Dissociation rate RRKM result

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]. 

The study of cyanobenzene ion treated an ion whose thermochemistry was already well studied by PEPICO. However, the TRPD result was at a substantially lower internal energy, so that the measured dissociation rate of 5 x 10 s at 4.10 eV internal energy was slower by more than an order of magnitude than the slowest dissociations probed by PEPICO. By extension of the known rate-energy curve nearer to threshold, this added quantitative confidence to the RRKM extrapolation and considerably strengthened the g value for Equation (5) of 3.02 eV assigned... 

When TRPD measurements are combined with PEPICO results, the dissociation rate-energy curve for styrene ion is known over perhaps the largest of any polyatomic ion s range. ° Simple RRKM theory gives an excellent fit (as does Klots thermodynamic formulation), and an extrapolated of 2.43 eV is derived. The thermochemistry for this dissociation to benzene ion plus acetylene [Equation (16)] is very well known from independent heats of formation, giving a calculated... 

To complete the RRKM calculations for the cluster dissociation rates and final bare 4EA molecule product distributions, the cluster binding energy E0 and the energy v of the chromophore vibrational state to be populated must be found. These can be estimated from selected fits to the experimental rates and intensities (Hineman et al. 1993a). The results of the rate and product distribution calculations are presented in Table 5-4. The predictions of the model are quite good—less than 30% error for all observations for the 4EA(N2)1 and 4EA(CH4), clusters. 

Figure 7.13 The effect of I on the benzene ion dissociation rate at a constant total energy of 5.3 eV. The solid lines are numerical results from an RRKM calculation in which the rotational constant of the H loss transition state was assumed to be identical to that of the benzene ion. K-mixing and no K-mixing are assumed in curves A and B, respectively. Taken with permission from Kiermeier et al. (1988).

Another time resolved approach involves measuring the natural fluorescence of the aniline back to the ground state. Figure 10.14 shows the product aniline formed with a rise time of 240 psec at an excitation energy of 718 cm. The slow decay is a result of the aniline fluorescence lifetime. However what governs the 240 psec rise time is it IVR, or the RRKM dissociation rate A clear answer to this question is not yet in hand in part because overlapping spectra for the dimer, the relaxed dimer, and... 

They confirmed the trend reported above the bigger the molecule is, the longer is its lifetime and the smaller is its dissociation rate constant (Table 7). Moreover, the dissociation rate constants so measured are in good agreement with RRKM calculations (Fig. 7) (72). All these results may be rationalized on the grounds of the following mechanism ... 

Such data collected at a number of ion energies leads to a k(E) vs E curve shov n in Figure 7. The solid lines in this figure are the results of a statistical theory calculation using the Rice-Rampserger-Kas-sel-Marcus (RRKM) formulation. Studies such as this one on many molecules have shov n that the RRKM theory is extremely useful and accurate in predicting the dissociation rate constants of ionic reactions. It is also very useful for determining the onset of dissociation. This is of interest both for fundamental reasons as v ell as for a very practical one. Dissociation onsets are often used to determine thermochemical properties of ions and free radicals. Consider the reaction... 

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. 

Results of a PEPICO study of the dissociation dynamics of 2-bromobutane ions have been analysed with tunnelling-corrected RRKM statistical theory using vibrational frequencies obtained from ab initio MO calculations. It has been concluded that the slow rate of loss of HBr, to form the but-2-ene ion, occurs via a concerted mechanism in which tunnelling is a feature of the proton transfer. 

Rice et al. [99] developed a global potential energy surface based on the Mowrey et al. [103] results and performed extensive classical trajectory calculations to study the dynamics of the CH2NN02 dissociation reactions. They calculated rates for reactions (III) and (IV) with classical barriers of 35 and 37 kcal/mol, respectively. They found that N-N bond fission dominates at low energy but that HONO elimination is competitive. Chakraborty and Lin [104] predict the opposite on the basis of their ab initio barriers and RRKM theory calculations. The two dissociations channels are closely competitive and it is not clear that ab initio methods are sufficiently reliable to distinguish between two reactions that have such similar energy requirements. Also, the Zhao et al. results [33] are not in accord with the theoretical predictions. 

Modern unimolecular theory has its origins in the work of Rice, Ramsberger and Kassel [44] who investigated the rate of dissociation of a molecule as a function of energy. Marcus and Rice [44] subsequently extended the theory to take account of quantum mechanical features. This extended theory, referred to as RRKM theory, is currently the most widely used approach and is usually the point of departure for more sophisticated treatments of unimolecular reactions. The key result of RRKM theory is that the microcanonical rate coefficient can be expressed as... 

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