{"id":14112,"date":"2015-06-10T16:44:19","date_gmt":"2015-06-10T15:44:19","guid":{"rendered":"http:\/\/www.ch.imperial.ac.uk\/rzepa\/blog\/?p=14112"},"modified":"2015-06-14T18:08:53","modified_gmt":"2015-06-14T17:08:53","slug":"natural-abundance-kinetic-isotope-effects-mechanism-of-the-baeyer-villiger-reaction","status":"publish","type":"post","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=14112","title":{"rendered":"Natural abundance kinetic isotope effects: mechanism of the Baeyer-Villiger reaction."},"content":{"rendered":"
\n

I have blogged before<\/a> about the mechanism of this classical oxidation reaction. Here I further explore computed models, and whether they match the observed kinetic isotope effects (KIE) obtained using the natural-abundance method described in the previous post<\/a>.<\/p>\n

\"BV\"<\/a><\/p>\n

There is much previous study of this rearrangement, and the issue can be reduced to deciding whether TS1<\/strong> or TS2<\/strong> is rate-limiting. The conventional text-book wisdom is that the carbon migration step TS2<\/strong> is the “rds” and it was therefore quite a surprise when Singleton and Szymanski[1]<\/a><\/span> obtained KIE which seemed to clearly point instead to TS1<\/strong> as being rate limiting, inferred from\u00a0a large 13<\/sup>C effect (~1.05) at the carbonyl carbon (blue star) and none\u00a0at the \u03b1-carbon (red star). This result (for this specific reaction and conditions, which is dichloromethane as solvent) is now routinely quoted[2]<\/a><\/span> when the mechanism is discussed. This latter article reports[2]<\/a><\/span> calculated energetics for TS1<\/strong> and TS2<\/strong> (see Table 1 in this article) and after exploring various models, the conclusion is that TS1<\/strong> and TS2<\/strong> are essentially isoenergic. However, no isotope effects are computed for their models, and so we do not know if TS1<\/strong> or TS2<\/strong> agrees better with the reported values.[2]<\/a><\/span> Since I had managed to get pretty good agreement with experimental KIEs using the \u03c9B97XD\/Def2-TZVPP\/SCRF=xylenes model for the Diels-Alder reaction, I thought I would try the same method to see how it performs for the Baeyer-Villiger.<\/p>\n

It is in fact non-trivial\u00a0to set up a consistent model. Using arrow pushing, one can on paper draw three variations for TS1, the formation of the peroxyhemiacetal tetrahedral intermediate (TI) and also often called the Criegee intermediate.<\/p>\n

\"BV2\"<\/a><\/p>\n

    \n
  1. TS1a<\/strong> is the “text-book” variation, involving the production of a zwitterionic intermediate which immediately undergoes a proton transfer (PT). The arrows tend not to be used for this last step, since the direct transfer would involve a 4-membered ring and a highly non-linear geometry at the transferring proton which is understood to be “unfavourable”. Such zwitterions involve a large degree of charge separation and hence a large dipole moment. In a non-protic solvent such as dichloromethane, one is very loath to use such species in a mechanism, and it’s not modelled here either.<\/li>\n
  2. Using just cyclohexanone and peracid, it is in fact difficult to avoid ionic species. TS1b<\/strong> is an attempt which shows the proton transfer is done first on the peracid to create a so-called carbonyl ylid, and this then reacts with the ketone<\/li>\n
  3. If however a proton transfer agent is introduced as TS1c<\/strong>, one can use this species (shown in red above) to transfer the proton as part of a concerted mechanism; this was in fact the expedient used in the earlier theoretical study[2]<\/a><\/span> and this route tends to avoid much if not all of the charge separation. The acid comes from the product of the reaction, and hence the kinetics may in fact have an induction period when this acid builds up. The initial proton transfer reagent may also\u00a0be traces of water present in reagents or solvent. Singleton and Szymanski in fact include no supporting information in their article and so we do not know what the concentrations used were (assumed for the\u00a0present discussion\u00a0as 1M) whether everything was rigorously dried, or indeed what the kinetic order in [peracid] turned out to be.<\/li>\n<\/ol>\n

    The same problem is faced with TS2<\/strong>; how to transfer a proton? Because we want to compare the relative energies of TS1<\/strong> and TS2<\/strong>, we also have to atom-balance the mechanism, and so the additional acid component introduced into TS1c<\/strong> is also retained in two alternative mechanisms for TS2<\/strong> (and for TS1b<\/strong>).<\/p>\n

    \"BV3\"<\/a><\/p>\n

      \n
    1. TS2a<\/strong> uses just the components of the tetrahedral intermediate (TI<\/strong>), but again in a fashion that requires no charge separation during the reaction. The additional acid component (red) plays a passive role, hydrogen bonding to the TI<\/strong>.<\/li>\n
    2. TS2b<\/strong> now incorporates the additional acid by expanding the ring (green) in\u00a0an active role.<\/li>\n<\/ol>\n

