Proton and deuteron position preferences in water clusters: an ab initio study.

In order to explore the effect of H-to-D substitution on the zero-point energy (ZPE) of water clusters, Hessians were computed for a database of 53 optimized (H2O)n clusters, 5 < or = n < or = 21, at the B3LYP6-311 + + G** level. The 53 clusters contained 1524 protons, which were sorted into 18 categories according to the type of their donor O and (if not free) acceptor O. Letting deltaZPE[H]* denote the change in ZPE when the proton H* is replaced by D, mean values for deltaZPE[H*] for the H-bonded categories ranged from -2172 cal mol(-1) for H* in a DDAA-DDAA bond to -2118 for H* in a DAA-DDA bond. Mean value for H* free on DAA (respectively, DA) was -2018 (respectively, -1969). For DAA-DDA bonds, and for short H bonds in general, there was a strong inverse correlation between /deltaZPE[H*]/ and the O-H* distance. deltaZPE for multiple H-to-D substitutions was additive, except for a cooperativity effect of -13.7 to -19.7 cal mol(-1) when two substituted protons were in the same H2O unit and a much smaller cooperativity when one proton's donor was the other's acceptor. Implications of these data include a relative preference for D to occupy H bonded rather than free positions in finite water clusters, a value of 3.82 for the disproportionation equilibrium constant of mixed ice at 150 K, increased occupation by H at surface positions of mixed ice, and a larger average coordination number for liquid D2O than for liquid H2O.