Bent Chain of Hydrogen Fluoride Molecules

FIGURE 9.3. Structure and internal coordinates of (HF)oo h and 02 and the FHF out-of-plane angles. Additional torsional coordinates Ti(H2F F2H2) and T2(HiF2F1HJ) were used. 

In contrast to the case of an isolated molecule, calculation of the force constants of a polymer is only possible if a further approximation is introduced. By definition, the crystal orbital method can only be applied to systems with perfect periodic symmetry. Energy surfaces were hence computed with all unit cells moving in phase. The force constants /y obtained by the fitting procedure thus correspond formally to the infinite sums 

9 Vibrational Spectra and Transport Properties of Polymers 

The harmonic force constants thus obtained have been used in a Wilson GF procedure modified by periodic boundary conditions to compute phonon dispersion curves. These curves enabled the phonon density of states to be evaluated in a manner similar to that employed in obtaining the electronic density of states from the electronic band structure. 

Previous force fields of (HF) used in lattice dynamical studies have always been obtained by a fit to experimental frequencies, relying on a reasonable choice of fundamentals. These force fields are not directly comparable to the present ones, partly owing to a different choice of internal coordinates, partly because fewer force constants were considered or because interchain force constants were also included. Nevertheless, some general features may be discussed. 

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