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

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) KH3/KD3 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 Hα 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.