined as supramolecular species and that are reported to exhibit luminescence and redox properties, and reviews several interesting systems such as polymer-appended metal.
Abstract: Great attention is currently paid to the synthesis of polynuclear transition metal complexes and the study of their photochemical, photophysical, and electrochemical properties. This interest is stimulated, in particular, by attempts to design and construct multicomponent systems (often called supramolecular species) capable of performing useful lightand/or redox-induced functions.1-16 A great deal of investigations on mononuclear transition metal complexes had previously shown that several families of these compounds are very interesting from the electrochemical, photochemical, and photophysical viewpoints.17-22 The metalligand interaction, in fact, is often (i) weak enough to allow the manifestation of intrinsic properties of metal and ligands (e.g., ligand-centered and metalcentered absorption bands and redox waves) and, at the same time, (ii) strong enough to cause the appearance of new properties, characteristic of the whole compound (e.g., metal-to-ligand or ligand-tometal charge-transfer bands). On passing from mononuclear to polynuclear transition metal complexes, the situation becomes even more interesting because in the latter (supramolecular) compounds one can find, besides properties related to each metal-based component, properties related to the structure and composition of the whole array. A suitable choice of the mononuclear building blocks and bridging ligands and an appropriate design of the (supramolecular) structure can in fact allow the occurrence of very interesting and potentially useful processes such as energy transfer along predetermined pathways, photoinduced charge separation, multielectron exchange at a predetermined potential, etc. The knowledge on the luminescence and redox properties of polynuclear transition metal complexes is rapidly accumulating, but it is disperse in a great number of journals. We have made an attempt to collect the available results, and we present them together with some fundamental introductory concepts and a few comments. One of the main problems, of course, was to delimit the field of this review. Using personal criteria which are related to our own research interests, we decided to consider only polynuclear transition metal complexes that can be defined as supramolecular species (section 2.2) and that are reported to exhibit luminescence. For such compounds only, the electrochemical properties have also been reviewed. Furthermore, we decided to include only classical (Werner-type) polynuclear transition metal compounds where the number of metal-based units is exactly known and the connection between the metal centers is provided only by bridging ligands. Thus, a number of interesting systems such as polymer-appended metal † In memoriam of Mauro Ciano. 759 Chem. Rev. 1996, 96, 759−833
2,076 citations
TL;DR: The 14 Å or less spacing of redox centres provides highly robust engineering for electron transfer, and may reflect selection against designs that have proved more vulnerable to mutations during the course of evolution.
Abstract: We have surveyed proteins with known atomic structure whose function involves electron transfer; in these, electrons can travel up to 14 A between redox centres through the protein medium. Transfer over longer distances always involves a chain of cofactors. This redox centre proximity alone is sufficient to allow tunnelling of electrons at rates far faster than the substrate redox reactions it supports. Consequently, there has been no necessity for proteins to evolve optimized routes between redox centres. Instead, simple geometry enables rapid tunnelling to high-energy intermediate states. This greatly simplifies any analysis of redox protein mechanisms and challenges the need to postulate mechanisms of superexchange through redox centres or the maintenance of charge neutrality when investigating electron-transfer reactions. Such tunnelling also allows sequential electron transfer in catalytic sites to surmount radical transition states without involving the movement of hydride ions, as is generally assumed. The 14 A or less spacing of redox centres provides highly robust engineering for electron transfer, and may reflect selection against designs that have proved more vulnerable to mutations during the course of evolution.
1,760 citations
TL;DR: Powerful first-order analysis of intraprotein electron transfer is developed from electron-transfer measurements both in biological and in chemical systems, finding selection of distance, free energy and reorganization energy are sufficient to define rate and directional specificity of biological electron transfer.
Abstract: Powerful first-order analysis of intraprotein electron transfer is developed from electron-transfer measurements both in biological and in chemical systems. A variation of 20 A in the distance between donors and acceptors in protein changes the electron-transfer rate by 10(12)-fold. Protein presents a uniform electronic barrier to electron tunnelling and a uniform nuclear characteristic frequency, properties similar to an organic glass. Selection of distance, free energy and reorganization energy are sufficient to define rate and directional specificity of biological electron transfer, meeting physiological requirements in diverse systems.
