Formulation of Phonon Band Calculation Scheme Using Intermolecular Stiffness Matrix Represented upon Coarse-grained Coordinate System

We have formulated a scheme for calculating phonon band structure based on our previously proposed coarse-graining theory, under the periodic boundary conditions. This coarse-graining method is unique in that the dimension of the atomic displacement vectors is reduced, unlike conventional ones in which the atomic positions are consolidated. The scheme was applied to a cyclic water hexamer, to demonstrate that the normal-mode vibration frequencies calculated with a full-atom calculation at the ab initio level were successfully reproduced. Even when the interactions among distant molecules were neglected, the stiffness matrix also gave a satisfactory result. Further, we attempted to rebuild the stiffness matrix using the block elements obtained from the normal-mode calculations for some partially-frozen clusters.