Use of Propagators in the Hückel Model. II. Propagators in Terms of Trigonometrical Functions

Abstract

The propagators of the chain molecules with and without the bond alternation are expressed in terms of trigonometrical functions. These expressions are convenient to practical manipulations. For exercises, the total energy, charge density and bond order are calculated.

Topological reference systems

“…Notably, the superscript, L, implies a chain molecule. In addition, a situation without bond alternation was considered to simplify the discussion; however, this limitation can be easily removed [11].…”

Model calculations of polarizabilities of polyene chains: Oligomers and infinite polymers

“…They derive the Green's functions of regular oligomers by a renormalization perturbation expansion and by the Lowdin partitioning method [ 281. They have also expressed the propagators in terms of trigonometrical functions [29] in order to provide analytical formulas of charge densities and of total energies. The renormalization perturbation expansion is also used through Dyson's equation to obtain atom-atom and bondbond polarizabilities [ 301, which are directly comparable to the results of standard Huckel tables (see, for example, Heilbronner [ 3 1 ] ) .…”