Quasi equilibrium theories

QET is not the sole theory in the field indeed, there are several apparently competitive statistical theories for describing rate constants of unimolecular reactions [10,48]. However, none of these theories has been able to quantitatively describe all reactions of a given ion. QET, however, is well established and even in its simplified form allows sufficient insight into the behavior of isolated ions. Thus, we start out the chapter from the basic assumptions of QET. Along this scheme we will be led from the neutral molecule to ions, and from transition states and reaction rates to fragmentation products and thus, through the basic concepts and definitions of gas phase ion chemistry. 

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. 

It is well known that the mass spectra of some polyatomic molecules are interpreted fairly well by the quasi-equilibrium theory (QET) developed by Eyring and co-workers [80]. 

In order to use this equation to calculate specific mass spectra, some more useful expressions for k(E, Eq ) and many parameters for molecular 

With so many adjustable parameters, the validity of the fundamental (equilibrium) assumption of the theory cannot be said to have been tested by quantitative agreement with experiment that has been observed for certain molecules. The current status of the theory and its application have been reviewed elsewhere [81—83]. 

While having such limitations and difficulties in the actual calculation as described above, there seem to be no reasons why the theory should not apply to the dissociation of the ion—molecule reaction complex. Rather, some favourable ion—molecule reactions would be expected to provide more suitable tests of the equilibrium assumption. Although the problem of not knowing the normal frequencies of the molecular ion (ion-molecule complex in this case) and activated complex remains and a new problem arises concerning the structure of the reaction complex, it is to be expected that the problem of the unknown distribution of excitation energies can be avoided if reactant ions formed at very low electron energies are used. In this hope, Buttrill [84] carried out a calculation of ion—molecule reaction product distribution for the reactions 

Dynamics and kinematic models of atom transfer reactions 

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Flere, we shall concentrate on basic approaches which lie at the foundations of the most widely used models. Simplified collision theories for bimolecular reactions are frequently used for the interpretation of experimental gas-phase kinetic data. The general transition state theory of elementary reactions fomis the starting point of many more elaborate versions of quasi-equilibrium theories of chemical reaction kinetics [27, M, 37 and 38]. 

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... 

Ros stock, H.M. Krauss, M. Quasi-Equilibrium Theory of Mass Spectra, in Mass Spectrometry of Organic Ions, 1st ed. McLafferty, F.W., editor Academic... 

Under ordinary mass spcctrometric conditions only unimolecular reactions of excited ions occur, but at higher ionization chamber pressures bimolecular ion molecule reactions are observed in which both the parent ions and their unimolecular dissociation product ions are reactants. Since it requires a time of 10 5 sec. to analyze and collect the ions after their formation all of the ions in the complete mass spectrum of the parent molecule are possible reactants. However, in radiation chemistry we are concerned with the ion distribution at the time between molecular collisions which is much shorter than 10 5 sec. For example, in the gas phase at 1 atm. the time between collisions is 10 10 sec. and in considering the ion molecule reactions that can occur one must know the amount of unimolecular decomposition within that time. By utilizing the quasi-equilibrium theory of mass spectra6 it is possible to calculate the ion distribution at any time. This has been done for propane at a time of 10 10 sec.,24 and although the parent ion is increased by a factor of 2 the relative ratios of the other ions are about the same as in the mass spectrum observed in 10 r> sec. Thus for gas phase radiolysis the observed mass spectrum is a fair first approximation to the ion distribution. In... 

Mass spectra of dibenzo[/Af]thiepine 32 and dibcnzo[/),e]thiepine 5,5 -dioxide 33 were studied via the classical approximation of the quasi-equilibrium theory. A good agreement was achieved between calculated and experimental data <1998RRC849>. 

Statistical methods represent a background for, e.g., the theory of the activated complex (239), the RRKM theory of unimolecular decay (240), the quasi-equilibrium theory of mass spectra (241), and the phase space theory of reaction kinetics (242). These theories yield results in terms of the total reaction cross-sections or detailed macroscopic rate constants. The RRKM and the phase space theory can be obtained as special cases of the single adiabatic channel model (SACM) developed by Quack and Troe (243). The SACM of unimolecular decay provides information on the distribution of the relative kinetic energy of the products released as well as on their angular distributions. 

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. 

The apparent success of the quasi-equilibrium theory in calculating the mass spectra of simple alkanes would now seem to be somewhat fortuitous since there is growing evidence that the structures of the molecular ions of alkanes cannot be equated to simple ground-state structures based on the molecules ionized. The loss of from pro-... 

The second major obstacle to application of molecular-orbital theory lies in the need to define the electronic state of the ion. Thus, it is possible to calculate groimd- and excited-state properties of molecules and compare the results with experimental observation, but there is no direct knowledge of the electron configimation in an ion produced by electron impact except perhaps immediately after ionization at threshold voltages. The quasi-equilibrium theory can be applied to any state the ion is known to exist in, but this knowledge is usually lacking. Some attempt has been made to define the electronic state of an ion as ground-state or excited-state from the appearance of metastable ions, as is... 

XII.2), namely, that the critical complex is always in effective equilibrium with the reacting species, we can feel justified in applying a quasi-equilibrium theory such as the transition-state theory to these reactions. The reaction can be represented by... 

For the reactions of medium-sized molecules we have the following Lindemann-Hinshelwood theory, RRK theory. Slater s harmonic theory, RRKM theory, phase-space theory, absolute reaction rate theory, quasi-equilibrium theory, and several others. All of those are grouped under the umbrella of "transition state theory" (Robinson Holbrook, 1972 Forst, 1973). Among these theories, some are regarded as "inaccurate" or "outdated." But several rivals remain as viable alternatives on which to base a theoretical study of a reaction system, at least as far as Joiunal referees are concerned. 

Such a distribution is shown in Figure 3 for both hexanes. The figures give the approximate G-values for a particular bond, when the disproportionation is neglected. Under the condition that the dispropor-tionation/combination ratio does not change on deuteration, they can be compared for a possible isotope effect of the fragmentation yielding radicals. The probability is the same for the split of a C-H bond—e.g., 0.8 for the sum of the four C-H bonds in position 2 of hexane—but a small inverse isotope effect is observed for C-C scission. Because of the above mentioned assumptions we are unable to decide if this corresponds to reality, however such an effect would be predicted on the basis of quasi-equilibrium theory. 

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