The vibrational proton potential in bulk liquid water and ice.

We present an empirical flexible and polarizable water model which gives an improved description of the position, momentum, and dynamical (spectroscopic) distributions of H nuclei in water. We use path integral molecular dynamics techniques in order to obtain momentum and position distributions and an approximate solution to the Schrodinger equation to obtain the infrared (IR) spectrum. We show that when the calculated distributions are compared to experiment the existing empirical models tend to overestimate the stiffness of the H nuclei involved in H bonds. Also, these models vastly underestimate the enormous increase in the integrated IR intensity observed in the bulk over the gas-phase value. We demonstrate that the over-rigidity of the OH stretch and the underestimation of intensity are connected to the failure of existing models to reproduce the correct monomer polarizability surface. A new model, TTM4-F, is parametrized against electronic structure results in order to better reproduce the polarizability surface. It is found that TTM4-F gives a superior description of the observed spectroscopy, showing both the correct redshift and a much improved intensity. TTM4-F also has a somewhat improved dielectric constant and OH distribution function. It also gives an improved match to the experimental momentum distribution, although some discrepancies remain.