Quasiequilibrium theory

Statistical theories treat the decomposition of the reaction complex of ion-molecule interactions in an analogous manner to that employed for unimolecular decomposition reactions.466 One approach is that taken by the quasiequilibrium theory (QET).467 Its basic assumptions are (1) the rate of dissociation of the ion is slow relative to the rate of redistribution of energy among the internal degrees of freedom, both electronic and vibrational, of the ion and (2) each dissociation process may be described as a motion along a reaction coordinate separable from all other internal... 

Figure 43. Schematic diagram of CH3+ fragment ion angular distribution from He (2 S) + CH4 compared with quasiequilibrium theory (QET).

The most widely accepted theory of unimolecular reactions of polyatomic ions remains the quasiequilibrium theory (QET) [591, 720, 883], which is a treatment in the spirit and tradition of absolute reaction rate theory. Thus it is assumed that the rate of reaction of an ion is slow relative to the rate of energy flow among its vibrational modes and that each reaction may be described as a motion along a reaction coordinate which is separable from all other internal coordinates and which passes through a critical configuration (the transition state ). It is further assumed that ions formed in excited electronic states rapidly redistribute such electronic energy over vibrational levels of the ground electronic state. One further assumption is necessary, and that is that the time involved in the ionization process is short compared with subsequent reaction times. The QET model is taken as the theoretical basis of this review. QET leads to... 

Perhaps the point to emphasise in discussing theories of translational energy release is that the quasiequilibrium theory (QET) neither predicts nor seeks to describe energy release [576, 720], Neither does the Rice— Ramspergei Kassel—Marcus (RRKM) theory, which for the purposes of this discussion is equivalent to QET. Additional assumptions are necessary before QET can provide a basis for prediction of energy release (see Sect. 8.1.1) and the nature of these assumptions is as fundamental as the assumption of energy randomisation (ergodic hypothesis) or that of separability of the transition state reaction coordinate (Sect. 2.1). The only exception arises, in a sense by definition, with the case of the loose transition state [Sect. 8.1.1(a)]. 

The electron-impact mass spectrum of thietane calculated by quasiequilibrium theory agrees well with the observed spectrum. The chemical ionization (CH4) mass spectrum of thietane has been obtained along with that of thiols, disulfides, and other sulfides. The M + 1) peak is prominent but is surpassed in intensity by an (M + 5) peak. The (2M + 1) peak is more intense than the peak for the molecular ion (M). 

Baer, T Mayer, P.M. Statistical Rice-Ramsperger-Kassel-Marcus Quasiequilibrium Theory Calculations in Mass Spectrometry, J. Am. Soc. Mass Spectrom. 8, 103-115 (1997). 

In the ion-molecule community RRKM theory is widely known as quasiequilibrium theory (QET) see Ref. [6],... 

The formation of the complex has, in fact, been verified at 1.43 and 3.25 eV (LAB) of ion kinetic energy by the crossed molecular beam study of Wolfgang and co-workers [103, 140] (see Section 4.4.2). Also we can find some evidence that the complex formed in the reaction of C2H4 + C2H4 is an intimate complex [277—279]. In such cases, the application of the quasiequilibrium theory of unimolecular reactions to the ion-molecule complex would yield information on the distribution of the... 

We consider two such approaches here, one based on the quasiequilibrium theory of mass spectra and the other on the phase-space theory. In neither case is the principal utility of the model the ability to predict absolute rate constants or cross sections for particular channels. Such absolute rate parameters would require knowledge of the same for the formation of the ion-molecule intermediate and is not available. Rather, the strength of these two theories is in the prediction of relative rate parameters or branching ratios for the various channels. 

Quantitative applications of quasiequilibrium theory have eliminated this uncertainty in the average value of , the internal energy, and in the dispersion of . Product spectra for the ion-molecule reaction may be obtained for a fixed collision energy, using, for example, the longitudinal tandem technique and these may be compared with the breakdown curve... 

We turn, now, to the second question. A necessary condition for the application of quasiequilibrium theory is that the lifetime of the intermediate should be long enough for the internal energy to be equilibrated. There will, of course, always be a distribution of lifetimes and no method exists to measure this distribution.f Three means exist to set qualitative lower bounds on the lifetimes randomization of isotopic labels, energy equilibration (as revealed by the translational energy of the ionic products), and the angular distribution of the products. In the absence of any definite information on the time scales for these processes, we present possible order-of-magnitude values for the purpose of this discussion. The first process can be extremely rapid and requires only a few bond vibrations, i.e., 5 X 10 sec. The second process requires more vibrations, but,... 

Finally, it may be noted that, in quasiequilibrium theory, it is the total internal energy of the intermediate which is the controlling parameter and therefore it should make no difference how this energy is presented, i.e., solely as relative translational energy or partly as internal energy of the reactants. It should prove possible to devise some simple experiments to test this. If the quasiequilibrium theory is modified to include conservation of angular momentum, this prediction will probably no longer be valid. 

Perhaps the simplest and most important task is to establish the conditions under which statistical models are applicable. Rate predictions using quasiequilibrium theory are an insensitive test since it is a many-parameter model measurement of product energy distributions would be a surer test. Application of phase-space theory is restricted to three-and four-atom reactions at present and its comparative lack of success is not therefore surprising. Other indirect approaches are discussed in Section 4.4.1. There will be increased interest in the lifetimes of complexes, with, one suspects, no means of measuring them. 

Phase-space calculations have been made for another four-atom system, where symmetrical angular distributions have been demonstrated at low energies. The system is 02 + and the experimental product ratios OH H20" = 10 1 1) are unexpected since the least endoergic channel yields Quasiequilibrium theory cannot predict this ... 

S. E. Buttrill, Jr., Calculation of ion-molecule reaction product distributions using the quasiequilibrium theory of mass spectra, J. Chem. Phys. 52, 6174-6183 (1970). 

The subsequent step, unimolecular dissociation, has been explained fully in terms of RRKM and quasiequilibrium theory (QET) theories (see Section 6.7). 

Methanol and other lower aliphatic alcohols have been studied in detail by use of the quasiequilibrium theory of mass spectra by Friedman et This was the reason that alcohols were the first larger molecules to be studied in the tandem machine at Stockholm. It is therefore interesting to find that the comparison of the breakdown graph and photoelectron spectrum of methanol in Fig. 10 indicates that the mass-spectrometric dissociation of at least this alcohol does not seem to be ruled by any statistical laws. 

Klots CE. Reformulation of the quasiequilibrium theory of ionic fragmentation. J Phys Chem. 1971 75 1526-32. 

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