The effect of solvent on the structure of the transition state for the S(N)2 reaction between cyanide ion and ethyl chloride in DMSO and THF probed with six different kinetic isotope effects

The secondary alpha- and beta-deuterium, the alpha-carbon, the nucleophile carbon, the nucleophile nitrogen, and the chlorine leaving group kinetic isotope effects for the S(N)2 reaction between cyanide ion and ethyl chloride were determined in the very slightly polar solvent THF at 30 degrees C. A comparison of these KIEs with those reported earlier for the same reaction in the polar solvent DMSO shows that the transition state in THF is only slightly tighter with very slightly shorter NC-C(alpha) and C(alpha)-Cl bonds. This minor change in transition state structure does not account for the different transition structures that were earlier suggested by interpreting the experimental KIEs and the gas-phase calculations, respectively. It therefore seems unlikely that the different transition states suggested by the two methods are due to the lack of appropriate solvent modeling in the theoretical calculations. Previously it was predicted that the transition state of S(N)2 reactions where the nucleophile and the leaving group have the same charge would be unaffected by a change in solvent. The experimental KIEs support this view.     

A theoretical investigation of alpha-carbon kinetic isotope effects and their relationship to the transition-state structure of S(N)2 reactions

[reaction: see text] The transition structures and alpha-carbon 12C/13C kinetic isotope effects for 22 S(N)2 reactions between methyl chloride and a wide variety of nucleophiles have been calculated using the B1LYP/aug-cc-pVDZ level of theory. Anionic, neutral, and radical anion nucleophiles were used to give a wide range of S(N)2 transition states so the relationship between the magnitude of the alpha-carbon kinetic isotope effect and transition-state structure could be determined. The results suggest that the alpha-carbon 12C/13C kinetic isotope effects for S(N)2 reactions will be large (near the experimental maximum) and that the curve relating the magnitude of the KIE to the percent transfer of the alpha-carbon from the nucleophile to the leaving group in the transition state has a broad maximum. This means very similar KIEs will be found for early, symmetric, and late transition states and that one cannot use the magnitude of these KIEs to estimate transition-state structure.     

A new insight into using chlorine leaving group and nucleophile carbon kinetic isotope effects to determine substituent effects on the structure of SN2 transition states

Chlorine leaving group k(35)/k(37), nucleophile carbon k(11)/k(14), and secondary alpha-deuterium [(kH/kD)alpha] kinetic isotope effects (KIEs) have been measured for the SN2 reactions between para-substituted benzyl chlorides and tetrabutylammonium cyanide in tetrahydrofuran at 20 degrees C to determine whether these isotope effects can be used to determine the substituent effect on the structure of the transition state. The secondary alpha-deuterium KIEs indicate that the transition states for these reactions are unsymmetric. The theoretical calculations at the B3LYP/aug-cc-pVDZ level of theory support this conclusion; i.e., they suggest that the transition states for these reactions are unsymmetric with a long NC-C(alpha) and reasonably short C(alpha)-Cl bonds. The chlorine isotope effects suggest that these KIEs can be used to determine the substituent effects on transition state structure with the KIE decreasing when a more electron-withdrawing para-substituent is present. This conclusion is supported by theoretical calculations. The nucleophile carbon k(11)/k(14) KIEs for these reactions, however, do not change significantly with substituent and, therefore, do not appear to be useful for determining how the NC-C(alpha) transition-state bond changes with substituent. The theoretical calculations indicate that the NC-C(alpha) bond also shortens as a more electron-withdrawing substituent is placed on the benzene ring of the substrate but that the changes in the NC-C(alpha) transition-state bond with substituent are very small and may not be measurable. The results also show that using leaving group and nucleophile carbon KIEs to determine the substituent effect on transition-state structure is more complicated than previously thought. The implication of using both chlorine leaving group and nucleophile carbon KIEs to determine the substituent effect on transition-state structure is discussed.     

