Isotope effect calculations

Indicate mechanisms that would account for the formation of each product. Show how the isotopic substitution could cause a change in product composition. Does your mechanism predict that the isotopic substitution would give rise to a primary or secondary deuterium kinetic isotope effect Calculate the magnitude of the kinetic isotope effect from the data given. 

Kinetic isotope effect. Calculate the kie for R-H/R-T and R-D/R-T, taking for a carbon-hydrogen bond a stretching frequency of 2900 cm 1. 

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. 

ZPEhhh — ZPEhdd) — [(ZPEhh — ZPEDd) — (ZPEH — ZPEd)] reactants] = —[(ZPEhhh — ZPEhdd) — (ZPEhh — ZPEDd)] > 0 since (ZPEhhh — ZPEhdd) < (ZPEhh — ZPEDd). The isotope effect calculated by TST is positive and reinforces the positive tunneling contribution (Table 10.1). The term semi-classical is often employed when referring to TST calculations because the motion over the barrier is classical . However the vibrational motion in the other 3N-7 (3N-6) coordinates is treated quantum mechanically, hence the term semi-classical . Still the term, although in wide use, is a bit misleading since these KIE s, like all vibrational isotope effects are quantum mechanical. Because the term semi-classical can be misleading we have chosen not to employ it in this text. 

Fig. 10.1 Zero point energy diagrams, (a) An H or D atom attacking an H2 molecule. The TST isotope effect is negative (inverse, kn > kn) because there is no zero point isotope effect in the ground state, and tunneling is ignored in the TST approximation, (b) An H atom attacking either an H2 or D2 molecule. The isotope effect calculated in the TST approximation is positive (normal, kH > kn) because the zero point isotope effect in the ground state is larger than that in the transition state.

The excellent agreement with the experimental and calculated isotope effect (calculated for formaldehyde, 3.22, and for acetaldehyde, 3.3 experimental value 2.9) supports the computational approach. This suggests that the computed transition structure for hydride transfer in the reaction of the lithium enolate of acetone with acetaldehyde (Figure 30) is realistic. 

Originally it was stated that the formation of 2-bromo-l,8-naphthyridine from 8-bromo-1,8-naphthyridine occurred for 27% via the SN(AE) ek mechanism.10-29 However, when the isotope effect—calculated from the deuterium enrichment in the recovered starting material-was taken into consideration, 45% of telesubstitution was found.21-24... 

The unexpected formation of the blue crystalline radical cation (97) from the reaction of triazinium salt (98) with tetracyanoethylene has been reported and the product identified by its EPR spectrum and by X-ray crystallography (Scheme 42).199 Carboxylic acids react with the photochemically produced excited state of N-t-a-phenynitrone (PBN) to furnish acyloxy spin adducts RCOOPBN. The reaction was assumed to proceed via ET oxidation of PBN to give the PBN radical cation followed by reaction with RCO2H.200 The mechanism of the protodiazoniation of 4-nitrobenzenediazonium fluoroborate to nitrobenzene in DMF has been studied.201 Trapping experiments were consistent with kinetic isotope effects calculated for the DMF radical cation. The effect of the coupling of radicals with different sulfur radical cations in diazadithiafulvalenes has been investigated.202... 

Extrapolated from measurements of dedeuteration at higher temperatures given in reference116, using a value for the isotope effect calculated using the correlation in reference117. 

The experimental KIEs were determined for the aliphatic Claisen rearrangement in p-cymene at 120°C and for the aromatic Claisen rearrangement either neat at 170°C or in diphenyl ether at 220°C. Changes in 2H, 13C or 170 composition were determined for unreacted substrates. For carbon analysis of allyl vinyl ether the C5 carbon was used as an internal standard. The C4 atom and rneta aryl protons were used as references in analysis of allyl phenyl ether. The 170 analysis was based on a new methodology. The results are summarized in Table 1, along with predicted isotope effects calculated for experimental temperatures by means of different computational methods. The absolute values of predicted isotope effects for C4 and C5 atoms varied with theoretical level and all isotope effects were rescaled to get reference effects equal to 1.000. 

These equations are not easily related to equations such as (2), since one proposes a mechanism (force constant asymmetry) for the fall of isotope effect, and the others ignore totally the isotope effect source, and merely assume that it exists, that is that Aq > Ah or that Cd > ch It would of course be possible to calculate the term "iH 4> associated with any particular maximum isotope effect determined by ehx — dx from the isotope effect calculated with Eq. 6 (or Eq. 8), but the force constants could not be so calculated, since there is no unique set of force constants giving a particular vih... 

Fig. 2. Variation of isotope effect, calculated by Eq. (6), with the symmetry measure p = Ea/(2 Ea - AH). The curve is calculated for the same value of and that were used in Fig. 1, but this curve is insensitive to this choice, except for very small values of...

A. T. Pudzianowski and G. H. Loew, /. Phys. Chem., 87, 1081 (1983). Hydrogen Abstractions from Methyl Groups by Atomic Oxygen. Kinetic Isotope Effects Calculated from MNDO/UHF Results and an Assessment of Their Applicability to Monooxygenase-Dependent Hydroxylations. 

Hydrogen isotope effect calculations on a more theoretical basis have been done by O Ferrall [141] who considered three-, four- and five-center models of proton transfer transition states. It was necessary to introduce some arbitrary assumptions concerning transition state bending force constants. 

Analysis of Isotope-effect Calculations Illustrated with Exchange Equilibria Among Oxynitrogen Compounds... 

MONSE ET AL. Isotope-effect Calculation Oxynitrogen Species Considered... 

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