Electron transfer theoretical aspects

The Role of Solvation in Electron Transfer Theoretical and Computational Aspects... 

These spectroscopic and theoretical developments have stimulated the recent advances on electron-transfer dynamics at ITIES. In addition to the correlation between structure and dynamics of charge transfer, fundamental problems in connection with the energetics of ET reactions remain to be fully addressed. We shall consider these problems primarily before discussing kinetic aspects in full detail. 

Most of the AIMD simulations described in the literature have assumed that Newtonian dynamics was sufficient for the nuclei. While this is often justified, there are important cases where the quantum mechanical nature of the nuclei is crucial for even a qualitative understanding. For example, tunneling is intrinsically quantum mechanical and can be important in chemistry involving proton transfer. A second area where nuclei must be described quantum mechanically is when the BOA breaks down, as is always the case when multiple coupled electronic states participate in chemistry. In particular, photochemical processes are often dominated by conical intersections [14,15], where two electronic states are exactly degenerate and the BOA fails. In this chapter, we discuss our recent development of the ab initio multiple spawning (AIMS) method which solves the elecronic and nuclear Schrodinger equations simultaneously this makes AIMD approaches applicable for problems where quantum mechanical effects of both electrons and nuclei are important. We present an overview of what has been achieved, and make a special effort to point out areas where further improvements can be made. Theoretical aspects of the AIMS method are... 

R. Bezman and L. R. Faulkner discussed theoretical and practical aspects for measurements of the efficiencies of chemiluminescent electron transfer reactions 189>. They also performed absolute measurements of the chemiluminescence of the fluoranthene- 10-methyl-phenothiazine system 211h... 

Prior to the 1970 s, electrochemical kinetic studies were largely directed towards faradaic reactions occurring at metal electrodes. While certain questions remain unanswered, a combination of theoretical and experimental studies has produced a relatively mature picture of electron transfer at the metal-solution interface f1-41. Recent interest in photoelectrochemical processes has extended the interest in electrochemical kinetics to semiconductor electrodes f5-151. Despite the pioneering work of Gerischer (11-141 and Memming (15), many aspects of electron transfer kinetics at the semiconductor-solution interface remain controversial or unexplained. 

A number of publications in recent years have demonstrated an active interest in the theoretical aspects of electron transfer (ET) processes in biological systems (1.-9). This interest was stimulated by the extensive experimental information regarding the temperature dependence of ET rates measured over a broad range of temperatures (10-16). The unimolecular rate of cyto-chrome-c oxidation in Chromatium (10-12), for example, exhibits the Arrhenius type dependence and changes by three orders of... 

The theoretical aspects of electron transfer mechanisms in aqueous solution have received considerable attention in the last two decades. The early successes of Marcus Q, 2), Hush (3, 4), and Levich (5) have stimulated the development of a wide variety of more detailed models, including those based on simple transition state theory, as well as more elaborate semi-clas-sical and quantum mechanical models (6-12). 

Two disciplines cover the majority of the theoretical and practical aspects of the mechanisms through which electron transfers proceed electrochemistry and photochemistry. In this book only mechanisms relating to electrochemistry will be considered. 

Like the 1994-issue of the series "Electron Transfer", the second volume again covers various aspects of this fundamental process. The articles are concerned with the experimental and theoretical aspects of electron transfer in chemistry and biology. In the latter, emphasis is given to energy transfer, which is also part of photosynthesis. 

Electronic and vibrational spectroscopy continues to be important in the characterization of iron complexes of all descriptions. Charge-transfer spectra, particularly of solvatochromic ternary diimine-cyanide complexes, can be useful indicators of solvation, while IR and Raman spectra of certain mixed valence complexes have contributed to the investigation of intramolecular electron transfer. Assignments of metal-ligand vibrations in the far IR for the complexes [Fe(8)3] " " were established by means of Fe/ Fe isotopic substitution. " A review of pressure effects on electronic spectra of coordination complexes includes much information about apparatus and methods and about theoretical aspects, though rather little about specific iron complexes. ... 

