A method is described for a rapid prediction of B3LYP-optimized geometries for polyhedral water clusters (PWCs). Starting with a database of 121 B3LYP-optimized PWCs containing 2277 H-bonds, linear regressions yield formulas correlating O-O distances, O-O-O angles, and H-O-H orientation parameters, with local and global cluster descriptors. The formulas predict O-O distances with a rms error of 0.85 pm to 1.29 pm and predict O-O-O angles with a rms error of 0.6degrees to 2.2degrees. An algorithm is given which uses the O-O and O-O-O formulas to determine coordinates for the oxygen nuclei of a PWC. The H-O-H formulas then determine positions for two H's at each O. For 15 test clusters, the gap between the electronic energy of the predicted geometry and the true B3LYP optimum ranges from 0.11 to 0.54 kcal/mol or 4 to 18 cal/mol per H-bond. Linear regression also identifies 14 parameters that strongly correlate with PWC electronic energy. These descriptors include the number of H-bonds in which both oxygens carry a non-H-bonding H, the number of quadrilateral faces, the number of symmetric angles in 5- and in 6-sided faces, and the square of the cluster's estimated dipole moment. (C) 2003 American Institute of Physics.