Determining the transition-state structure for different SN2 reactions using experimental nucleophile carbon and secondary alpha-deuterium kinetic isotope effects and theory

Nucleophile (11)C/ (14)C [ k (11)/ k (14)] and secondary alpha-deuterium [( k H/ k D) alpha] kinetic isotope effects (KIEs) were measured for the S N2 reactions between tetrabutylammonium cyanide and ethyl iodide, bromide, chloride, and tosylate in anhydrous DMSO at 20 degrees C to determine whether these isotope effects can be used to determine the structure of S N2 transition states. Interpreting the experimental KIEs in the usual fashion (i.e., that a smaller nucleophile KIE indicates the Nu-C alpha transition state bond is shorter and a smaller ( k H/ k D) alpha is found when the Nu-LG distance in the transition state is shorter) suggests that the transition state is tighter with a slightly shorter NC-C alpha bond and a much shorter C alpha-LG bond when the substrate has a poorer halogen leaving group. Theoretical calculations at the B3LYP/aug-cc-pVDZ level of theory support this conclusion. The results show that the experimental nucleophile (11)C/ (14)C KIEs can be used to determine transition-state structure in different reactions and that the usual method of interpreting these KIEs is correct. The magnitude of the experimental secondary alpha-deuterium KIE is related to the nucleophile-leaving group distance in the S N2 transition state ( R TS) for reactions with a halogen leaving group. Unfortunately, the calculated and experimental ( k H/ k D) alpha's change oppositely with leaving group ability. However, the calculated ( k H/ k D) alpha's duplicate both the trend in the KIE with leaving group ability and the magnitude of the ( k H/ k D) alpha's for the ethyl halide reactions when different scale factors are used for the high and the low energy vibrations. This suggests it is critical that different scaling factors for the low and high energy vibrations be used if one wishes to duplicate experimental ( k H/ k D) alpha's. Finally, neither the experimental nor the theoretical secondary alpha-deuterium KIEs for the ethyl tosylate reaction fit the trend found for the reactions with a halogen leaving group. This presumably is found because of the bulky (sterically hindered) leaving group in the tosylate reaction. From every prospective, the tosylate reaction is too different from the halogen reactions to be compared.     

A new interpretation of chlorine leaving group kinetic isotope effects; a theoretical approach

The chlorine leaving group kinetic isotope effects (KIEs) for the S(N)2 reactions between methyl chloride and a wide range of anionic, neutral, and radical anion nucleophiles were calculated in the gas phase and, in several cases, using a continuum solvent model. In contrast to the expected linear dependence of the chlorine KIEs on the C(alpha)-Cl bond order in the transition state, the KIEs fell in a very small range (1.0056-1.0091), even though the C(alpha)-Cl transition state bond orders varied widely from approximately 0.32 to 0.78, a range from reactant-like to very product-like. This renders chlorine KIEs, and possibly other leaving-group KIEs, less useful for studies of reaction mechanisms than commonly assumed. A partial explanation for this unexpected relationship between the C(alpha)-Cl transition state bond order and the magnitude of the chlorine KIE is presented.     

Temperature dependence of carbon-13 kinetic isotope effects of importance to global climate change

We report here a theoretical study of the 13C kinetic isotope effect (KIE) and its temperature dependence for the reaction OH + CH4 --> H2O + CH3, the major sink of atmospheric methane in the troposphere. The KIE values at various atmospherically significant temperatures were determined by direct dynamics using variational transition state theory with multidimensional tunneling contributions (VTST/MT). The potential energy surfaces (PESs) were generated by hybrid density functional theory as well as by recently developed doubly hybrid density functional theory methods. Comparisons of our calculated KIEs with experimental data and theoretical values in the literature reveal the critical contributions due to multidimensional tunneling and torsion anharmonicity as well as the critical issue of the choice of internal rotational axis.     

The effect of solvent on a Lewis acid catalyzed Diels-Alder reaction,using computed and experimental kinetic isotope effects

A new transition structure for the Diels-Alder reaction between isoprene and acrolein catalyzed by Et(2)AlCl is found to reconcile reported discrepancies between computed and observed secondary kinetic isotope effects (KIEs). Including the effect of solvent realigns the computed results with experiment demonstrating the importance of nonbond interactions at transition structures. Comparison of experimental and newly predicted KIE data reaffirms the ability of theory and experiment to probe the mechanism and transition structure geometry of organic reactions.     

Transition structures, energetics, and secondary kinetic isotope effects for cope rearrangements of cis-1,2-divinylcyclobutane and cis-1,2-divinylcyclopropane: a DFT study

The minimum energy reaction paths and secondary kinetic isotope effects (KIE) for the Cope rearrangements of cis-1,2-divinylcyclobutane and cis-1,2-divinylcyclopropane obtained by (U)B3LYP calculations are reported. Both reactions proceed through endo-boatlike reaction paths, and have aromatic transition states. The predicted activation energies are in agreement with the experimental data. The reaction paths of the rearrangements are intervened by enantiomerization saddle points of the products (and the reactant in the case of divinylcyclobutane). The calculated KIEs are similar in the two systems, and consistent with the geometries of the transition structures. There is computational evidence that the isotope effect associated with the conversion of a pure sp(2) C-H bond into a pure sp(3) one might be the same in all molecules. The predicted KIEs agree with experiment for divinylcyclopropane, but not for divinylcyclobutane.     

