Raman Studies on the Self-localized Excitations in Lightly and Heavily Doped trans-Polyacetylene with Sodium

When finite becomes infinite: convergence properties of vibrational spectra of oligomer chains

We present a computational study of convergence properties of vibrational IR and Raman spectra for a series of increasingly long units of polyethylene, cis- and trans-polyacetylenes, and polyynes. Convergent behavior to the spectra of infinitely long polymers was observed in all cases when chains reached lengths of approximately 60 carbon atoms, both with respect to the positions of the bands and to their intensities. The vibrational spectra of longer chains are practically indistinguishable. The convergence rate depends on the degree of the π conjugation in a studied system: Vibrational spectra for oligoethylenes converge noticeably faster than the spectra for the conjugated systems. The slowest convergence is observed for skeletal motions of the oligomer chains, which may require more than a hundred carbon atoms in the chain to show deviations smaller than 1 cm^-1 to the corresponding solid-state calculations. The results suggest that the boundary between the properties of finite and infinite molecular systems fades away for a surprisingly small number of atoms.