The mean amplitude of the OH...O hydrogen bond in ice and liquid water

The r.m.s. (root-mean-square) amplitude of the OH ... O hydrogen bond was evaluated for ice and liquid water from the hydrogen bond force constant. The force constant for ice was found from the literature and that for liquid water was estimated from the force constant for ice with the use of spectroscopic data. An approximate expression for the mean-square amplitude given by Morino et al. [Y. Morino, K. Kuchitsu, A. Takahashi and K. Maeda, J. Chem. Phys., 21 (1953) 1927] was used, since it is applicable even to a system for which the structure of vibrationally correlated aggregates is not known, as in the case of a liquid, only if the relevant force constant is available. The evaluated r.m.s. amplitudes are 0.16 +/- 0.01 Angstrom for ice near the melting point and 0.18 - 0.22 Angstrom for liquid water at 25 degrees C. In the latter the static distribution of the OH ... O distance suggested by spectroscopic studies is taken into consideration. This result for liquid water is comparable to that obtained by an analysis of X-ray diffraction intensities, 0.17 +/- 0.01 Angstrom, but not in complete agreement.