Ensemble-averaged QM/MM kinetic isotope effects for the S(N)2 reaction of cyanide anions with chloroethane in DMSO solution

The existence of solvent fluctuations leads to populations of reactant-state (RS) and transition-state (TS) configurations and implies that property calculations must include appropriate averaging over distributions of values for individual configurations. Average kinetic isotope effects 〈KIE〉 for NC(-) + EtCl → NCEt + Cl(-) in DMSO solution at 30?°C are best obtained as the ratio 〈f(RS)〉/〈f(TS)〉 of isotopic partition function ratios separately averaged over all RS and TS configurations. In this way the hybrid AM1/OPLS-AA potential yields 〈KIE〉 values for all six isotopic substitutions (2° α-(2)H(2), 2° β-(2)H(3), α-(11)C/(14)C, leaving group (37)Cl, and nucleophile (13)C and (15)N) for this reaction in the correct direction as measured experimentally. These thermally-averaged calculated KIEs may be compared meaningfully with experiment, and only one of them differs in magnitude from the experimental value by more than one standard deviation from the mean. This success contrasts with previous KIE calculations based upon traditional methods without averaging. The isotopic partition function ratios are best evaluated using all (internal) vibrational and (external) librational frequencies obtained from Hessians determined for subsets of atoms, relaxed to local minima or saddle points, within frozen solvent environments of structures sampled along molecular dynamics trajectories for RS and TS. The current method may perfectly well be implemented with other QM or QM/MM methods, and thus provides a useful tool for investigating KIEs in relation to studies of chemical reaction mechanisms in solution or catalyzed by enzymes.     

Deuterium kinetic isotope effects in microsolvated gas-phase E2 reactions: Methanol and ethanol as solvents

The gas-phase reactions of F(-)(CH(3)OH) and F(-)(C(2)H(5)OH) with t-butyl bromide have been investigated to explore the effect of the solvent on the E2 transition state. Kinetic isotope effects (KIEs) were measured using a flowing afterglow-selected ion flow tube (FA-SIFT) mass spectrometer upon deuteration of both the alkyl halide and the alcohol. Kinetic isotope effects are significantly more pronounced than those previously observed for similar reactions of F(-)(H(2)O) with t-butyl halides. KIEs for the reaction of F(-)(CH(3)OH) with t-butyl bromide are 2.10 upon deuteration of the neutral reagent and 0.74 upon deuteration of the solvent. KIEs for the reaction of F(-)(C(2)H(5)OH) with t-butyl bromide are 3.84 upon deuteration of the neutral reagent and 0.66 upon deuteration of the solvent. The magnitude of these effects is discussed in terms of transition-state looseness. Additionally, deuteration of the neutral regent and deuteration of the solvent do not produce completely separable isotope effects, which is likely due to a crowded transition state. These results are compared to our previous work on S(N)2 and E2 solvated systems.     

Calculations of substituent and solvent effects on the kinetic isotope effects of Menshutkin reactions

Nitrogen, deuterium, halogen, and carbon kinetic isotope effects have been modeled for the Menshutkin reaction between methyl halides and substituted N,N-dimethylaniline at the HF/6-31G(d) level of theory augmented by the C-PCM continuum solvent model for several solvents. Systematic changes in geometries of the transition states and Gibbs free energies of activation have been found with phenyl ring substituents, solvent, and the leaving group. Kinetic isotope effects also change systematically; however, these changes are predicted to be small, inside the usual precision of the experimental measurements. On the contrary, no correlation has been found between the kinetic isotope effects and the Hammett constants for para substituents. Thus opposite to previous assumptions, our results indicate that kinetic isotope effects on the Menshutkin reaction cannot be used to predict the position of the transition state on the reaction coordinate.     

Deuterium kinetic isotope effects in microsolvated gas-phase E2 reactions

This work describes the first experimental studies of deuterium kinetic isotope effects (KIEs) for the gas-phase E2 reactions of microsolvated systems. The reactions of F(-)(H(2)O)(n) and OH(-)(H(2)O)(n), where n = 0, 1, with (CH(3))(3)CX (X = Cl, Br), as well as the deuterated analogs of the ionic and neutral reactants, were studied utilizing the flowing afterglow-selected ion flow tube technique. The E2 reactivity is found to decrease with solvation. Small, normal kinetic isotope effects are observed for the deuteration of the alkyl halide, while moderately inverse kinetic isotope effects are observed for the deuteration of the solvent. Minimal clustering of the product ions is observed, but there are intriguing differences in the nature and extent of the clustering process. Electronic structure calculations of the transition states provide qualitative insight into these microsolvated E2 reactions.     

