Reaction mechanisms, uncertainty principle

The considerations presented above were based on the specific assumption that the catalytic reaction of the serine proteases involves mechanism a of Fig. 7.2. However, one can argue that the relevant mechanism is mechanism b (the so-called charge-relay mechanism ). In principle the proper procedure, in case of uncertainty about the actual mechanism, is to perform the calculations for the different alternative mechanisms and to find out which of the calculated activation barriers reproduces the observed one. This procedure, however, can be used with confidence only if the calculations are sufficiently reliable. Fortunately, in many cases one can judge the feasibility of different mechanisms without fully quantitative calculations by a simple conceptual consideration based on the EVB philosophy. To see this point let us consider the feasibility of the charge-relay mechanism (mechanism b) as an alternative to mechanism a. Starting from Fig. 7.2 we note that the energetics of route b can be obtained from the difference between the activation barriers of route b and route a by... 

If there are more than two free radical intermediates, the mechanism (of a reaction) cannot be deduced by a kinetic study based upon analysis of all products and reactants (32)—the uncertainty principle of reaction mechanism. 

Scheme C is sufficiently complex that Johnstons uncertainty principle applies. It is therefore impossible to prove the scheme without relying heavily on data acquired from other areas. Such information and particularly the general consistency of the rate constants required by the mechanism suggest that it is probably near the truth. Assuming its correctness, the experimental data can be treated moderately rigorously if it is noted that at 100 °C. all the ROO radicals which abstract H give hydroperoxide, and that the only small additional source of hydroperoxide will be reaction of ROO with CH30, while the remaining ROO radicals will first form RO and then either acetone or tert-butyl alcohol. Measurement of the ratio (hydroperoxide)/(acetone + tert-butyl alcohol)172 will then give /c7/fc41/2.

An often-overlooked aspect of standard reaction mechanistic thought is that it really addresses only half of the picture. We talk about the positions of the atoms during the course of the reaction and the relative energies of points along the reaction path, but no mention is made of the time evolution of this process. In classical mechanics, description of a reactive system requires not just the particle positions but their momenta as well. The same is true for a quantum mechanical description, though one must keep in mind the limits imposed by the Heisenberg Uncertainty Principle. A complete description of a molecular reaction requires knowledge of both the position and the momenrnm of every atom for the entire time it takes for reactants to convert into products. This kind of description falls under the term molecular dynamics (MD). 

All these reactions are highly exothermic, and these disproportionations occur at a rate of the same order of magnitude as the corresponding recombinations.Thus none of them can be excluded a -priori. For the recombination, there are six reactions and six different products. For the disproportionations, there are nine reactions but only six products (one of which is the reactant). Here is an example of the uncertainty principle of reaction mechanisms. Each of the products is produced by three different reactions thus a kinetic study based on analysis of products alone will never characterize any of the reactions. 

HIRSCHPELDER and WIGRER /6/ first discussed the validity of activated complex theory from the viewpoint of quantum mechanics. They showed that the notion of an activated complex is compatible with Heisenberg s uncertainty principle only when the potential V(x) along the reaction path in the saddle-point region is sufficiently flat that the condition... 

This model of reactions does not violate the Heisenberg uncertainty principle. Reaction mechanisms, defined as these homotopy equivalence classes, are fully quantum chemical within the context of any potential energy surface model. 

One might wonder since classical trajectory calculations on quite complicated reactions have been performed for some time [20], why the coordinate problem described above really is so obtrusive in the quantum mechanical case. The reason for this is simply that quantum mechanical calculations must, by virtue of the Uncertainty Principle describe all regions of the available coordinate space at once. Classical trajectory calculations effectively access only a single point in this space at a time, which by comparison is a great deal easier to arrange. In fact the coordinate problem encumbers clas-... 

S. A. Rice My answer to Prof. Manz is that, as I indicated in my presentation, both the Brumer-Shapiro and the Tannor-Rice control schemes have been verified experimentally. To date, control of the branching ratio in a chemical reaction, or of any other process, by use of temporally and spectrally shaped laser fields has not been experimentally demonstrated. However, since all of the control schemes are based on the fundamental principles of quantum mechanics, it would be very strange (and disturbing) if they were not to be verified. This statement is not intended either to demean the experimental difficulties that must be overcome before any verification can be achieved or to imply that verification is unnecessary. Even though the principles of the several proposed control schemes are not in question, the implementation of the analysis of any particular case involves approximations, for example, the neglect of the influence of some states of the molecule on the reaction. Moreover, for lack of sufficient information, our understanding of the robustness of the proposed control schemes to the inevitable uncertainties introduced by, for example, fluctuations in the laser field, is very limited. Certainly, experimental verification of the various control schemes in a variety of cases will be very valuable. 

The reflection principle approach (see article by Jost in this issue) produces essentially perfect agreement with experiment but it is not able to provide vibrational structure. Therefore the time-dependent techniques are important for indirect photodissociation, of which there are many examples in atmospheric chemistry, including HCHO, SO2, NO2,02, CO, HCl, H2O and O3. Many studies have shown how isotopic analysis is able to provide valuable insight concerning atmospheric photochemical reactions, and emissions sources and loss mechanisms. One of the largest uncertainties in projections of future climate is the ability to predict greenhouse gas concentrations, which depend on accurate knowledge of their sources, sinks and atmospheric photochemistry. 

Reaction rate constants represent the quantitative base for the kinetic model of a chemical transformation. However, while some are quite accurate, the range of uncertainty of others is very broad. Overcoming this problem is a question of principle when studying the mechanism of a multistep chemical reaction. 

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