Longitudinal polarizability of long polymeric chains: Quasi-one-dimensional electrostatics as the origin of slow convergence

The longitudinal linear polarizability α (N) of a stereoregular oligomer of size N is proportional to N in the large- N limit, provided the system is nonconducting in that limit. It has long been known that the convergence of α (N) N to the asymptotic α∞ value is slow. We show that the leading term in the difference between α (N) N and α∞ is of the order of 1N. The difference [α (N) -α (N-1)], as well as αcenter (N) (when computationally accessible), also converge to α∞, but faster, the leading term being of the order of 1 N2. We also present evidence that in these cases the power law convergence behavior is due to quasi-one-dimensional electrostatics, with one exception. Specifically, in molecular systems the difference between α (N) N and α∞ has not just one but two sources of the O (1N) term, with one being due to the aforementioned Coulomb interactions, and the second due to the short ranged exponentially decaying perturbations on chain ends. The major role of electrostatics in the convergence of the remainders is demonstrated by means of a Clausius-Mossotti-type classical model. The conclusions derived from the model are also shown to be applicable in molecular systems, by means of test-case ab initio calculations on linear stacks of H2 molecules, and on polyacetylene chains. The implications of the modern theory of polarization for extended systems are also discussed.