Isotope effects and heavy-atom tunneling in the Roush allylboration of aldehydes

Intermolecular (13)C kinetic isotope effects (KIEs) for the Roush allylboration of p-anisaldehyde were determined using a novel approach. The experimental (13)C KIEs fit qualitatively with the expected rate-limiting cyclic transition state, but they are far higher than theoretical predictions based on conventional transition state theory. This discrepancy is attributed to a substantial contribution of heavy-atom tunneling to the reaction, and this is supported by multidimensional tunneling calculations that reproduce the observed KIEs.     

Kinetic isotope effects calculated with the instanton method

The ring-opening reaction of the cyclopropylcarbinyl radical proceeds via heavy-atom tunneling at low temperature. We used instanton theory to calculate tunneling rates and kinetic isotope effects with on-the-fly calculation of energies by density functional theory (B3LYP). The accuracy was verified by explicitly correlated coupled-cluster calculations (UCCSD(T)-F12). At cryogenic temperatures, we found protium/deuterium KIEs up to 13 and inverse KIEs down to 0.2. We also studied an intramolecular tautomerization reaction. A simple and computationally efficient method is proposed to calculate KIEs with the instanton method: the instanton path is assumed to be independent of the atomic masses. This results in surprisingly good estimates of the KIEs for the cyclopropylcarbinyl radical and for the secondary KIEs of the tautomerization. Challenges and capabilities of the instanton method for calculating KIEs are discussed.     

Multicoefficient Gaussian-3 calculation of the rate constant for the OH + CH4 reaction and its 12C/13C kinetic isotope effect with emphasis on the effects of coordinate system and torsional treatment

Rate constants and (12)C/(13)C kinetic isotope effects are calculated by direct dynamics for the OH + CH(4) --> H(2)O + CH(3) reaction. The electronic structure calculations required to generate the implicit potential energy surface were carried out by the high-level multicoefficient Gaussian-3/version-3 (MCG3) method and compared to two other multilevel methods, MC3BB and MC3MPW, and three density functional methods, M06-2X, BB1K, and MPW1K. The rate constants and (12)C/(13)C kinetic isotope effects are shown to depend strongly on the coordinate system used to calculate the frequencies as well as on the method used to account for the torsional anharmonicity of the lowest-frequency vibrational mode of the generalized transition states.     

Kinetic isotope effects in cycloreversion of rhenium (V) diolates

Cycloreversion of 4-methoxystyrene from the corresponding Tp'Re(O)(diolato) complex (Tp' = hydrido-tris-(3,5-dimethylpyrazolyl)borate) was measured competitively for various isotopomers at 103 degrees C. Primary ((12)C/(13)C) and secondary ((1)H/(2)H) kinetic isotope effects were determined. The primary KIEs were k(12C)/k(13C) = 1.041 +/- 0.005 at the alpha position and 1.013 +/- 0.006 at the beta position. Secondary KIEs were k(H)/k(D) = 1.076 +/- 0.005 at the alpha position and 1.017 +/- 0.005 at the beta position. Computational modeling (B3LYP/LACVP+) located a transition state for concerted cycloreversion of styrene from TpRe(O)(OCH(2)CHPh) exhibiting dramatically different C-O bond lengths. A Hammett study on cycloreversions of substituted styrenes from a series of Tp'Re(O)(diolato) showed dichotomous behavior for electron donors and electron-withdrawing groups as substituents: rho = -0.65 for electron donors, but rho = +1.13 for electron-withdrawing groups. The data are considered in light of various mechanistic proposals. While the extrusion of 4-methoxystyrene is concluded to be a highly asynchronous concerted reaction, the Hammett study reflects a likelihood that multiple reaction mechanisms are involved.     

