Amplitudes, reaction path states

Free cw-azobenzene, excited at 480 nm displays a biexponential decay of the excited state Si with time constants of 0.1 ps and 0.9 ps. Here the ultrafast kinetic component dominates the absorption change (it contains 90 % of the whole amplitude). A direct interpretation would relate the fast component to a free isomerizational motion, where the most direct reaction path on the Si and So potential energy surface is used without disturbance. The slower process may be assigned to a less direct motion due to hindrance by the surrounding solvent molecules. This interpretation is supported by the observation of the absorption changes in the APB and AMPB peptides. Here both reaction parts are slowed down by a factor of 2 - 3 and both show similar amplitudes The peptide molecules hinder the motion of the azobenzene switch and slow down considerably the initial kinetics. However, in all samples the transition to the ground state is finished within a few picoseconds. 

Figure 19b. Characterization of the reaction path curvature k(s) (thick solid line) in terms of adiabatic mode-curvature coupling amplitudes An,s(s) (dashed lines). The curve k(s) has been shifted by 0.5 units to more positive values to facilitate the distinction between k(s) and An s(s). For a definition of the internal coordinates, compare with Figure 17. The position of the transition state corresponds to s = 0 amul/2 Bohr and is indicated by a vertical line.

The quantity Q tS = Qts(R T) is the pseudo-partition function of the system at the transition state, the transition state location Rt being that value of the reaction coordinate R which, at a given T, minimizes Qts(R T). This partition function has its zero of energy on the reaction path where the potential is Vt = Vrxnpath(R ) The form of Qts will be described in detail below. Qreact is the partition function of the reactants a/at is the ratio of reactant and transition state symmetry factors and ge is the ratio of electronic degeneracy factors for the reactants and transition state. The incorporation of large amplitude transition state motion is through Oxg. 

Cycled Feed. The qualitative interpretation of responses to steps and pulses is often possible, but the quantitative exploitation of the data requires the numerical integration of nonlinear differential equations incorporated into a program for the search for the best parameters. A sinusoidal variation of a feed component concentration around a steady state value can be analyzed by the well developed methods of linear analysis if the relative amplitudes of the responses are under about 0.1. The application of these ideas to a modulated molecular beam was developed by Jones et al. ( 7) in 1972. A number of simple sequences of linear steps produces frequency responses shown in Fig. 7 (7). Here e is the ratio of product to reactant amplitude, n is the sticking probability, w is the forcing frequency, and k is the desorption rate constant for the product. For the series process k- is the rate constant of the surface reaction, and for the branched process P is the fraction reacting through path 1 and desorbing with a rate constant k. This method has recently been applied to the decomposition of hydrazine on Ir(lll) by Merrill and Sawin (35). 

The essential difference in the adiabatic treatment of torsion at the transition state is the need to use of two slow large amplitude degrees freedom, x, and the reaction coordinate,. s. The reaction coordinate may be described as the path of steepest descent from the saddlepoint, or through some other convenient method. Both of degrees of freedom (s,x) are treated adiabatically and thus are assumed to be slow compared to the -vibrations, although no particular time scale separation is presumed to exist between x and. s themselves. 

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