Effect of quantum nuclear motion on hydrogen bonding
  This work considers how the properties of hydrogen bonded complexes, D-H....A, are modified by the quantum motion of the shared proton. Using a simple two-diabatic state model Hamiltonian, the analysis of the symmetric case, where the donor (D) and acceptor (A) have the same proton affinity, is carried out. For quantitative comparisons, a parametrization specific to the O-H....O complexes is used. The vibrational energy levels of the one-dimensional ground state adiabatic potential of the model are used to make quantitative comparisons with a vast body of condensed phase data, spanning a donor-acceptor separation (R) range of about 2.4-3.0 A, i.e., from strong to weak bonds. The position of the proton and its longitudinal vibrational frequency, along with the isotope effects in both are discussed. An analysis of the secondary geometric isotope effects, using a simple extension of the two-state model, yields an improved agreement of the predicted variation with R of frequency isotope effects. The role of the bending modes in also considered: their quantum effects compete with those of the stretching mode for certain ranges of H-bond strengths. In spite of the economy in the parametrization of the model used, it offers key insights into the defining features of H-bonds, and semi-quantitatively captures several experimental trends. 
Ross H. McKenzie, Christiaan Bekker, Bijyalaxmi Athokpam, and Sai G.   Ramesh
physics.chem-ph cond-mat.mtrl-sci