Fermion-propagator calculations of excitations in polyenes with the use of a Heisenberg (XYZ) Hamiltonian. I. Formalism and parametrization

An effective spin operator of the Heisenberg type is used for studying the low-lying excitation spectrum of linear polyenes. A Jordan-Wigner transformation allows one to write the spin Hamiltonian in terms of fermion operators, and a single-fermion propagator is employed for calculating the excitation energies of the system. The correlated reference states for the propagator are expressed in terms of neutral valence-bond fermion configurations. Results are given for small linear polyenes with N sites. Some results for small rings are also given.