      IRCs using the 6-311G(d,p) basis) for TS1[3]<\/a><\/span> and TS2[4]<\/a><\/span> are interesting in revealing relative synchronicity of the proton transfers for TS1 but asynchronicity for TS2\u00a0involving a hidden intermediate<\/em>.
      \n      \"BV1a\"<\/a><\/p>\n

      \"BV2a\"<\/a><\/p>\n

      The energy, energy gradient and dipole moment magnitudes for this second step are particularly fascinating. The dipole moment starts off quite small (3.1D) at the TI, and is still so at the TS, but almost immediately afterwards, it shoots up to ~12D as the hidden intermediate develops (IRC ~4) Two successive proton transfers (IRC ~6, 7) then reduce the value down again.
      \n      \"BV2E\"<\/a>
      \n      \"BV2G\"<\/a>
      \n      \"BV2D\"<\/a><\/p>\n

      A table of results can now be constructed for these various models, evaluating two different basis sets for the calculation.<\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n
      system<\/th>\n\u0394\u0394G298<\/sub>\u00a0(1M)
      \n\u03c9B97XD\/6-311G(d,p)\/SCRF=DCM, kcal\/mol<\/th>\n      		Dipolemoment,D<\/th>\n\u0394G298<\/sub>\u00a0(1M)
      \n\u03c9B97XD\/Def2-TZVPP\/SCRF=DCM<\/th>\n<\/tr>\n
      Reactants<\/th>\n+1.4a<\/sup><\/td>\n–<\/td>\n-3.3a<\/sup>[5]<\/a><\/span>,[6]<\/a><\/span>,[7]<\/a><\/span><\/td>\n<\/tr>\n
      Complexed state<\/th>\n0.0[8]<\/a><\/span><\/td>\n5.0<\/td>\n0.0[9]<\/a><\/span><\/td>\n<\/tr>\n
      TS1a<\/th>\nn\/a<\/td>\nn\/a<\/td>\nn\/a<\/td>\n<\/tr>\n
      TS1b<\/th>\n32.9[10]<\/a><\/span><\/td>\n8.6<\/td>\n32.2[11]<\/a><\/span><\/td>\n<\/tr>\n
      TS1c<\/th>\n14.9[12]<\/a><\/span><\/td>\n3.0<\/td>\n16.1[13]<\/a><\/span><\/td>\n<\/tr>\n
      TI<\/th>\n-1.7[14]<\/a><\/span><\/td>\n3.1<\/td>\n-0.3[15]<\/a><\/span><\/td>\n<\/tr>\n
      TS2a<\/th>\n22.2[16]<\/a><\/span><\/td>\n9.3<\/td>\n25.0[17]<\/a><\/span><\/td>\n<\/tr>\n
      TS2b<\/th>\n20.2[12]<\/a><\/span><\/td>\n5.4<\/td>\n22.7[18]<\/a><\/span><\/td>\n<\/tr>\n
      Product<\/th>\n-69.8[19]<\/a><\/span><\/td>\n5.3<\/td>\n[20]<\/a><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      a<\/sup>This value is corrected to a standard state of 1M for a termolecular reaction by 3.78 kcal\/mol from the computed free energies at 1 atm as described previously.[21]<\/a><\/span><\/small><\/p>\n

        \n
      1. Firstly, one must note that the resting state<\/i> for the reactants depends on the concentration. At 1M at the higher basis set, its the separated reactants, but at the lower it is the hydrogen bonded complex between them. Increasing the concentration would favour the latter.<\/li>\n
      2. TS1c is significantly lower in free energy than TS2b, a result somewhat at variance with the earlier report.[2]<\/a><\/span> The functional used in the present calculation, the basis set, the dispersion model and the solvation model are all improvements on the original work.<\/li>\n
      3. Likewise, the energy of TI, the Criegee intermediate emerges as\u00a0similar to the reactants. Coupled with the magnitude of the barrier for TS1c this does tend to point to a relatively rapid pre-equilibrium and that TS2b determines the rate of reaction.<\/li>\n<\/ol>\n

        Kinetic isotope effects for our models<\/h2>\n

        Having constructed models, we can now subject them to testing against the measured kinetic isotope effects.[1]<\/a><\/span><\/p>\n

        \"bv4\"<\/a><\/p>\n

          \n
        1. The measured values are shown above. The first set (a) are what are described as intermolecular<\/em><\/strong> isotope effects and result from measuring changes in the isotopic abundance obtained by recovering unreacted starting material after a large proportion of the reaction has gone to completion. This was interpreted as indicating TS1<\/strong> was rate limiting. Using instead the uncomplexed cyclohexanone has only a small effect (C1: 1.023 complexed, 1.021 uncomplexed).<\/li>\n
        2. The values in parentheses were obtained using the TS1c<\/strong> model above and are relative to the complexed reactant involving hydrogen bonds between the cyclohexanone, the peracid and the acid catalyst. The agreement can only be described as partial.\n