When we transfer the theoretical aspects of these models to or nometallic chemistry, we are aware of the fact that, e.g. when altering the number of rr-electrons by two (67T-, 4ir- or 2Tr-electrons) in the elementary steps of organometallic reactions, we have, step-by-step to await a change in the type of process (S or A) (in analogy to Fig. 1 in Scheme 2.1-3). On the other hand, we also can learn that the energies of the FMO s change systematically, going from 6n- to 4ir- to 27r-electron stems (from e.g. bis-ir-allyl- to rr-allyl-a-allyl to bis-o-allyl-ntetal-complexes). 

The kineties of eleetron-transfer reactions, which is also affected by the electrode potential and the metal-water interface, is more difficult and complex to treat than the thermodynamic aspects. While the theoretical development for electron transfer kinetics began decades ago, a practical implementation for surface reactions is still unavailable. Popular transition state-searching techniques such as the NEB method are not designed to search for minimum-energy reaction paths subject to a constant potential. Approximations that allow affordable quantum chemistry calculations to get around this limitation have been proposed, ranging from the electron affinity/ionization potential matching method to heuristic arguments based on interpolations. 

In Chap. 2, the analysis of diffusion-limited reaction rates of Smolu-chowski, Collins and Kimball, and that of Noyes is followed. The considerable literature on reaction rates between solute species is also presented. Additional and important other factors which influence the rate of reaction are a coulomb interaction between reactants, long-range energy or electron transfer and an angular dependence of the rate of reaction. These topics are considered in the Chaps. 3—5. The experimental and theoretical work are compared and contrasted. When the reactants are formed in pairs (by bond fission of a precursor), the rate or probability of recombination can be measured and is of considerable interest. Chapters 6 and 7 discuss the theoretical aspects of the recombination of neutral and ionic radical pairs and also appeal to the extensive literature on the experimentally measured rate of recombination. The weaknesses of this theoretical... 

The discussion in the previous section was helpful in identifying the factors at the molecular level which are involved when electron transfer occurs. Two different theoretical approaches have been developed which incorporate these features and attempt to account for electron transfer rate constants quantitatively. The first, by Marcus34 and Hush,35 is classical in nature, and the second is based on quantum mechanics and time dependent perturbation theory. The theoretical aspects of electron transfer in chemical36-38 and biological systems39 have been discussed in a series of reviews. 

The reader is also referred to the innovative nonphotochemical electron transfer studies of Weaver et al. [147], These authors have been exploring dynamical solvent effects on ground state self-exchange kinetics for or-ganometallic compounds. This work has explored many aspects of solvent control on intermediate barrier electron transfer reactions, including the effect on a distribution of solvation times. The experimental C(t) data on various solvents have been incorporated into the theoretical modeling of the ground state electron transfer reactions studied by Weaver et al. [147]. 

The underlying motivation of the work presented in this paper is to provide a theoretical understanding of basic physical and chemical properties and processes of relevance in photoelectrochemical devices based on nanostructured transition metal oxides. In this context, fundamental problems concerning the binding of adsorbed molecules to complex surfaces, electron transfer between adsorbate and solid, effects of intercalated ions and defects on electronic and geometric structure, etc., must be addressed, as well as methodological aspects, such as efficiency and reliability of different computational schemes, cluster models versus periodic ones, etc.. 

Multi-electronic processes (like those consisting of two-electron transfers, EE mechanism) have been widely treated in the literature, both in their theoretical and applied aspects [4, 10, 56-68]. This high productivity measures in some way the great presence and relevance of these processes in many fields, and hence the importance of understanding them. 

Recent progress in understanding the theoretical basis of electron transfer has been rapid. Theoretical aspects of electron transfer are addressed in detail in other contributions to this series, and authoriative, up-to-date reviews are available [9-14], For our purposes, it will be sufficient to review some very basic electron transfer theory which will serve as a framework for the discussion of artificial photosynthetic systems which follows. 

Kinetic and Theoretical Aspects of Outer-Sphere Electron Transfer Reactions... 

Theoretical Aspects of Electron Transfer from Solid Proteins to Ions in Solution... 

A number of excellent reviews on the theoretical aspects of photoinduced electron transfer have appeared in the literature and the interested reader may refer to these original articles. Due to the fundamental importance of the electron transfer step for the title process and in order to facilitate reading this chapter a brief introduction on PET will be given [2,6]. 

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