Kinetic shifts

Note The kinetic shift denotes the overestimation of AEs due to the contribution of excess energy in the transition state necessary to yield rate constants larger than 10 s The determination of lEs does not suffer from kinetic shift as there are no kinetics involved in electron or photon ionization. 

The techniques used for the determination of appearance energies are essentially identical to those described above for lEs. However, even when using the most accurately defined electron or photon energies, great care has to be taken when determining AEs because of the risk of overestimation due to kinetic shift. Provided that there is no reverse activation energy for the particular reaction, the AE value also delivers the sum of heats of formation of the dissociation products. If substantial KER is observed, the AE may still be used to determine the activation energy of the process. 

Fragment ion abundances observed by means of any mass spectrometer strongly depend on ion lifetimes within the ion source and on ion internal energy distributions, i.e., kinetic aspects play an important role for a mass spectrum s appearance. 

Whether or not ions decomposing according to k(E0) are detected depends directly upon the sensitivity of the instrument and indirectly upon the time window over which the ions are collected. The energy distribution, P(E)y also affects whether or not the ions are detected. In terms of eqn. (9), ions are only detected as a signal above the noise if the number (per time), /ml, of ions m arriving at the detector exceeds a certain limiting value Iml (min). In order to detect ions at a critical energy, the inequality 

Ion cyclotron resonance [343] and ion trapping in electron space charge [332, 533] are other techniques which have been used to vary source residence times [i.e. vary the limit t2 of the observation window, eqn. (9)] and thereby obtain estimates of kinetic shifts. 

Consider a mass spectrometer in which the source residence time, t2, for the reactant ion M+ is 1 ps and the lifetimes of metastable M+ ions 

The relative values of the AEs for m+ formed in the source and from metastable ions depend upon the relative values of 7m (source) and 7m (m ) as the ionizing energy, and hence Emax, is reduced. Whether 7m (source) 7m(m ), or vice versa, at any particular ionizing energy depends upon the relative values of the collection efficiencies Gm (source) and Gm (m ), the form of P(E) at that energy and the magnitude of the rate coefficient at the critical energy. 

It is fairly safe to say that Gm (source) Gm (m ), i.e. the ions from the source are detected at least as efficiently as metastable ions. The effect of the form of P(E) can be to favour either 7m (source) or7m (m ) and cannot be treated in general terms. Gaps in the energy distribution, P(E), can influence the determination of appearance energies in just the same way as they influence metastable ion abundances. 

PIPECO experiments have provided direct estimates of kinetic shifts. The limit of the observation window has been varied and the changes in the measured appearance energies observed. The limit t2 is the source residence time and was known in these experiments, being determined by a delay prior to applying the drawout pulse. Changing from 0.7 to 

7 jUS reduced the appearance energy of (CaHs) from allene by 40meV, but no effect could be detected with (CHa) from methane [806]. A larger kinetic shift was found with chlorobenzene where the AE of (CeHs) was reduced by 400 meV on extending from 0.7 to 8.9 ps [716]. Bromobenzene has also been studied [717]. 

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Armentrout et al.69 have developed a method with which the kinetic shift can be taken into account in the curve fitting procedure. The fitting procedure, which corrects for the kinetic shift, includes only the fraction of the precursor ions which... 

Without correction for kinetic shift, internal energy change, AHG° enthalpy change for reaction M L = M + L. 

With collection for kinetic shift, the two lowest frequencies are 30 cm"1 for both K and Na complexes. With correction for kinetic shift, the two lowest frequencies are 10 cm"1 for Na complexes and 5 cm"1 for K complexes. This set is considered to be the best. For a discussion, see Klassen et al.64 Experimental determinations based on ion-molecule equilibria, Sunner et al.94 Theoretical calculations, HF/6-31G, combined with a semiempirical correction. Roux and Karp us.,5c Theoretical calculations, HF/6-31G, combined with a semiempirical correction. Roux and Karplus.,5c Theoretical calculations, 6-31+G(2d) MP2, Jensen.93 Succinamide. 

The experimentally determined threshold energy E0 obtained for the immonium ion and corrected for the kinetic shift is 0 = 44 kcal/mol (see Table 10) and thus in very good agreement with the predicted activation energy. This agreement provides strong support for the proposed mechanism.1003... 

