A General Matrix Method for Treating Elastic Constants of Molecular Crystals; Application to Orthorhombic Polyethylene

A general method is developed for treating elastic constants of molecular crystals, with the B matrices as commonly used in normal-coordinate treatments. Equations are written in matrix forms, convenient for calculating elastic constants from intramolecular and intermolecular force field and are readily programed for electronic computations. Partial derivatives of elastic constants with respect to force constants are also derived, for least-square adjustments of force fields with reference to experimental elastic constants as well as vibrational frequencies. Matrix treatments of elastic constants are much simplified by the use of crystal symmetry, just as are treatments of normal vibrations. The matrix methods are explained for the example of orthorhombic polyethylene.