Unimolecular decay

At higher concentrations in solution, the photodimerization of tS has been studied by means of picosecond electronic absorption spectroscopy. The 5i state of tS in benzene at 22°C is quenched with a diffusion-controlled rate constant of 2.03 X lO M s to give a new reactive intermediate exhibiting an absorption maximum at 480 nm. This new species decays unimolecularly with a rate constant of (2.40 0.37) X 10 s. It has tentatively been assigned to either the excimer or a biradicaloid species located at the pericyclic minimum. 

The fate of G in the absence of any additive is as yet unknown. It decays bimo-lecularly with a rate constant of some 108 dm3 mol-1 s 1 (Faraggi et al. 1996), but there is increasing evidence that in competition, at least at elevated pH [pKa(G-) = 10.8], its radical anion also decays unimolecularly [k = 5 x 103 s 1 at pH 11 in the case of Guo and dGuo Faraggi and Klapper 1994 Faraggi et al. 1996]. The nature of this unimolecular transformation is as yet unknown. 

Examples radioactive decay, unimolecular decomposition, SN1,E1 (carbocation), molecular rearrangement... 

When AB v) is vibrationally excited, the transient complex [AB. CX may either decay unimolecularly back to the reactants or, alternatively, undergo vibrational predissociation into AB v < v) + C, with a rate constant k p. 

In order to estimate the stability of triplet carbenes (19) under ambient conditions, laser flash photolysis ( LFP) [26] was carried out on the precursor diazomethanes (18) in solution at room temperature. The transient absorption bands formed upon the flash were recorded by a multi-channel detector. These bands were assigned to the triplet carbenes (19) by comparison with those obtained in matrix at low temperature. The kinetic information was then available by monitoring the decay of the transient absorption with oscillographic tracer. When triplet carbenes decayed unimolecularly, which is often so, lifetime (x) can be determined. However when the decay did not follow a single exponential, which is sometimes the case, x cannot be determined. In this case, a half-life (ti/2) is estimated from the decay curve as a rough measure of the stability. 

On the other hand, 31c decayed unimolecularly almost exclusively with of... 

A specific unimolecular rate constant for the decay of a highly excited molecule at energy E and angular momentum J takes the fomr... 

A situation that arises from the intramolecular dynamics of A and completely distinct from apparent non-RRKM behaviour is intrinsic non-RRKM behaviour [9], By this, it is meant that A has a non-random P(t) even if the internal vibrational states of A are prepared randomly. This situation arises when transitions between individual molecular vibrational/rotational states are slower than transitions leading to products. As a result, the vibrational states do not have equal dissociation probabilities. In tenns of classical phase space dynamics, slow transitions between the states occur when the reactant phase space is metrically decomposable [13,14] on the timescale of the imimolecular reaction and there is at least one bottleneck [9] in the molecular phase space other than the one defining the transition state. An intrinsic non-RRKM molecule decays non-exponentially with a time-dependent unimolecular rate constant or exponentially with a rate constant different from that of RRKM theory. 

In the above discussion it was assumed that the barriers are low for transitions between the different confonnations of the fluxional molecule, as depicted in figure A3.12.5 and therefore the transitions occur on a timescale much shorter than the RRKM lifetime. This is the rapid IVR assumption of RRKM theory discussed in section A3.12.2. Accordingly, an initial microcanonical ensemble over all the confonnations decays exponentially. However, for some fluxional molecules, transitions between the different confonnations may be slower than the RRKM rate, giving rise to bottlenecks in the unimolecular dissociation [4, ]. The ensuing lifetime distribution, equation (A3.12.7), will be non-exponential, as is the case for intrinsic non-RRKM dynamics, for an mitial microcanonical ensemble of molecular states. 

To detect tlie initial apparent non-RRKM decay, one has to monitor the reaction at short times. This can be perfomied by studying the unimolecular decomposition at high pressures, where collisional stabilization competes with the rate of IVR. The first successful detection of apparent non-RRKM behaviour was accomplished by Rabinovitch and co-workers [115], who used chemical activation to prepare vibrationally excited hexafluorobicyclopropyl-d2 ... 

Miller W H, Hernandez R, Moore C B and Polik W F A 1990 Transition state theory-based statistical distribution of unimolecular decay rates with application to unimolecular decomposition of formaldehyde J. Chem. Phys. 93 5657-66... 

Mandelshtam V A and Taylor H S 1997 Spectral analysis of time correlation function for a dissipative dynamical system using filter diagonalization application to calculation of unimolecular decay rates Phys. Rev. Lett. 78 3274... 

From this expression, it is obvious that the rate is proportional to the concentration of A, and k is the proportionality constant, or rate constant, k has the units of (time) usually sec is a function of [A] to the first power, or, in the terminology of kinetics, v is first-order with respect to A. For an elementary reaction, the order for any reactant is given by its exponent in the rate equation. The number of molecules that must simultaneously interact is defined as the molecularity of the reaction. Thus, the simple elementary reaction of A P is a first-order reaction. Figure 14.4 portrays the course of a first-order reaction as a function of time. The rate of decay of a radioactive isotope, like or is a first-order reaction, as is an intramolecular rearrangement, such as A P. Both are unimolecular reactions (the molecularity equals 1). 

