Extrapolation methods for improving the convergence of oligomer calculations to the infinite chain limit of quasi-one-dimensional stereoregular polymers

Quasi-one-dimensional stereoregular polymers as for example polyacetylene are currently of considerable interest, both experimentally as well as theoretically. There are basically two different approaches for doing electronic structure calculations: one method, the so-called crystal orbital method, uses periodic boundary conditions and is essentially based on concepts of solid state theory. The other method is essentially a quantum chemical method since it approximates the polymer by oligomers consisting of a finite number of monomer units, i.e., by molecules of finite size. In this way, the highly-developed technology of quantum chemical molecular programs can be used. Unfortunately, oligomers of finite size are not necessarily able to model those features of a polymer which crucially depend on its in principle infinite extension. However, in such a case extrapolation techniques can be extremely helpful. For example, one can perform electronic structure calculations for a sequence of oligomers with an increasing number of monomer units. In the next step, one then can try to determine the limit of this sequence for an oligomer of infinite length with the help of suitable extrapolation methods. Several different extrapolation methods are discussed which are able to accomplish an extrapolation of energies and properties of oligomers to the infinite chain limit. Calculations for the ground state energy of polyacetylene are presented which demonstrate the practical usefulness of extrapolation methods.