Irreversible decay

Koppel [180] has performed exact time-dependent quantum wave-packet propagations for this model, the results of which are depicted in Fig. 2A. He showed that the initially excited C state decays irreversibly into the X state within 250 fs. The decay is nonexponential and exhibits a pronounced beating of the C and B state populations. This model will allow us to test mixed quantum-classical approaches for multistate systems with several conical intersections. 

Thus, the primary ESR spectra decayed irreversibly at temperatures characteristic for the substrate, typically near 100 K they were replaced by a second type of spectrum, in which the protons at one cyclopropane center no longer interact with the electron spin. This coupling pattern was interpreted as evidence for a ring-opened trimethylene species (109) in which one terminal carbon has rotated into an orthogonal orientation [293, 296, 297],... 

Finally, the spontaneous liberation of free radicals via the unimolecular decay of CIII is feasible, since the peroxyl radical is not covalently bound to the porphyrin (pathway 2). This assumption is supported by experimental evidence, which demonstrates that in the presence of excess H202 and no reductant, CIII decays irreversibly into GS and superoxide species in lignin peroxidase [46], horseradish peroxidase [104], myeloperoxidase [51, 105, 106]. 

Of course, nickel alcoholate can give a classical P elimination21 leading to starting ketone and nickel hydride species. These latter reduce again or decay irreversibly thus explaining the reappearance of the ketone. 

The statistical limit for IVR is attained when the initially prepared zero-order state j) is coupled to a sufficiently large number of other zero-order states, /, so that s) appears to decay irreversibly and practically to zero, within the experimental time scale. A recent theoretical treatment of this model has been given by Voth (1987, 1988). For this situation the probability cj(t)p, Eq. (4.17), of being in the initially prepared state js) is given by the exponential... 

Equation (7) expresses the time-dependent quantum mechanical motion of the system to all orders. As it turns out formally and compufafionally, for an isolafed unsfable stafe decaying irreversibly into a pure continuum, there are three principal regions of fime durafion thaf distinguish fhe behavior of a t), e.g.. Refs. [6,7,37,89,94 and chapfers 7 and 9 in this volume] ... 

Evidence for M---H-S interaction is less clear, but protonation of [Fe(SMe)-(CO)3(PEt3)] at -80°C gives a species with an abnormal high-field NMR resonance for the S-H proton near 5 — 8. This resonance decays irreversibly on wanning, and an isomeric mixture of hydride-thiolate complexes results. Low-temperature (-57°C) IR spectra of the initial protonation product in Eq. (13.13) shows a Vco band at 1870 cm consistent with an Fe" rather than an Fc" complex. On warming, the band converts to others that match those observed for the hydride-... 

A a radical was first generated radical. Ratio of monoradicals to biradicals is about 5 4. Mixture (1 5) of meso and rac. diastereoisomers. The biradical has a triplet ground state, zero field coupling D = 9.28 mT and = 0 mT. Above 130 K, signals decayed irreversibly. 

Signal intensity decays irreversibly upon raising the temperature. No resolved hyperfine coupling due to methyl hydrogens. 

Radioactive decay Irreversible decline in the activity of a radionuclide Important attenuation mechanism when file half-life for decay is < residence time in flow system results in by-products... 

The key equation in the analysis, however, is the boimdary condition giving the local reaction rate r. For simplicity we assume that the reaction proceeds by formation of an activated complex C in equihbrium with the reactants A and S. The equilibrium constant for this reaction is taken as K. The complex then decays irreversibly with a rate constant fc, to form the product B in the fluid phase thus we have... 

Above 193K t-Bu02 decay irreversibly with second-order kinetics, i.e., ... 

There have been several reports of t-butylperoxy radicals undergoing self-reaction with first-order kinetics (21,26). Now it is well known that decay of certain radicals can be first-order if the radical is in equilibrium with a diamagnetic dimer and substantial concentrations of dimer are present at the decay temperature (27-28). t-Butylperoxy radicals do not fall into this category because the tetroxide is completely dissociated before irreversible radical decay occurs. Other less persistent t-ROa do, however, decay irreversibly in the presence of tetroxide and in these cases first-order decay kinetics are observed (29) because radical decay monitors tetroxide decomposition. 

There is evidence from e.p.r. studies (29>36) that S-RO2 exist in equilibrium with a tetroxide below 1T3K and in this respect behave analogously to t-ROa . Unfortunately s-ROa decay irreversibly before the tetroxide is completely dissociated and values of the equilibrium constant cannot be estimated. It would, however, appear that the thermodynamic parameters for s-ROa are similar to those for t-ROa, e.g., AH° -7 kcal mol and AS° <-25 cal deg mol for isopropylperoxy. 

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