Dynamics Bixon-Jortner

Figure 3,17. Level structure for the primary charge separation in photosynthetic reaction centers, (a) unistep superexchange dynamics (b) two-step sequential dynamics (Bixon and Jortner, 1999) Reproduced with permission.

In intermediate or small systems, their population dynamic behaviors often exhibit nonexponential decay or even oscillatory decay like the vibrational relaxation of C6H5NH2 in Sect. 5.2. To show how the density matrix method can be applied to study these systems, the Bixon-Jortner model is considered in this section. For this purpose, we consider the following model (see Fig. 4.2). 0) and /)(i = 1, ) are the eigenstates of the Hamiltonian Ho. For simplicity, we assume that only the perturbation matrix elements between 0) and /) states are nonzero. That is. 

The main reason for choosing the treatment of vibrationai reiaxation of (H20)2 and C6H5NH2 is to show that the quantum chemistry programs can now provide the anharmonic vibrationai potentiais so that the first-principie caicuiation of vibrational relaxation has become possible. Their dynamical behaviors may be described by the density matrix method through the Bixon-Jortner model (see Sect. 4.3). 

The dynamics of inter- vs intrastrand hole transport has also been the subject of several theoretical investigations. Bixon and Jortner [38] initially estimated a penalty factor of ca. 1/30 for interstrand vs intrastrand G to G hole transport via a single intervening A T base pair, based on the matrix elements computed by Voityuk et al. [56]. A more recent analysis by Jortner et al. [50] of strand cleavage results reported by Barton et al. [45] led to the proposal that the penalty factor depends on strand polarity, with a factor of 1/3 found for a 5 -GAC(G) sequence and 1/40 for a 3 -GAC(G) sequence (interstrand hole acceptor in parentheses). The origin of this penalty is the reduced electronic coupling between bases in complementary strands. 

In this book we shall write the Hamiltonian as an (algebraic) operator using the appropriate Lie algebra. We intend to illustrate by many applications what we mean by this cryptic statement. It is important to emphasize that one way to represent such a Hamiltonian is as a matrix. In this connection we draw attention to one important area of spectroscopy, that of electronically excited states of larger molecules,4 which is traditionally discussed in terms of matrix Hamiltonians, the simplest of which is the so-called picket fence model (Bixon and Jortner, 1968). A central issue in this area of spectroscopy is the time evolution of an initially prepared nonstationary state. We defer a detailed discussion of such topics to a subsequent volume, which deals with the algebraic approach to dynamics. 

J. Jortner and M. Bixon, in Electron Transfer From Isolated Molecules to Biomolecules, Dynamics and Spectroscopy, Advances in Chemical Physics, Vols. 106 and 107, Wiley, New York, 1999. 

Involvement of intramolecular high-frequency vibrational modes in electron transfer was considered (Efrima and Bixon, 1974 Nitzan et al., 1972 Neil et al., 1974, Jortner and Bixon, 1999b Hopfield, 1974 Grigorov and Chernyavsky, 1972 Miyashita et al. 2000). As an example, when the high-frequency mode (hvv) is in the low-temperature limit and solvent dynamic behavior can be treated classically (Jortner and Bixon, 1999 and references therein), the rate constant for non-adiabatic ET in the case of parabolic terms is given by... 

Fainberg, B. D. and Huppert, D. (1999) Theoretical and experimental study of ultrafast solvation dynamics by transient four-phonon spectroscopy, in Jortner, J. and Bixon. (eds.), Advances in Chemical Physics 107, Part 1, John Wiley Sons. NY., pp 191-262. 

Bixon, M., Michel Beyerle, M. E., and Jortner, J., 1988, Formation dynamics, decay kinetics and singlet-triplet splitting of the (bacteriochlorophyll dimer)-positive (bacteriopheophytin)-negative radical pair in bacterial photosynthesis. Isr. J. Chem., 28 1559168. 

This chapter reviews several gas-phase studies involving atoms, simple molecules, van der Waals complexes and clusters. Electron-transfer reactions are central processes in a variety of scientific disciplines as outlined in a recent review by Bixon and Jortner [1]. We highlight here the current understanding in the dynamics of the gas-phase electron-transfer reactions, and end the chapter by presenting work which intends to bridge the gap between the standard knowledge of electron-transfer reactions in the gas phase and in condensed phases. 

M. Bixon, J. Jortner, M. Plato, and M. E. Michel-Beyerle, The Bacterial Reaction Center, Structure and Dynamics, J. Breton and A. Vermeglio, Eds., Plenum, New York, 1988, pp. 399-419. 

Forty years after Kramers seminal paper on the effect of solvent dynamics on chemical reaction rates (Kramers, 1940), Zusman (1980) was the first to consider the effect of solvent dynamics on ET reactions, and later treatments have been provided by Friedman and Newton (1982), Calef and Wolynes (1983a, 1983b), Sumi and Marcus (1986), Marcus and Sumi (1986), Onuchic et al. (1986), Rips and Jortner (1987), Jortner and Bixon (1987) and Bixon and Jortner (1993). The response of a solvent to a change in local electric field can be characterised by a relaxation time, r. For a polar solvent, % is the longitudinal or constant charge solvent dielectric relaxation time given by, where is the usual constant field dielectric relaxation time... 

Bixon M. and Jortner J. (1993), Solvent dynamics and electron transfer , Chem. Phys. 176, 467-481. 

J. Jortner and M. Bixon, in Femtochemistry and Femtobiology Ultrafast Reaction Dynamics on Atomic-Scale Resolution, V. Sundstrdm, ed.. Imperial College Press, 1977, p. 349. 

The theory of the dynamics of molecules after optical excitation has been known for a very long time. In particular, we note the contributions of Bixon and Jortner,1 Tramer and Voltz,2 and Robinson and Langhoff.3 The effects of the coherence widths of the light sources used has received less attention 4 we therefore give a rather more detailed treatment here. 

When a bright basis-state is embedded in a dense manifold (quasi-continuum) of dark basis-states, a variety of dynamical processes ensue (Bixon and Jortner, 1968 Rhodes, 1983). These include Intramolecular Vibrational Redistribution (IVR), Inter-System Crossing (ISC), and Internal Conversion (IC). At t = 0, the bright basis state, which is not an eigenstate of H, is prepared, k(O) = bright ... 

ELECTRON TRANSFER DYNAMICS IN PHOTOSYNTHESIS JOSHUA JORTNER and M. BIXON... 

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