Any forward reaction that can take place is also accompanied, in principle at least, by the corresponding reverse reaction. Therefore, the unimolecular decay of 03 in step 1 of the two-step mechanism is accompanied by the formation reaction... 

The equation for the decay of a nucleus (parent nucleus - daughter nucleus + radiation) has exactly the same form as a unimolecular elementary reaction (Section 13.7), with an unstable nucleus taking the place of a reactant molecule. This type of decay is expected for a process that does not depend on any external factors but only on the instability of the nucleus. The rate of nuclear decay depends only on the identity of the isotope, not on its chemical form or temperature. 

As in a unimolecular chemical reaction, the rate law for nuclear decay is first order. That is, the relation between the rate of decay and the number N of radioactive nuclei present is given by the law of radioactive decay ... 

Collisions at low ion energies (where Equation 1 can be applied) lead to a short-lived complex between the ion and the molecule—i.e., both collision partners move with the same linear velocity in the direction of the incident ion. The decay of the complex may be described by the theory of unimolecular rate processes if its excess energy can fluctuate between the various internal degrees of freedom. For example, the isotope effect in the reaction of Ar+ with HD may be explained by the properties of... 

Three basic types of fundamental processes are recognized unimolecular, bimolecular and termolecular. Unimolecular processes are reactions involving only one reactant molecule. Radioactive decay is an example of a unimolecular process ... 

Hence the steady-state population of triplets should increase under heavy-atom perturbation. However, this conclusion is valid only if unimolecular decay is the main route leading to triplet state depopulation. If bimolecular triplet quenching as shown below is more important than unimolecular decay by several orders of magnitude, kd could be increased as much or more than klte without decreasing the steady state triplet population<136) ... 

The overall trend is explainable, at least qualitatively, with simple unimolecular decay theory. When a correction term is incorporated into the theoretical collision limit to account for the intrinsic surface site reactivity in the bulk, excellent agreement is obtained with the overall reactivity. In considering the overall trends, certain clusters, namely Cu+, Cuj, and Cu in particular, displayed somewhat anomalous reactivities which might be associated with structural and/or electronic effects. 

In general, intramolecular isomerization in coordinatively unsaturated species would be expected to occur much faster than bimolecular processes. Some isomerizations, like those occurring with W(CO)4CS (47) are anticipated to be very fast, because they are associated with electronic relaxation. Assuming reasonable values for activation energies and A-factors, one predicts that, in solution, many isomerizations will have half-lives at room temperature in the range 10 7 to 10 6 seconds. The principal means of identifying transients in uv-visible flash photolysis is decay kinetics and their variation with reaction conditions. Such identification will be difficult if not impossible with unimolecular isomerization, particularly since uv-visible absorptions are not very sensitive to structural changes (see Section I,B). These restrictions do not apply to time-resolved IR measurements, which should have wide applications in this area. 

The development of comprehensive models for transition metal carbonyl photochemistry requires that three types of data be obtained. First, information on the dynamics of the photochemical event is needed. Which reactant electronic states are involved What is the role of radiationless transitions Second, what are the primary photoproducts Are they stable with respect to unimolecular decay Can the unsaturated species produced by photolysis be spectroscopically characterized in the absence of solvent Finally, we require thermochemical and kinetic data i.e. metal-ligand bond dissociation energies and association rate constants. We describe below how such data is being obtained in our laboratory. 

Most importantly, the careful kinetic analysis of the rise and decay of the transient species in equation (69) shows that the decarboxylation of Ph2C(OH)CO occurs within a few picoseconds (kc c = (2-8) x 1011 s-1). The observation of such ultrafast (decarboxylation) rate constants, which nearly approach those of barrier-free unimolecular reactions, suggests that the advances in time-resolved spectroscopy can be exploited to probe the transition state for C—C bond cleavages via charge-transfer photolysis. 

Next, we discuss the J = 0 calculations of bound and pseudobound vibrational states reported elsewhere [12] for Li3 in its first-excited electronic doublet state. A total of 1944 (1675), 1787 (1732), and 2349 (2387) vibrational states of A, Ai, and E symmetries have been computed without (with) consideration of the GP effect up to the Li2(63 X)u) +Li dissociation threshold of 0.0422 eV. Figure 9 shows the energy levels that have been calculated without consideration of the GP effect up to the dissociation threshold of the lower surface, 1.0560eV, in a total of 41, 16, and 51 levels of A], A2, and E symmetries. Note that they are genuine bound states. On the other hand, the cone states above the dissociation energy of the lower surface are embedded in a continuum, and hence appear as resonances in scattering experiments or long-lived complexes in unimolecular decay experiments. They are therefore pseudobound states or resonance states if the full two-state nonadiabatic problem is considered. The lowest levels of A, A2, and E symmetries lie at —1.4282,... 

Wahner, A., Zetzsch, C. (1983) Rate constants for the addition of hydroxyl radicals to aromatics (benzene, p-chloroaniline, and o-, m- and p-dichlorobenzene) and the unimolecular decay of the adduct. Kinetics into a quasi-equilibrium. J. Phys. Chem. 87, 4945 -951. 

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