Kinetic isotope effects of L-Dopa decarboxylase

A mixed centroid path integral and free energy perturbation method (PI-FEP/UM) has been used to investigate the primary carbon and secondary hydrogen kinetic isotope effects (KIEs) in the amino acid decarboxylation of L-Dopa catalyzed by the enzyme L-Dopa decarboxylase (DDC) along with the corresponding uncatalyzed reaction in water. DDC is a pyridoxal 5'-phosphate (PLP) dependent enzyme. The cofactor undergoes an internal proton transfer between the zwitterionic protonated Schiff base configuration and the neutral hydroxyimine tautomer. It was found that the cofactor PLP makes significant contributions to lowering the decarboxylation barrier, while the enzyme active site provides further stabilization of the transition state. Interestingly, the O-protonated configuration is preferred both in the Michaelis complex and at the decarboxylation transition state. The computed kinetic isotope effects (KIE) on the carboxylate C-13 are consistent with that observed on decarboxylation reactions of other PLP-dependent enzymes, whereas the KIEs on the α carbon and secondary proton, which can easily be validated experimentally, may be used as a possible identification for the active form of the PLP tautomer in the active site of DDC.     

Temperature dependence of the kinetic isotope effects in thymidylate synthase. A theoretical study

In recent years, the temperature dependence of primary kinetic isotope effects (KIE) has been used as indicator for the physical nature of enzyme-catalyzed H-transfer reactions. An interactive study where experimental data and calculations examine the same chemical transformation is a critical means to interpret more properly temperature dependence of KIEs. Here, the rate-limiting step of the thymidylate synthase-catalyzed reaction has been studied by means of hybrid quantum mechanics/molecular mechanics (QM/MM) simulations in the theoretical framework of the ensemble-averaged variational transition-state theory with multidimensional tunneling (EA-VTST/MT) combined with Grote-Hynes theory. The KIEs were calculated across the same temperature range examined experimentally, revealing a temperature independent behavior, in agreement with experimental findings. The calculations show that the H-transfer proceeds with ～91% by tunneling in the case of protium and ～80% when the transferred protium is replaced by tritium. Dynamic recrossing coefficients are almost invariant with temperature and in all cases far from unity, showing significant coupling between protein motions and the reaction coordinate. In particular, the relative movement of a conserved arginine (Arg166 in Escherichia coli ) promotes the departure of a conserved cysteine (Cys146 in E. coli ) from the dUMP by polarizing the thioether bond thus facilitating this bond breaking that takes place concomitantly with the hydride transfer. These promoting vibrations of the enzyme, which represent some of the dimensions of the real reaction coordinate, would limit the search through configurational space to efficiently find those decreasing both barrier height and width, thereby enhancing the probability of H-transfer by either tunneling (through barrier) or classical (over-the-barrier) mechanisms. In other words, the thermal fluctuations that are coupled to the reaction coordinate, together with transition-state geometries and tunneling, are the same in different bath temperatures (within the limited experimental range examined). All these terms contribute to the observed temperature independent KIEs in thymidylate synthase.     

Kinetic isotope effects in the active site of B. subtilis chorismate mutase

Kinetic isotope effects are determined for the enzyme‐catalyzed Claisen rearrangement of chorismate to prephenate using computational methods. The calculated kinetic isotope effects (KIEs) compare reasonably with the few available experimental values with both the theory and experiment obtaining a large KIE for the ether oxygen, indicating large polarization of the transition‐state geometry. Because there is a question of the extent that the experimental rate constants are for chemistry as the rate‐limiting step, the KIEs for all the atoms of the substrate are reported with the exception of the carboxylate groups. A substantial number of large regular and inverse isotope effects are predicted for the hydrogens on the cyclohexadienyl ring related to activation of the reactant and charge reorganization in the transition state. A large KIE is predicted for the hydrogen atom bound to the ether carbon atom because the largest valency change and charge transfer occurs at the ether bond in both the reactant and tansition state. Observation of the overall pattern of predicted KIEs would ensure that conditions are favorable for the rate‐limiting chemistry. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 94: 287–292, 2003     

Correction of pre-steady-state KIEs for isotopic impurities and the consequences of kinetic isotope fractionation

We show, both experimentally and by kinetic modeling, that enzymatic single-turnover (pre-steady-state) H-transfer reactions can be significantly complicated by kinetic isotope fractionation. This fractionation results in the formation of more protiated than deuterated product and is a unique problem for pre-steady-state reactions. When observed rate constants are measured using rapid-mixing (e.g., stopped flow) methodologies, kinetic isotope fractionation can lead to a large underestimation of both the magnitude and temperature dependence of kinetic isotope effects (KIEs). This fractionation is related to the isotopic purity of the substrates used and highlights a major problem with experimental studies which measure KIEs with substrates that are not isotopically pure. As it is not always possible to prepare isotopically pure substrates, we describe two general methods for the correction, for known isotope impurities, of KIEs calculated from pre-steady-state measurements.