Product energy distribution prior

Information theory was first applied [177] to chemical reactions in an attempt to compact and classify the energy distributions of reaction products. This is achieved by surprisal analysis, where the observed product energy distribution, say for vibration, P(v ), is compared with a non-specific prior distribution P°(v ). Then, the surprisal, I(v ), is given by... 

The other difference between the usual prior distribution and PST is that the former includes all of the product rotational degrees of freedom. Because of detailed angular momentum conservation in PST the rotational product energy distributions are no longer so simple. The details are explained in the section on PST. However, it is useful to summarize the results here. In the limit of the total J the full... 

In expressing the product energy distribution, we now use the degeneracies rather than the density of states and sum over the quantum numbers, rather than integrate over the energies. The prior PED for the NO + O products is thus given by ... 

The rotational PEDs for the dissociation of state-selected NO2 have been measured and analyzed using both the prior model and PST (Robie et al., 1992 Hunter et al., 1993). A convenient approximation is to assume that the product energy distributions are independent of the NO2 M and K quantum numbers. Three product angular momenta, 7no> - o> and must be combined to add up to the total angular momentum, convenience, the NO ii value is included in the Jj q term thereby adding either 0.5 or 1.5 to the rotational quantum number. The angular momenta are combined in two steps. The intermediate J is introduced which is defined by the vector addition J = Jno + that... 

A major difference between the prior and PST product energy distributions is that in PST the rotational degeneracies of the 0 atom and NO are intimately intertwined. On the other hand, in the prior distribution, the two terms are independent of each other so that the rotational degeneracies of the O atom and NO are simply multiplied together as in Eq. (9.24). 

Consider that the final effect of these collisionally induced internal energy deposition processes are the production of molecular species with a wide internal energy distribution, as shown in Fig. 3.14. Area A corresponds to the molecular species that have experienced a low internal energy uptake, while areas B and C correspond to molecular species experiencing internal energy deposition, so as to promote decomposition processes. In the case of C, the decomposition will take place inside the source prior to acceleration (and the decomposition products will be consequently detected in the usual MALDI spectrum),... 

Figure 3 Surprisal plots (18) for the HF vibrational state distribution from the exoergic H atom abstraction reaction F + (CH,)4C - (CH,),CCH2 + HF(v). (Bottom panel) The observed (by D. J. Bogan and D. W. Setser, J. Chem. Phys. 64 586 (1976)) distribution, P(v), open dots connected by a line, and the (so called, prior) distribution, P (v) full symbols, vs. the HF vibrational energy. The prior distribution is the one expected when all products final states are equally probable (18). The observed distribution is qualitatively different from the prior one and their deviance, the surprisal, —In(P(v)/P"(v)) is plotted vs. E/Ev, where Ev is the HF vibrational energy and E is the total energy, in the upper panel. One can interpret the linear dependence of the surprisal on the HF vibrational energy as reflecting the presence of a quantity which is conserved by the dynamics. (See, for example, ref. (108)). In this sense, surprisal analysis is analogous to the search for quantum numbers that are not destroyed by the intramolecular couplings.

Let us briefly discuss this approach. Its idea is the comparison of the experimentally obtained distribution with the so-called the prior distribution, which would be obtained under the condition of the equiprobable energy distribution over all degrees of freedom of the products. Prior distributions, which we designate as p° ( V) and / (n), have a maximum entropy and, hence, give the minimum of information about the dynamics of the reaction. The real distribution obtained in experiment has lower entropy than that of the a priori one. As model trajectory calculations and analysis of data of numerous experiments show, the distribution functions over rotational P N) and vibrational P n) states can be expressed through the corresponding a priori distributions as follows ... 

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