KIE computational methods

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. 

This extremely large KIE is probably an artefact of the computational methods used. 

The ability to accurately compute kinetic isotope effects (KIEs) for chemical reactions in solution and in enzymes is important because the measured KIEs provide the most direct probe to the nature of the transition state and the computational results can help rationalize experimental findings. This is illustrated by the work of Schramm and co-workers, who have used the experimental KIEs to develop transition state models for the enzymatic process catalyzed by purine nucleoside phosphorylase (PNP), which in turn were used to design picomolar inhibitors. In principle, Schramm s approach can be applied to other enzymes however, in order to establish a useful transition state model for enzymatic reactions, it is often necessary to use sophisticated computational methods to model the structure of the transition state and to match the computed KIEs with experiments. The challenge to theory is the difficulty in accurately determining the small difference in free energy of activation due to isotope replacements, especially for secondary and heavy isotope effects. Furthermore, unlike studies of reactions in the gas phase, one has to consider... 

Computational methods for treating organic reactions in solution have been reviewed in Japanese. Examples quoted include solvolysis, the Finkelstein reaction and the Menshutkin reaction. The same author carried out ab initio MO calculations at various levels on the hydrolysis of methyl chloride, in which up to 13 solvent water molecules were explicitly considered.It was found that the attacking H2O molecule kept two hydrogen atoms at the transition state, and the proton transfer from the attacking water to the water cluster began to occur after the transition state. Solute and solvent KIEs were calculated and compared with experimental results. The calculations for the system with 13 solvent water molecules reproduced the experimental energetics and deuterium KIEs fairly well. 

We have recently used QM/MM computational methods to show that the H-transfer during the RHR of MR with NADH occurs predominantly (>99%) by quantum mechanical tunnelling.In this case, the H-transfer does not occur via a classical transition state (over-the-barrier) but rather tunnels about 25 kJ mol below the top of the reaction barrier (which is 80 kJ mol high). This is considered a deep tunnelling reaction (see Figure 3.10). Experiments have shown that the KIE on this reaction is strongly temperature dependent (AAFf 8 kJ and we have interpreted these data... 

The impressive match between the experimentally and computationally determined KIE value grants validity to the mechanistic proposal and shows the power of computational methods in elucidating even small, otherwise hardly accessible, mechanistic details. 

Today a good understanding of transition state structure can be obtained through a combination of experimental measurements of kinetic isotope effects (KIE) and computational chemistry methods (Schramm, 1998). The basis for the KIE approach is that incorporation of a heavy isotope, at a specific atom in a substrate molecule, will affect the enzymatic reaction rate to an extent that is correlated with the change in bond vibrational environment for that atom, in going from the ground state to the... 

The application of isotope effects studies of reaction mechanism includes comparison of experimental values of isotope effects and predicted isotope effects computed for alternative reaction pathways. On the basis of such analysis some of the pathways may be excluded. Theoretical KIEs are calculated using the method of Bigeleisen and Mayer.1 55 KIEs are a function of transition state and substrate vibrational frequencies. Equilibrium isotope effects are calculated from substrate and product data. Different functionals and data sets are used in these calculations. Implementation of a one-dimensional tunnelling correction into conventional transition-state theory significantly improved the prediction of heavy-atom isotope effects.56 Uncertainty of predicted isotope effect can be assessed from the relationship between KIEs and the distances of formed or broken bonds in the transition states, calculated for different optimized structures.57 Calculations of isotope effects from sets of frequencies for optimized structures of reactants and transition states are facilitated by adequate software QUIVER58 and ISOEFF.59... 

Another more general comment on the interplay of KIE and SE is indicated. Primary KIEs associated with hydrogen migrations depend on the intrinsic structural details of the key step of bond activation where ring sizes and steric constraints of the intermediates can be regarded as minor perturbations. In contrast, the local details of the TSs are more or less identical for transfer of di-astereotopic H(D) atoms while conformational aspects of the backbone play a pivotal role. Therefore, KIEs and SEs provide complementary information on the reactions observed. With respect to the level of sophistication of contemporary ab initio methods, an explicit computational treatment of the KIEs and SEs in one of the above systems is therefore desirable. 

On the other hand, DFT performs extraordinarily well. Spin contamination is a problem with DFT methods snch as B3LYP and so an unrestricted wavefunction must be used and spin correction appUed. Using this approach, Houk found 4 to lie 3.4 kcal mol" below 6 and 2.8 kcal mol below 7. Coupled with the computed KIEs, discussed next, the results of computational studies indicate that the Diels-Alder reaction proceeds by the concerted mechanism. 

All of the ab initio calcnlations that include electron correlation to some extent clearly favor the concerted pathway for Reaction 4.1. All of these computations also identified a transition state with Q symmetry, indicating perfectly synchronons bond formation. One method for distinguishing a synchronous from an asynchronous transition state is by secondary kinetic isotope effects (KIEs). Isotopic snbstitution alters the frequencies for all vibrations in which that isotope is involved. This leads to a different vibrational partition function for each isotopicaUy labeled species. Bigeleisen and Mayer determined the ratio of partition functions for isotopicaUy labeled species. Incorporating this into the Eyring transition state theory results in the ratio of rates for the isotopicaUy labeled species (Eq. (d. ))." Computation of the vibrational frequencies is thus... 

Houk first examined the 2°-KIE for Reaction 4.1 using the MP2, CASSCF, and UHF methods to optimize the appropriate transition states and compute the necessary vibrational frequencies." The computed KIE are compared with experimental results for analogous reactions in Table 4.5. While the agreement between experimental and computation is not exact, one important result can be readily extracted the predicted KIEs for the concerted fransition state are in much better agreement with experiment than those for the stepwise fransition state. In particular, note that the stepwise KIEs are all normal and the concerted are all inverse, in agreement with the experimental inverse KIEs. 

The immediate future is relatively clear. Continued advances in instrumental techniques, particularly in mass spectrometry and NMR, will make it possible to measure increasingly accurate and precise KIEs on increasingly small amounts of material. At the same time, continued growth in computational power and in the methods of KIE interpretation will make TS analysis an increasingly powerful tool. Currently, one major drawback is that it is too time consuming at present for application in the pharmaceutical industry. TS analysis will have to become much faster to see wide application outside of academia. 

The experimental KIE can be compared with KIEs calculated from transition structures on the basis of the vibrational frequencies associated with specific bonds. This information is available from computed transition structures, and the comparison can provide a direct experimental means of evaluating the computed transition structures.The method has also been used to measure KIE in reactions such as the bromination of pentene and epoxidation of propene. Those transition stmctures that are inconsistent with the observed KIE can be excluded. 

Several other path integral-based approaches to compute KIE exist, which however do not use QI approximation. These include, for example, approaches using other quantum TSTs [55-60] or the quantized classical path method [7,61,62]. 

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