Bixon-Jortner approach

Sharf and Fischer14) have developed a new approach to account for the lack of a complete cancellation of intensity at the dip in the Fano line, in terms of the Fano treatment of a discrete state and a number of continua. It was shown that the Bixon-Jortner description of the quasi-continuum as a manifold of equally spaced levels with constant interactions with the discrete state and with constant transition moments from the ground state, does not comply with the quantum-... 

Figure 9.22. Arrhenius plot of experimental data [156b] (dash-dotted) and several theoretical predictions for the ET reaction rate in betaine-30 in glycerol triacetine Sumi-Marcus [89] (-H), Jortner-Bixon [96a] ( ), Bixon-Jortner [96b] (O), Walker et al. [156b] (dashed), and Fuchs-Schriber [127] (solid and error bars). The latter is based on the Markovian discretized reduced density matrix approach. (Reproduced from [127] with permission. Copyright (1996) by the American Institute of Physics.)...

The student of chemical kinetics wishing to explore these matters will soon lind his or her way to the classic paper of O. K. Rice in 1933 [33.R] via the reformulation of Fano [61.F2] and further development by Bixon Jortner [68.B1]. Stepping stones in the treatment of randomisation in unimolecular reactions include those of Gill Laidler [59.G], Slater [59.S2,67.S1], Mies Krauss [66.M], Sole [67.S2], Gelbart, S. A. Rice Freed [70.G1], O. K. Rice [71.Rl], Bunker Hase [73.B2], but the approaches represented are quite varied a review of some of these ideas can be found in [79.0]. 

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. 

In the golden rule approach, developed by Jortner, Bixon and others (Kestner et al., 1974 Ulstrap and Jortner, 1975 Jortner, 1976 Siders and Marcus, 1981a and 1981b Bixon and Jortner, 1982), D and A are treated as weakly coupled but distinct entities and ET as a nonadiabatic radiationless transition between them governed by Fermi s golden rule, which may be written in the form... 

As the bright state mixes with more and more dark states, the resultant lineshape evolves toward a smooth Lorentzian shape (Bixon and Jortner, 1968). The width of this composite line approaches that predicted by Fermi s Golden rule formula... 

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