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

Abstract

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 (K H /K D ) 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.

Critical evaluation of anharmonicity and configurational averaging in QM/MM modelling of equilibrium isotope effects

“…There was a near-perfect linear correlation between the EIE values resulting from the full and atomic Hessians over the range of relative permittivity 2 r e r 80: all the variation was captured by the influence of the dielectric upon the isotopically substituted atom alone. 12 The QM/MM rigid potential-energy scans along the three H a normal modes of the CH, THP, CP and THF cations indicate that the harmonic approximation is very good for small displacements from equilibrium, just as it was previously shown to be for the symmetric CH stretch mode of the methyl cation. 11…”

“…Very recently we calculated the harmonic EIE K H /K D for transfer of two oxacarbenium cations (tetrahydrofuranyl, THF and tetrahydropyranyl, THP) and their carbocyclic congeners (cyclopentyl, CP and cyclohexyl, CH) from water to cyclohexane by means of QM/MM modelling with explicit solvent. 12 Atomic Hessian analysis, whereby the full Hessian was reduced to the elements belonging to a single atom at the site of isotopic substitution, revealed a remarkable result: the influence of the solvent environment on the EIEs was essentially captured completely by only a 3 Â 3 block of the Hessian, although these values needed to reflect correctly the influence of the whole environment.…”

Computational Investigations of Position-Specific Vapor Pressure Isotope Effects in Ethanol—Toward More Powerful Isotope Models for Food Forensics

“…The applicability of a Hessian calculated only for few atoms out of a larger system being isotopically substituted for the correct prediction of isotope effects has been addressed in a very recent study on the effect of dielectric environments on isotope effects. 31 Świderek et al in their work have demonstrated that a small set of atoms (a moiety isotopically substituted) instead of the entire system can be used for isotope effect prediction because as long as the influence of the whole environment on this small set is reflected from the IEs obtained from these two approaches are basically the same. This is in contrast to our observation of improved prediction when only a subset of total number of normal modes of a system is used for isotope effect prediction.…”

Transition-State Vibrational Analysis and Isotope Effects for COMT-Catalyzed Methyl Transfer

“…It is often assumed that trends in KIEs may be related to structural changes in TSs understood in terms of geometries and bond orders, 10 , 22 but recent computational studies have suggested that changes in the electrostatic environment of a TS 20 , 21 , 23 , 24 or its stabilization by C α H···O hydrogen-bonding interactions might also be significant. 21 , 25 As part of a program of investigation into factors underlying 2° KIEs and their meaningful interpretation, the possible contribution of anharmonicity has also been considered, but this has not been found to be significant for equilibrium isotope effects (EIEs).…”

“…However, the values of the force constants in this symmetrical 3 × 3 matrix must accurately reflect the influence of the whole supramolecular environment. 24 …”