A posteriori symmetry analysis of polymer electronic band structures

In an attempt to illustrate how to apply abstract line group theoretical results to electronic structure polymer calculations, an a posteriori symmetry analysis is carried out on the extended Hückel energy band structures of two model chains of H2 molecules, whose symmetries are respectively characterized by the 𝕃;312 and 𝕃;63/mcm line groups. The symmetry quantum numbers have been assigned to the bands, and the compatibility relations and selection rules for direct optical absorption are derived.