Topology-energy relationships and lowest energy configurations for pentagonal dodecahedral (H2O)20X clusters, X=empty, H2O, NH3, H3O+: The importance of O-topology

Abstract

For (H(2)O)(20)X water clusters consisting of X enclosed by the 5(12) dodecahedral cage, X = empty, H(2)O, NH(3), and H(3)O(+), databases are made consisting of 55-82 isomers optimized via B3LYP/6-311++G(**). Correlations are explored between ground state electronic energy (Ee) or electronic energy plus zero point energy (Ee+ZPE) and the clusters' topology, defined as the set of directed H-bonds. Linear regression is done to identify topological features that correlate with cluster energy. For each X, variables are found that account for 99% of the variance in Ee and predict it with a rms error under 0.2 kcal/mol. The method of analysis emphasizes the importance of an intermediate level of structure, the "O-topology," consisting of O-types and a list of O pairs that are bonded but omitting H-bond directions, as a device to organize the databases and reduce the number of structures one needs to consider. Relevant variables include three parameters, which count the number of H-bonds having particular donor and acceptor types; absolute value(M)(2), where M is the cluster's vector dipole moment; and the projection of M onto the symmetry axis of X. Scatter diagrams for Ee or Ee+ZPE versus absolute value(M) show that clusters fall naturally into "families" defined by the values of certain discrete parameters, the "major parameters," for each X. Combining "family" analysis and O-topologies, a small group of clusters is identified for each X that are candidates to be the global minimum, and the minimum is determined. For X = H(3)O(+), one cluster with central hydronium lies just 2.08 kcal/mol above the lowest isomer with surface hydronium. Implications of the methodology for dodecahedral (H(2)O)(20)(NH(4)(+)) and (H(2)O)(20)(NH(4)(+))(OH(-)) are discussed, and new lower energy isomers are found. For MP2/TZVP, the lowest-energy (H(2)O)(20)(NH(4)(+)) isomer features a trifurcated H-bond. The results suggest a much more efficient and comprehensive way of seeking low-energy water cluster geometries that may have wide applicability.