Unimolecular dissociation lifetime

C. Radiative and Unimolecular Dissociation Lifetimes of Chemically Activated Ions... 

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. 

A covalent bond (or particular nomial mode) in the van der Waals molecule (e.g. the I2 bond in l2-He) can be selectively excited, and what is usually observed experimentally is that the unimolecular dissociation rate constant is orders of magnitude smaller than the RRKM prediction. This is thought to result from weak coupling between the excited high-frequency intramolecular mode and the low-frequency van der Waals intemiolecular modes [83]. This coupling may be highly mode specific. Exciting the two different HE stretch modes in the (HF)2 dimer with one quantum results in lifetimes which differ by a factor of 24 [84]. Other van der Waals molecules studied include (NO)2 [85], NO-HF [ ], and (C2i J )2 [87]. 

Hase s trajectory value for the association rate constant, /cp of 1.04 cm- s maybe used in conjunction with the above Langevin value of the collisional stabilization rate constant to yield a unimolecular dissociation rate constant of 3.75 x 10 ° s and a lifetime of 27 ps. In each case, these values are in excellent agreement with the order of magnitude of lifetimes predicted by Hase s calculations for cr/CHjCl collisions at relative translational energies of 1 kcal mor , rotational temperatures of 300 K, and vibrational energies equal to the zero-point energy of the system. 

The relatively long timescales of the ionization, isolation, thermalization, reaction, and detection sequences associated with low-pressure FTICR experiments are generally thought to preclude the use of this technique as a means of examining the unimolecular dissociation of conventional metastable ions occurring on the microsecond to millisecond timescale. Nonetheless, as just demonstrated (Section IIIC), intermediates with this order of magnitude of lifetime are routinely formed in the bimolecular reactions of gaseous ions with neutral molecules at low pressures in the FTICR cell, as in Equation (13). 

If the distribution of transient intermediate lifetimes is similar to the time required for rf ejection, some of these species will be ejected from the FTICR cell before undergoing unimolecular dissociation and the overall intensity corresponding to the abundance of ejected ions will be lost from the second spectrum. The difference spectrum then corresponds to the mass spectrum of unimolecular dissociation products of those transient species that did live long enough to be ejected from the cell. If the intermediate is weakly bound, and/or contains relatively few atoms, a... 

Figure 16. Metastable ion cyclotron resonance (MICR) spectra for the unimolecular dissociation of the chemically activated adduct ion derived from association of the methoxymethyl cation with pivaldehyde during a 2-s reaction delay at a pressure of pivaldehyde of 1.0 x 10 torr. The three spectra correspond to values of rf amplitude appropriate to eject transient intermediates with lifetimes longer than (a) 60 ps, (b) 80 ps, and (c) 1 70 ps. A partial pressure of CH4 of 1.0 x 10 torr was also present to thermalize ions. The peak at m/z 125 is a secondary reaction product of m/z 85.

These, and similar data for other systems, demonstrate the tremendous potential that the MICR technique has for the qualitative elucidation of potential energy surfaces of relatively complex organic reactions. Once implementation of the quadrupolar excitation technique has been effected to relax ions to the cell center, the technique will become even more powerful, in that the determination of highly accurate unimolecular decomposition lifetimes of chemically activated intermediates will also become possible. No other technique offers such a powerful array of capabilities for the study of unimolecular dissociation mechanisms and rates. 

Whenever the absorbing species undergoes one or more processes that depletes its numbers, we say that it has a finite lifetime. For example, a species that undergoes unimolecular dissociation has a finite lifetime, as does an excited state of a molecule that decays by spontaneous emission of a photon. Any process that depletes the absorbing species contributes another source of time dependence for the dipole time correlation functions C(t) discussed above. This time dependence is usually modeled by appending, in a multiplicative manner, a factor exp(-ltl/x). This, in turn modifies the line shape function I(co) in a manner much like that discussed when treating the rotational diffusion case ... 

Diffusion of molecules in rigid glasses is negligible within the lifetimes of excited molecules, so that the main reactions are unimolecular dissociations and isomerization. These are rather similar to liquid state reactions, but the fragments cannot separate through diffusion and often recombine to restore the reactants. There are exceptions when the photoproducts are in fact more stable than the reactants, as in the case of photoeliminations. 

Additional experimental investigations and theoretical treatments of collisional deactivation processes have recently been reported from several laboratories,250 253 Temperature effects on the lifetimes of intermediate adducts formed in the 0 -C02 interaction and in other relatively simple processes have been examined by Meisels and co-workers.252 254 Here the theoretical treatment involves application of a modified RRKM approach to the unimolecular dissociation of the adduct and/or of the termolecular collision complex consisting of the adduct plus the deactivating species M,. 

If the lifetime of the excited resonance state is too long for direct measurement of the rate via the widths of the spectral features, one can use a third laser (the probe laser in Fig. 11) to resonantly promote the molecules from this level to a rovibrational level in the excited electronic state. The decrease of the total LIF signal as function of the delay time between pump and probe laser reflects the state-specific dissociation rate. The limitation of the SEP technique is that an excited state has to be found, which lives long enough and which is accessible by all three lasers. Molecules, which have been studied by SEP spectroscopy in the context of unimolecular dissociation, are HCO, DCO, HFCO and CH3O. 

Trim-ethylene is a moiety with a shallow potential energy well on the reaction path connecting cyclopropane and propylene. Its very short unimolecular lifetime, following different types of initial excitations, has been calculated from classical trajectories [343,344] and compared with both experiment [391] and quantum dynamics [392]. Excellent agreement is found. This is an example of a rather large molecule, for which classical mechanics accurately describes the unimolecular dissociation because of the shallow potential energy minimum and, thus, very short lifetime. 

In this chapter, we discussed the principle quantum mechanical effects inherent to the dynamics of unimolecular dissociation. The starting point of our analysis is the concept of discrete metastable states (resonances) in the dissociation continuum, introduced in Sect. 2 and then amply illustrated in Sects. 5 and 6. Resonances allow one to treat the spectroscopic and kinetic aspects of unimolecular dissociation on equal grounds — they are spectroscopically measurable states and, at the same time, the states in which a molecule can be temporally trapped so that it can be stabilized in collisions with bath particles. The main property of quantum state-resolved unimolecular dissociation is that the lifetimes and hence the dissociation rates strongly fluctuate from state to state — they are intimately related to the shape of the resonance wave functions in the potential well. These fluctuations are universal in that they are observed in mode-specific, statistical state-specific and mixed systems. Thus, the classical notion of an energy dependent reaction rate is not strictly valid in quantum mechanics Molecules activated with equal amounts of energy but in different resonance states can decay with drastically different rates. 

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