Quantum-mechanical oligomer approach for the calculation of vibrational spectra of polymers

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Abstract
The force‐constant matrix of an oligomer, composed of five or more repeat units with appropriate terminal groups, can be used to construct the force‐constant matrix of the corresponding planar or helical polymer. The calculations on some typical polymers (polymeric sulfur, polyacetylene, and polyethylene) show that the oligomer approach is accurate enough to duplicate the vibrational frequencies of frozen‐phonon calculations. The oligomer approach has much more predictive power if used in conjunction with some form of empirical scaling (scaled quantum‐mechanical oligomer force field for polymers). ir and Raman selection rules for helical polymers are also discussed. Vibrational frequencies and intensities of polymeric sulfur and polyethylene have been calculated at the ab initio STO‐3G, 4‐31G, 6‐31G, and 6‐31G* basis‐set levels. The agreement of frequencies with experiment is excellent. The quality of calculation is limited by the basis set and theoretical model used rather than the oligomer approach.

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