OHO Hydrogen Bond Geometries and NMR Chemical Shifts: From Equilibrium Structures to Geometric H/D Isotope Effects, with Applications for Water, Protonated Water, and Compressed Ice

Hydrogen bond geometries and 1H NMR chemical shifts of OHO hydrogen-bonded systems have been analyzed using an improved valence bond order model. This model predicts that the heavy atom hydrogen bond coordinate q2 = r1 + r2 is a function of the proton coordinate q1 = (r1 - r2), where r1 and r2 represent the OH and the HO distances. In the first part, it is shown that this correlation reproduces published equilibrium geometries of the Zundel cation H5O2+ as well as those of water clusters in the gas phase and embedded in the fullerene C180. Using the example of the water hexamer, it is shown that changing the level of calculation shifts the calculated geometries along the correlation curve, but not away from the curve. In order to take quantum zero-point vibrational effects (QZPVE) into account, an empirical correction is proposed. It is shown that this correction properly describes the calculated classical and quantum hydrogen bond geometries of compressed ice as well as calculated geometric H/D isotope effects. The improved valence bond order model is used to analyze a large number of OHO hydrogen bond geometries contained in the Cambridge Structural Database. In the second part, a relation between the geometries and the 1H NMR chemical shieldings of OHO hydrogen bonded systems is established using the valence bond order model. GIAO calculations of the isolated symmetric Zundel cation where H is located in the hydrogen bond center show only a small dependence of the chemical shifts on the O…O distance. This result is rationalized in terms of neighbor group effects and deshielding in the naked proton. The consequence is that the 1H NMR chemical shifts are not much affected by QZPVE. Calculations on water clusters indicate that the influence of the chemical environment of the OHO hydrogen bonds on their 1H NMR chemical shifts is smaller for the strong hydrogen bond regime but large for the weak hydrogen bond regime. A simple chemical shift vs. q1 relation is then used to calculate the average chemical shifts of water clusters in the regime of fast hydrogen bond exchange between hydrogen bonded and free OH groups. It is shown that average chemical shifts of about 6 ppm are possible as the clusters considered exhibit a broad distribution of stronger and weaker hydrogen bonds. The implications for water in organic solvents and for liquid water are discussed, based on published data on the 1H chemical shift distribution in the latter.