Proton Distribution in Ice and the Kirkwood Correlation Factor

4096 molecules of water forming an ice Ic structure and 2048 molecules forming an ice Ih structure, with standard periodic boundary conditions in each case, have been used to calculate the dipole correlations which arise from proton allocation to the oxygen nuclei according to the Bernal-Fowler ice rules. The calculations reveal a substantial antiparallel correlation in the coordination shells at about twice the distance of the nearest neighbors in the lattice. The value of gK, the Kirkwood correlation factor, is found to be 2.07±0.02 for ice Ih. For ice Ic the value, determined with less precision, is 2.11±0.10. In connection with Kirkwood's dielectric formula the value of gK implies an effective dipole moment, μs, of the molecule in the solid ice Ih phase equal to 2.92 D.