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.