1,671 citations
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46,339 citations
TL;DR: In this article, the resonance theory of Forster, which involves only allowed transitions, is extended to include transfer by means of forbidden transitions which, it is concluded, are responsible for the transfer in all inorganic systems yet investigated.
Abstract: The term ``sensitized luminescence'' in crystalline phosphors refers to the phenomenon whereby an impurity (activator, or emitter) is enabled to luminesce upon the absorption of light in a different type of center (sensitizer, or absorber) and upon the subsequent radiationless transfer of energy from the sensitizer to the activator The resonance theory of Forster, which involves only allowed transitions, is extended to include transfer by means of forbidden transitions which, it is concluded, are responsible for the transfer in all inorganic systems yet investigated The transfer mechanisms of importance are, in order of decreasing strength, the overlapping of the electric dipole fields of the sensitizer and the activator, the overlapping of the dipole field of the sensitizer with the quadrupole field of the activator, and exchange effects These mechanisms will give rise to ``sensitization'' of about 103−104, 102, and 30 lattice sites surrounding each sensitizer in typical systems The dependence of transfer efficiency upon sensitizer and activator concentrations and on temperature are discussed Application is made of the theory to experimental results on inorganic phosphors, and further experiments are suggested
7,635 citations
TL;DR: In this paper, a mechanism for electron transfer reactions is described, in which there is very little spatial overlap of the electronic orbitals of the two reacting molecules in the activated complex, and a quantitative theory of the rates of oxidation reduction reactions involving electron transfer in solution is presented.
Abstract: A mechanism for electron transfer reactions is described, in which there is very little spatial overlap of the electronic orbitals of the two reacting molecules in the activated complex. Assuming such a mechanism, a quantitative theory of the rates of oxidation‐reduction reactions involving electron transfer in solution is presented. The assumption of "slight‐overlap" is shown to lead to a reaction path which involves an intermediate state X* in which the electrical polarization of the solvent does not have the usual value appropriate for the given ionic charges (i.e., it does not have an equilibrium value). Using an equation developed elsewhere for the electrostatic free energy of nonequilibrium states, the free energy of all possible intermediate states is calculated. The characteristics of the most probable state are then determined with the aid of the calculus of variations by minimizing its free energy subject to certain restraints. A simple expression for the electrostatic contribution to the free energy of formation of the intermediate state from the reactants, ΔF*, is thereby obtained in terms of known quantities, such as ionic radii, charges, and the standard free energy of reaction.
This intermediate state X* can either disappear to reform the reactants, or by an electronic jump mechanism to form a state X in which the ions are characteristic of the products. When the latter process is more probable than the former, the over‐all reaction rate is shown to be simply the rate of formation of the intermediate state, namely the collision number in solution multiplied by exp(—ΔF*/kT). Evidence in favor of this is cited. In a detailed quantitative comparison, given elsewhere, with the kinetic data, no arbitrary parameters are needed to obtain reasonable agreement of calculated and experimental results.
5,265 citations
TL;DR: In this paper, a model for polaron motion is described, in simplified form, incorporating the principal physical features of the problem, and the conditions under which the size of the polaron becomes comparable to a lattice spacing (small) are discussed.
2,465 citations
TL;DR: In this article, a review is concerned with the neglected class of inorganic compounds, which contain ions of the same element in two different formal states of oxidation, and a number of references cite that many individual examples of this class have been studied, yet they have very rarely been treated as a class, and there has never before, to our knowledge, been a systematic attempt to classify their properties in terms of their electronic and molecular structures.
Abstract: Publisher Summary This review is concerned with the neglected class of inorganic compounds, which contain ions of the same element in two different formal states of oxidation. Although the number of references cited in our review show that many individual examples of this class have been studied, yet they have very rarely been treated as a class, and there has never before, to our knowledge, been a systematic attempt to classify their properties in terms of their electronic and molecular structures. In the past, systems containing an element in two different states of oxidation have gone by various names, the terms “mixed valence,” nonintegral valence,” “mixed oxidation,” “oscillating valency,” and “controlled valency” being used interchangeably. Actually, none of these is completely accurate or all-embracing, but in our hope to avoid the introduction of yet another definition, we have somewhat arbitrarily adopted the phrase “mixed valence” for the description of these systems. The concept of resonance among various valence bond structures is one of the cornerstones of modern organic chemistry.
2,208 citations