Notes "Threshold energies, E , in kcal/mol. Data from Klassen et al Fragment ion notation a, y, b2 as used in peptide sequencing work. For details see Harrison et al.l00c Threshold energies include correction for the kinetic shift. 

The kinetic shifts for the immonium a, ion formation from (Gly)H+ (0.4), (GlyNH2)H+ (0.7), (GlyNHCH3)H+ (10), and (Gly-Gly)H+ (21), where the values in brackets give the kinetic shift in kcal/mol (see Table 12), illustrate the very rapid increase of the kinetic shift with increasing size of the precursor ion. For (Gly-Gly)H+ the kinetic shift is close to 50% of the true threshold, E0 = 44 kcal/mol. Obviously unless an accurate evaluation of the kinetic shift is possible, reliable threshold values cannot be obtained with precursor ions of this size. 

Figure 3 shows the results of varying the CO pressure. The maximum activity appears to lie near 600 psi for benzaldehyde reduction. Figure 3 is an attempt to elucidate an apparent reaction order with respect to the arithmetically averaged CO pressure. At pressures less than 400 psi, the order is nearly first order. The situation at higher pressures is not clear however, it is reasonable to speculate that the dominant aspects of the kinetics shift at these pressures. The data suggest the shift is to zero-order dependance. 

In summary, both the kinetic shift and the recombination barrier lead to thermodynamic values of the appearance energy that are too large and to upper limits of A 7/°(A+, g). We now illustrate the procedures and conventions just described... 

Figure 4.4 An energy profile for the unimolecular decomposition of AB+, showing a reverse activation barrier (free) and a kinetic shift (fkjn)- Adapted from [65],...

Despite the problems that can afflict experimental cyclic voltammograms, when the method for deriving standard redox potentials is used with caution it affords data that may be accurate within a few tens of mV (10 mV corresponds to about 1 kJ mol-1), as remarked by Tilset [335]. Kinetic shifts are usually the most important error source The deviation (A If) of the experimental peak potential from the reversible value can be quite large. However, it is possible to estimate AEp if the rate constant of the chemical reaction is available. For instance, in the case of a second order reaction (e.g., a radical dimerization) with a rate constant k, the value of AEV at 298.15 K is given by equation 16.24 [328,339] ... 

Fig. 2.12. Kinetic shift. The excess energy in the transition state affects AE measurements in the way that it always causes experimental values to be too high.

These observations are in accord with a scheme involving a reversible electron transfer, followed by a reaction that depletes the concentration of the initially formed reduced species, R. They are also reminiscent of the observations made earlier in regard to the electrohydrocyclization process. The greater the rate of the follow-up process, the more significant its effect on the concentration of R in a given time period, that associated with the CV scan rate, for example. From a moments consideration of the Nernst equation, it is clear that this event should manifest itself in terms of a shift in the peak potential to a more positive value, as observed for 255 and 257b [4]. In the present instance, it is suggested that a rapid or concerted loss of the mesylate anion in the reductive cyclization is likely to be associated with this so-called kinetic shift of the peak potentials [69]. 

Figure 2. RRKM calculations of the kinetic shift for model hydrocarbon ion dissociations as a function of ion size. Calculations are shown both for a fairly weakly bonded ion (1.86 eV) and a fairly strongly bonded one (3.10 eV), and in each case both the conventional and the intrinsic kinetic shifts are plotted.

Methylnaphthalene ion presented an interesting case where the dissociation energy was essentially unknown, because a kinetic shift of the order of 2 eV completely masks the true threshold in threshold appearance measurements. TRPD at two wavelengths, with RRKM extrapolation, assigned an Eg of 2.25 eV for the loss of H from the molecular ion, shown in Equation (7). We found that this energy... 

Another ion for which the large number of degrees of freedom results in unmanageable kinetic shifts is the tri-r-butylbenzene ion, ° Equation (8). This is... 

The near-linear dependence of the kinetic shifts on the number of degrees of freedom N is notable, but not surprising. A reasonable functional form for the energy dependence of itjiss is the modified semiclassical RRK expression... 

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