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

Abstract

Anharmonic effects upon vibrational frequencies and isotopic partition function ratios are modelled computationally by means of quantum mechanics/molecular mechanics (QM/MM) methods for two systems. First, the methyl cation in explicit water is considered using a B3LYP/6-31+G(d)/TIP3P method in order to check the previous prediction of an inverse equilibrium isotope effect (EIE) K_H3/K_D3 for transfer from vacuum to water at 298 K. A full QM/MM treatment including Lennard-Jones interactions predicts significantly inverse contributions from both internal (0.843 ± 0.001) and external (0.894 ± 0.001) modes of the solute. This treatment yields a much larger harmonic EIE (0.753 ± 0.002, averaged over 928 independent solvent configurations) than is obtained either by projecting out the translational and rotational contributions (0.853) or by treating the solvent by a point-charge representation (0.9360 ± 0.0006, harmonic; 0.9366 ± 0.0006, anharmonic). The contribution of anharmonicity to the EIE affects the value only in the 3rd significant figure. Second, anharmonicity is investigated by means of QM/MM potential-energy scans along 12 normal modes for internal and external vibrations of methyl cation in water and for three modes (one stretching and two bending) for the H_α atom at the carbenium-ion centre in cyclopentyl, cyclohexyl, tetrahydrofuranyl and tetrahydropyranyl cations in explicit water and cyclohexane solvents, as obtained by means of atomic Hessian analysis.