Abstract
Expressions for the multipole interaction elements of the dynamical matrix are obtained using the rigid molecule approximation and the Coulomb interaction between the composite ions of the molecules in an ionic molecular crystal. It is shown that this formulation includes the electronic polarization effects. The monopole, dipole, quadrupole, and octupole contributions are calculated for model crystals of simple cubic structure having linear and tetrahedral molecules as basis. The effect of multipole interactions is found to be very significant. The neglect of multipole interactions in the calculation of translation coefficients of the lattice with linear molecule basis introduces errors as large as 30% along the [q00] direction. A similar calculation with the more complex tetrahedral molecule basis shows an increase in the errors to as large as 240%. In general the magnitude of multipole coefficients is seen to increase with the increasing complexity of the molecular basis.
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