Isotope theoretical calculations

Recently, this view of secondary a-deuterium KIEs has had to be modified in the light of results obtained from several different theoretical calculations which showed that the Ca—H(D) stretching vibration contribution to the isotope effect was much more important than previously thought. The first indication that the original description of secondary a-deuterium KIEs was incorrect was published by Williams (1984), who used the degenerate displacement of methylammonium ion by ammonia (equation (4)) to model the compression effects in enzymatic methyl transfer (SN2) reactions. 

The molecular ion of Ci2H27SnCl is expected to produce a very complex pattern, because of the combination of the characteristic natural abundances of the isotopes of Sn, Cl and C. The theoretical calculation of the intensity pattern has taken into account all the ten isotopes of Sn, the two isotopes of Cl, three distinct contributions due to the 12 carbons (144, 145, 146), and the two significant contributions due to the 27 hydrogens (27 and 28). Of the 120 combinations, many overlap. 

It should be noted in passing that Mulliken also examined the isotope effect on the quadratic terms in the equations for the band heads. These ratios should theoretically show an isotope effect proportional to the reduced masses of the diatomic molecules (rather than the square root of the reduced masses). While Mulliken concludes that these ratios also confirm that the molecule is BO rather than BN, the four experimental ratios show a fairly large scatter so that the case for identifying the molecule is not as strong as that from the experimental a and b ratios. He also measured some of the rotational lines in the spectra of BO and considered the measured and theoretical isotope effects. Here one experimental isotope ratio checks the theoretically calculated ratio quite well, but for the other two the result was unsatisfactory. However, Mulliken judged the error to be within the experimental uncertainty. 

Equation A1.3 shows that isotope effects calculated from standard state free energy differences, and this includes theoretical calculations of isotope effects from the partition functions, are not directly proportional to the measured (or predicted) isotope effects on the logarithm of the isotopic pressure ratios. Rather they must be corrected by the isotopic ratio of activity coefficients. At elevated pressures the correction term can be significant, and in the critical region it may even predominate. Similar considerations apply in the condensed phase except the fugacity ratios which define Kf are replaced by activity ratios, a = Y X and a = y C , for the mole fraction or molar concentration scales respectively. In either case corrections for nonideality, II (Yi)Vi, arising from isotope effects on the activity coefficients can be considerable. Further details are found in standard thermodynamic texts and in Chapter 5. 

Fig. 5.5 PlotofT2 ln(fc/fg) = T2 I n (fc / fv) for some isotopically substituted cthylcncs. The solid lines are theoretically calculated from the isotope independent force field in Table 5.7 (Reused with permission from Bigeleisen, J., Fuks, S., Ribnikar, S. V., and Yato, Y., J. Chem. Phys. 66, 1689 (1977). Copyright 1977, American Institute of Physics)...

Abstract This chapter describes a number of examples of kinetic isotope effects on chemical reactions of different types (simple gas phase reactions, Sn2 and E reactions in solution and in the gas phase, a and 3 secondary isotope effects, etc.). These examples are used to illustrate many aspects of the measurement, interpretation, and theoretical calculation of KIE s. The chapter concludes with an example of an harmonic semiclassical calculation of a kinetic isotope effect. 

Wolfsberg, M. and Stem, M. J. Validity of some approximation procedures used in the theoretical calculation of isotope effects. Pure Appl. Chem. 8, 225 (1964) Secondary isotope effects as probes for force constant changes. Ibid. 8, 325 (1964). 

Figure 7. Using a theoretically determined equilibrium fractionation to interpret measured isotopic fractionations in a hypothetical mineral-solution system. Three sets of data are shown. The theoretical equilibrium fractionation for this system is indicated by the gray arrow. The first set of data, indicated by circles, closely follow the calculated fractionation, suggesting a batch equilibrium fractionation mechanism. The second set of data (stars) is displaced from the theoretical curve. This may either indicate a temperature-independent kinetic fractionation superimposed on an equilibrium-like fractionation, or that the theoretical calculation is somewhat inaccurate. The third set of data (crosses) shows much greater temperature sensitivity than the equilibrium calculation this provides evidence for a dominantly non-equilibrium fractionation mechanism. For the first data set, the theoretical fractionation curve can be used to extrapolate beyond the measured temperature range. The second data set can also be extrapolated along a scaled theoretical curve (Clayton and Kieffer 1991).

Theoretical calculations predict that, compared to other amino acids, arginine may dimerize and trimeiize in the zwitterionic state. Soft-sampling ESI of the racemate of arginine, with one of the enantiomer isotopically labeled, reveals the formation of stable trimers with NOj" present as counterion. No preference for... 

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