QET theory

For X = Cl particular attention was devoted to the metastable loss of HC1 and Cl from 29-33. It was found that ionized CD3CH2C1 loses only DC1, suggesting the involvement of ion 29122. However, it was pointed out that, according to the RRKM-QET theory, the critical energy involved in HC1 loss from 29 is too low (ca 30 kcal moT1 above its ground... 

For a decade, a rival theory due to Slater (1955, 1959) provided considerable motivation for more detailed experimental as well as theoretical investigations. This, very interesting and elegant theory, which is discussed in more detail by Robinson and Holbrook (1972) and Nikitin (1974), as well as in chapter 8, is more akin to a dynamical than a statistical theory. Because the Slater theory treats the vibrations classically, it also requires the use of fewer oscillators to fit the experiment (sec fig. 1.1). Its flawed fundamental hypothesis that the molecule s modes were strictly harmonic, thereby preventing energy flow among them, and its failure to account quantitatively for the experimentally measured rates led to its being quickly overshadowed by the successes of the RRKM/QET theory. 

While the statistical RRKM/QET theory was being used to fit fall-off curves and the results of chemical activation studies, its fundamental assumptions were also being tested by classical trajectory calculations, an approach pioneered by Bunker (1962,... 

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

Quasi-Equilibrium theory (QET) Theory of mass spectra based on rapid internal conversion of excited electronic states produced by electron impact to the ground electronic state. Statistical redistribution of energy on the-ground state surface, followed by vibrational predissociation, determines the rate of fragmentation. 

It has often been naggingly remarked that the RRKM-QET theory can fit anything and predict nothing. To counter this criticism, many authors have multiplied skilful consistency checks (study of isotope effects, preparation of the ion via a bimo-lecular reaction or via charge reversal in addition to electron or photon impact, time-resolved studies all the way from the millisecond to the nanosecond timescales, etc.) and have removed arbitrariness via ab initio calculations of frequencies. However, it should be realized that ability to fit the experiments by no means implies that the theory is exact and that its basic assumptions (full energy randomization and existence of a good transition state) are fulfilled. It has been seen that Equation [1] cannot be grossly in error because of a mechanism of cancellation of errors. In contradistinction, KERDs (for which the cancellation of errors does not work because they basically depend on the numerator only) provide a much better way to test the validity of the... 

QET. quasi-equilibrium theory (of mass spectrometric fragmentation)... 

The quasi-equilibrium theory (QET) is the most widely used theoretical framework for the discussion of the fragmentation pattern of the parent ion in a uni-molecular process. Although other unimolecular theories (see Levine, 1966) have been subsequently proposed, the QET has traditionally been applied for... 

The quasi-equilibrium theory (QET) of mass spectra is a theoretical approach to describe the unimolecular decompositions of ions and hence their mass spectra. [12-14,14] QET has been developed as an adaptation of Rice-Ramsperger-Marcus-Kassel (RRKM) theory to fit the conditions of mass spectrometry and it represents a landmark in the theory of mass spectra. [11] In the mass spectrometer almost all processes occur under high vacuum conditions, i.e., in the highly diluted gas phase, and one has to become aware of the differences to chemical reactions in the condensed phase as they are usually carried out in the laboratory. [15,16] Consequently, bimolecular reactions are rare and the chemistry in a mass spectrometer is rather the chemistry of isolated ions in the gas phase. Isolated ions are not in thermal equilibrium with their surroundings as assumed by RRKM theory. Instead, to be isolated in the gas phase means for an ion that it may only internally redistribute energy and that it may only undergo unimolecular reactions such as isomerization or dissociation. This is why the theory of unimolecular reactions plays an important role in mass spectrometry. 

The QET is not the only theory in the field indeed, several apparently competitive statistical theories to describe the rate constant of a unimolecular reaction have been formulated. [10,14] Unfortunately, none of these theories has been able to quantitatively describe all reactions of a given ion. Nonetheless, QET is well established and even the simplified form allows sufficient insight into the behavior of isolated ions. Thus, we start out the chapter from the basic assumptions of QET. Following this trail will lead us from the neutral molecule to ions, and over transition states and reaction rates to fragmentation products and thus, through the basic concepts and definitions of gas phase ion chemistry. 

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... 

In conclusion, it is worth reflecting on a classical trajectory study of neutral ethane [335] in which it was found that there were dynamical restrictions to intramolecular energy transfer among C—H motions and between these and C—C motions. It was pointed out [335] that this non-ergodicity might not produce results observable at present levels of experimental resolution. This is probably the situation in mass spectrometry. QET is a respected theory in mass spectrometry because, proceeding from clearly stated assumptions, it is mathematically tractable and is able to explain the currently available experimental data. 

To invoke microscopic reversibility and obtain a rate expression for a unimolecular reaction through considering the association of its products is an idea with a long history [706] and has been taken up in recent years in mass spectrometry [486, 489]. There are a number of treatments [165, 166, 486, 489], which are similar to each other and all of which can be considered to be, in essence, reformulations of QET. There is a tendency to refer to these reformulations, either individually of collectively, as phase space theory [165, 166, 452, 485] and this term is used in a collective sense here. 

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)]. 

QET (or RRKM theory) does predict the relative translational energies of the incipient fragments at the transition state. The predicted distribution of relative translational energies is given by [cf. eqn. (1)]... 

The loose transition state is the transition state considered by phase space theory [164], where the transition state is described in terms of the vibrations and rotations of the products. Treatment of the loose transition state by QET demands that angular momentum be given proper consideration. It is in the case of the loose transition state that phase space theory and QET (with full consideration of the restrictions imposed... 

Theories of quasi-equilibrium (QET) [28] and RRKM [29] explain the monomolec-ular fragmentation of ions. R.A. MARCUS receives the Nobel Prize in 1992. 

Two almost identical theories explaining the phenomena observed in the case of unimolec-ular reactions in the gas phase at high vacuum were proposed in 1952. One of them, the quasi-equilibrium theory (QET), was suggested by Rosenstock et al. [2] and applies to mass spectrometry. The other is named after the initials of its authors, RRKM, standing for Rice, Rampsberger, Kassel and Marcus [3], and deals with neutral molecules. 

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