Silbey

Pfuegl W, Brown F L FI and Silbey R J 1998 Variance and width of absorption lines of single molecules in low temperature glasses J. Phys. Chem 108 6876-83... 

The simplest scheme that accounts for the destruction of phase coherence is the so-called stochastic interruption model [Nikitin and Korst 1965 Simonius 1978 Silbey and Harris 1989]. Suppose the process of free tunneling is interrupted by a sequence of collisions separated by time periods vo = to do After each collision the system forgets its initial phase, i.e., the off-diagonal matrix elements of the density matrix p go to zero, resulting in the density matrix p ... 

Therefore, at extremely low temperatures one may equally choose between TLS and say oscillator bath. The latter is usually supposed to be simpler to handle, but the TLS bath model, apart from its apparent relevance for glass theory, has some very attractive features [Mermin 1991 Suarez and Silbey 1991b Shimshoni and Cefen 1991]. 

There is a vast field in chemistry where the spin-boson model can serve practical purposes, namely, the exchange reactions of proton transfer in condensed media [Borgis et al. 1989 Suarez and Silbey 1991a Borgis and Hynes 1991 Morillo et al. 1989 Morillo and Cukier 1990]. 

The early approaches to this model used perturbative expansion for weak coupling [Silbey and Harris 1983]. Generally speaking, perturbation theory allows one to consider a TLS coupled to an arbitrary bath via the term where / is an operator that acts on the bath variables. The equations of motion in the Heisenberg representation for the a operators, 8c/8t = ih [H, d], have the form... 

Borgis et al. 1989 Suarez and Silbey 1991a], where q is a particular coupling coordinate from the set qj which modulates the barrier (we assume for simplicity that there is only one such coordinate), and the exponential form of A is accounted for by the Gamov-factor nature of this term. 

The analytic results for the spin-boson Hamiltonian with fluctuating tunneling matrix element (5.67) are investigated in detail by Suarez and Silbey [1991a]. Here we discuss only the situation when the qi vibration is quantum, i.e., (o P P 1. When the bath is classical, cojP, j 1, the rate... 

The role of two-phonon processes in the relaxation of tunneling systems has been analyzed by Silbey and Trommsdorf [1990]. Unlike the model of TLS coupled linearly to a harmonic bath (2.39), bilinear coupling to phonons of the form Cijqiqja was considered. In the deformation potential approximation the coupling constant Cij is proportional to (y.cUj. There are two leading two-phonon processes with different dependence of the relaxation rate on temperature and energy gap, A = (A Two-phonon emission prevails at low temperatures, and it is... 

R.A. Alberty, R.J. Silbey, Physical Chemistry, John Wiley, New York, 1996. 

Boudreaux DS, Chance RR, Wolf JF, Shacklette LW, Bredas JL, Themans B, Andre JM, Silbey R (1986) J. Chem. Phys. 85 4584... 

There are two principal chemical concepts we will cover that are important for studying the natural environment. The first is thermodynamics, which describes whether a system is at equilibrium or if it can spontaneously change by undergoing chemical reaction. We review the main first principles and extend the discussion to electrochemistry. The second main concept is how fast chemical reactions take place if they start. This study of the rate of chemical change is called chemical kinetics. We examine selected natural systems in which the rate of change helps determine the state of the system. Finally, we briefly go over some natural examples where both thermodynamic and kinetic factors are important. This brief chapter cannot provide the depth of treatment found in a textbook fully devoted to these physical chemical subjects. Those who wish a more detailed discussion of these concepts might turn to one of the following texts Atkins (1994), Levine (1995), Alberty and Silbey (1997). 

Intersystem crossing from Si to and higher triplet states has also been reported in some aromatic molecules Li, R. Lim, E.C. Chem. Phys., 1972, 57, 605 Sharf, B. Silbey, R. 

R. A. Alberty and R. J. Silbey (1996) Physical Chemistry, 2nd edition (John Wiley Sons, New York). 

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