Polyhedral water clusters, I: Formal consequences of the ice rules

Polyhedral water clusters (PWCs) are (H2O)(n) Clusters in which every oxygen is 3-coordinated. An analog of the Bernal-Fowler ice rules, when combined with graph-theoretic facts about polyhedra, leads to a rich variety of mathematical relationships regarding structural descriptors of PWCs. These relationships are developed and rigorously proved. The emphasis is on relationships involving four structural parameters which are correlated with the electronic energy of PWCs. Principal results are the recognition of the importance of three levels of information in the H-bonding pattern of a PWC; the definition and classification of the 'F-components' and 'L-coraponents' of a PWC; a method for generating all PWCs obeying the ice rules for a given polyhedral pattern; and a method based on the four-color theorem for producing low energy PWCs that have a property called 'contiguity two'. (C) 2002 Elsevier Science B.V. All rights reserved.