Influence of Dielectric Environment upon Isotope Effects on Glycoside Heterolysis: Computational Evaluation and Atomic Hessian Analysis.

Isotope effects depend upon the polarity of the bulk medium in which a chemical process occurs. Implicit solvent calculations with molecule-shaped cavities show that the equilibrium isotope effect (EIE) for heterolysis of the glycosidic bonds in 5'-methylthioadenosine and in 2-(p-nitrophenoxy)tetrahydropyran, both in water, are very sensitive in the range 2 ≤ ε ≤ 10 to the relative permittivity of the continuum surrounding the oxacarbenium ion. However, different implementations of nominally the same PCM method can lead to opposite trends being predicted for the same molecule. Computational modeling of the influence of the inhomogeneous effective dielectric surrounding a substrate within the protein environment of an enzymic reaction requires an explicit treatment. The EIE (KH/KD) for transfer of cyclopentyl, cyclohexyl, tetrahydrofuranyl and tetrahydropyranyl cations from water to cyclohexane is predicted by B3LYP/6-31+G(d) calculations with implicit solvation and confirmed by B3LYP/6-31+G(d)/OPLS-AA calculations with averaging over many explicit solvation configurations. Atomic Hessian analysis, whereby the full Hessian is reduced to the elements belonging to a single atom at the site of isotopic substitution, reveals a remarkable result for both implicit and explicit solvation: the influence of the solvent environment on these EIEs is essentially captured completely by only a 3 × 3 block of the Hessian, although these values must correctly reflect the influence of the whole environment. QM/MM simulation with ensemble averaging has an important role to play in assisting the meaningful interpretation of observed isotope effects for chemical reactions both in solution and catalyzed by enzymes.