Nonstatistical product distribution

Degenerate rearrangement of bicyclo[3.1.0]hex-2-ene (Chart 2) has a PES, in which four degenerate products are separated through four degenerate TSs with the common energy plateau on the surface.9 Here, four compounds are identical except for the position of deuterium. The rearrangement from 4-exo isomer (6x) is expected to afford 4-endo (6n), 6-exo (7x), and 6-endo (7n) isomers in equal amount if the reaction follows statistical reaction theory (TST). Thus, this reaction provides a situation previously presented by Carpenter to predict nonstatistical product distribution due to dynamics effect.1... 

Flash vacuum thermolysis of the formal Diels-Alder adduct (10) of acetyl-methyloxirene to tetramethyl-l,2,4,5-benzenetetracarboxylate to give acetyl-methylketene (15, in Scheme 1) was examined in an attempt to find an example of nonstatistical dynamics effect on product distribution.29 With two carbon-13-labeled starting materials ( and show the labeled carbon in separated experiments), the reaction yielded 15 with different 13C locations. It was originally expected that 10 would give 12, which then via carbene formation would yield 15a and 15b. The ratio of the two products was anticipated to show the occurrence of nonstatistical product distributions. Compound 15c might be formed via 12 and 13, but this route was considered to be minor since 13 was much unstable than 14. 

When a reaction involves multiple bonding changes, a question may arise whether the bonding changes occur by a stepwise or concerted pathway. An answer to such a question based on the classical reaction theory is that the reaction proceeds by a concerted pathway, by a stepwise pathway, or by a mixture of the two separate pathways. However, if one takes into account dynamic effects, the answer to the question of concerted versus stepwise may be much more complex. It is interesting to point out here that the case reported by Singleton for the ene reaction affords a case, where stepwise mechanism can dynamically operate on a concerted PES. This contrasts with the reactions described in section Nonstatistical Product Distribution , in which the... 

The dynamics effect on path bifurcation and nonstatistical product distribution on a slightly perturbed symmetrical PES have also been reported for the C=N isomerization of benzylideneanilines.60... 

Second, there is no difference in the product distribution at different temperatures. This is a sign of nonstatistical dynamics. 

This notion of a molecule taking a direct path suggests that product distribution should be time dependent the path to the rs well is shorter than the paths across the caldera to the ii or ia wells. During the first 150 fs of trajectory time, virtually, the only product formed is rs. After 200 fs, the ii and rs products are formed equally. The ia product slowly accrues. This time dependence is another indicator of nonstatistical dynamics. 

The nonstatistical population is the group of molecules that directly cross the diradical and produce 32x. Carpenter hypothesized that with increasing pressure, collisions will become more common such that energy will be redistributed away from the modes that lead to direct crossing of the diradical, yielding a more statistical product distribution. In other words, collisions provide the barrier so that the momentum can be redirected. The reaction of 2>l-d2 was carried out in supercritical propane in order to control the pressure. The ratio of 32x to 32n did... 

To try to distinguish whether 102 is intervening, Carpenter carried out the photolysis of a different labeled version of 98 (namely, 98 ). The resulting product distribution is shown in Scheme 8.13. It appears that the reaction predominantly passes through 102, but the ratio of products that come from 100 nonetheless shows nonstatistical behavior. 

Rice J, Baronavski A (1991) Nonstatistical CO product distributions from the hot H-atom reaction, H + CO2 OH -F CO. J Chem Phys 94 1006... 

A kinetic isotope effect observed by a single reactant, having isotopic atoms at equivalent reactive positions, which reacts to produce isotopomeric products with a nonstatistical distribution. The pathway favored will be the one having lower force constants for the displacement of the isotopic nuclei in the transition state. 

A strong motivation for the Rice et al. [99] simulations was to try to interpret the Zhao et al. [33] observations that the HONO elimination channel dominates while the N-N bond rupture reaction does not occur. A possible explanation is that the nascent CH2NN02 product of the RDX ring fission reaction is highly excited and has a nonstatistical distribution of energy. Sewell and Thompson [35] estimated that it may be formed with 55 to 65 kcal/mol of energy, which is well in excess of the predicted energy... 

Recent years have also witnessed exciting developments in the active control of unimolecular reactions [30,31]. Reactants can be prepared and their evolution interfered with on very short time scales, and coherent hght sources can be used to imprint information on molecular systems so as to produce more or less of specified products. Because a well-controlled unimolecular reaction is highly nonstatistical and presents an excellent example in which any statistical theory of the reaction dynamics would terribly fail, it is instmctive to comment on how to view the vast control possibihties, on the one hand, and various statistical theories of reaction rate, on the other hand. Note first that a controlled unimolecular reaction, most often subject to one or more external fields and manipulated within a very short time scale, undergoes nonequilibrium processes and is therefore not expected to be describable by any unimolecular reaction rate theory that assumes the existence of an equilibrium distribution of the internal energy of the molecule. Second, strong deviations Ifom statistical behavior in an uncontrolled unimolecular reaction can imply the existence of order in chaos and thus more possibilities for inexpensive active control of product formation. Third, most control scenarios rely on quantum interference effects that are neglected in classical reaction rate theory. Clearly, then, studies of controlled reaction dynamics and studies of statistical reaction rate theory complement each other. 

The situation when the gas is isotopically scrambled, however, is very different and indeed the experimentally observed measured quantity is also very different. When the gas is isotopically scrambled, one does not measure these specific ratios of rate constants. Instead, a statistical steady-state, such as Q -F OO QOO QO + O and in the above example O + QQ OQQ OQ + Q, exists at all energies, and now the energy distribution of the vibrationally excited intermediates is that which is dictated by the steady-state equations for the above reactions, and not by that of a vibrationally hot intermediate formed solely via one channel. Under such conditions all energies of the intermediate are statistically accessible, if not from one side of the reaction intermediate then from the other. Phrased differently, the isotopic composition of the collisionally stabilized product Q3 or QO2 or will typically differ from that of the vibrationally excited species Q or QO2, since the intrinsic lifetime of the latter is isotope-dependent, as discussed in [15]. The usual RRKM-type pressure-dependent rate expression and conventional isotope effect results, modified by the nonstatistical effect discussed earlier [15]. 

Isotope effects like the above, involving a direct or indirect comparison of the rates of reaction of iso-TOPOLOGUEs, are called intermolecular, in contrast to intramolecular isotope effects, in which a single substrate reacts to produce a nonstatistical distribution of isotopologue product molecules. 

E. Tenailleau, P.Lancelin, R.J. Robins, S. Akoka (2004 a) NMR approach to the quantification of nonstatistical distribution in natural products vaniUin. Anal. Chem. 72, 3818-3825... 

Figure 21 Surprisal plot for the vibrationally hot HF product from the four-center elimination reaction CH,CF, - CH2 = CF + HF. The energy rich, long living, CH,CF, is produced via two routes as shown. The HF vibrational distribution is rather nonstatistical, but is almost the same for both routes. (Adapted from E. Zamir and R. D. Levine, Chem. Phys. 52 253 (1980).) For recent experimental studies of elimination reactions see E. Arunan, S. J. Wategaonker, and D. W. Setser, J. Phys. Chem. 95 1539 (1991) T. R. Fletcher and R. Leone, J. Chem. Phys. 88 4720 (1988).)...

Rectangular velocity or energy spectra are not often observed because slow statistical dissociations of polyatomics form the products in a distribution of the translational energies, or because nonstatistical and direct dissociations generally are not characterized by isotropic product velocity distributions. 

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