Analysis of nuclear quantum effects on hydrogen bonding

The impact of nuclear quantum effects on hydrogen bonding is investigated for a series of hydrogen fluoride (HF)_n clusters and a partially solvated fluoride anion, F^-(H₂O). The nuclear quantum effects are included using the path integral formalism in conjunction with the Car-Parrinello molecular dynamics (PICPMD) method and using the second-order vibrational perturbation theory (VPT2) approach. For the HF clusters, a directional change in the impact of nuclear quantum effects on the hydrogen-bonding strength is observed as the clusters evolve toward the condensed phase. Specifically, the inclusion of nuclear quantum effects increases the F-F distances for the (HF)_n=2-4 clusters and decreases the F-F distances for the (HF)_n>4 clusters. This directional change occurs because the enhanced electrostatic interactions between the HF monomers become more dominant than the zero point energy effects of librational modes as the size of the HF clusters increases. For the F^-(H ₂O) system, the inclusion of nuclear quantum effects decreases the F-O distance and strengthens the hydrogen bonding interaction between the fluoride anion and the water molecule because of enhanced electrostatic interactions. The vibrationally averaged ¹⁹F shielding constant for F^-(H₂O) is significantly lower than the value for the equilibrium geometry, indicating that the electronic density on the fluorine decreases as a result of the quantum delocalization of the shared hydrogen. Deuteration of this system leads to an increase in the vibrationally averaged F-O distance and nuclear magnetic shielding constant because of the smaller degree of quantum delocalization for deuterium.