Extrapolation Methods for Improving the Convergence of Oligomer Calculations to the Infinite Chain Limit of Quasi-Onedimensional Stereoregular Polymers

摘要

Quasi-onedimensional stereoregular polymers as for example polyacetylene arecurrently of considerable interest. There are basically two differentapproaches for doing electronic structure calculations: One method isessentially based on concepts of solid state theory. The other method isessentially a quantum chemical method since it approximates the polymer byoligomers consisting of a finite number of monomer units. In this way, thehighly developed technology of quantum chemical molecular programs can be used.Unfortunately, oligomers of finite size are not necessarily able to model thosefeatures of a polymer which crucially depend of its in principle infiniteextension. In such a case extrapolation techniques can be extremely helpful.For example, one can perform electronic structure calculations for a sequenceof oligomers with an increasing number of monomer units. In the next step, onethen can try to determine the limit of this sequence for an oligomer ofinfinite length with the help of suitable extrapolation methods. Severaldifferent extrapolation methods are discussed which are able to accomplish anextrapolation of energies and properties of oligomers to the infinite chainlimit. Calculations for the ground state energy of polyacetylene are presentedwhich demonstrate the practical usefulness of extrapolation methods.