Secondary isotope effects computations

Table 4-2. Computed and experimental primary 12C/13C and secondary 14N/15N kinetic isotope effects for the decarboxylation of N-methyl picolinate at 25 °C in water...

Experimental and computational studies of the pericyclic Meisenheimer rearrangement and a competitive rearrangement of A-propargyl morphol i nc N-oxide revealed a novel inverse secondary kinetic isotope effect (kn/kD 0.8) for the rate-determining cyclization step, probably occurring because of a C(sp) to C(sp2) change in hybridization at the reaction center (Scheme 3).5... 

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... 

Cui et al. found an RGM breakdown in their computational study of alcohol dehydrogenase of when tunneling was included, but no breakdown when tunneling was omitted from the calculation. They found for the primary hydrogen isotope effect, = 1.10 at 300 K and attributed it to the coupled motion of the secondary and primary hydrogen sites along the reaction path. 

The results of Cha et al. [90] illustrate these tendencies. Their isotope effect results give an unexceptional primary mixed exponent, r = 3.58 + 0.08, and a much larger secondary mixed exponent, = 10.2 + 2.0. These mixed exponents have been studied recently in several large-scale computational projects [14, 38, 47, 91]. Many other experimental studies [89, 92] involving mixed isotopic exponents are the subject of several reviews [93-96]. 

Evidence in favor of the [2+2] mechanism is circumstantial, but it does include several types of studies. This evidence includes nonlinear free energy relationships between the substituent parameters on vinylarenes and the rates of the dihydroxylation, and it includes temperature effects on selectivity. It also includes the results of studies on the cleavage of Cp Re(0)(diolate) complexes to Cp ReOj and free olefin. The electronic effects, enthalpy of activation versus the strain of the olefin, and secondary deuterium isotope effects obtained from these studies on the rhenium complex support a stepwise cleavage process that could occur by initial formation of an oxametallacyclobutane intermediate. In the end, however, the combination of computational data and isotope-effect measurements seem to have led the community to accept that osmium tetroxide reacts by the direct [3+2] pathway. The mechanism of the reaction of OjOsNR with olefins during aminohydroxylation presumably follows the same type of [3+2] pathway. 

Stradiotto and Tobisch collaborated to investigate the proposed mechanism for lr(l)-catalyzed cyclohydroamination of unactivated aUcenes with primary and secondary amines. A combination of kinetic investigations, including kinetic isotope effects, reaction monitoring, substrate scope investigations, and computational... 

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... 

The centroid path integral method described above enable us to conveniently determine KIEs by directly computing the ratio of the quantum partition functions for two different isotopes through free energy perturbation (FEP) theory. The use of mass perturbation in free-particle bisection sampling scheme results in a major improvement in computation accuracy for KIE calculations such that secondary kinetic isotope effects and heavy atom isotope effects can be reliably obtained. The PI-FEP/UM method is the only practical approach to yield computed secondary KIEs sufficiently accurate to be compared with experiments. ... 

Computed primary (1°) and secondary (2°) kinetic isotope effects, and computed and experimental total deuterium isotope effects for the proton transfer from nitroethane to Asp402 in NAO and to acetate ion in water. ... 

The latter method, called the PI-FEP/UM approach, allows accurate primary and secondary kinetic isotope effects to be computed for enzymatic reactions. These methods are illustrated by applications to three enzyme systems, namely, the proton abstraction and reprotonation process catalyzed by alanine race-mase, the enhanced nuclear quantum effects in nitroalkane oxidase catalysis, and the temperature (in)dependence of the wild-type and the M42W/G121V double mutant of dihydrofolate dehydrogenase. These examples show that incorporation of quantum mechanical effects is essential for enzyme kinetics simulations and that the methods discussed in this chapter offer a great opportunity to more accurately model the mechanism and free energies of enzymatic reactions. 

In order to confirm the validity of proposed mechanisms, secondary kinetic isotope effects (SKIEs) can be evaluated and compared with experimental data. SKIEs have been computed for both the concerted and the biradical mechanism of the butadiene-I-ethylene reaction, showing that the two pathways lead to very different effects, the ones computed for the concerted mechanism being in good agreement with experiment (Figure 1). 

Secondary kinetic isotope effects have been determined for the reactions between butadiene and acrolein (1) and between isoprene (2) and maleic anhydride (3). In both cases, the computed values for the asynchronous transition states are in very good agreement with the experimental values. 

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