The step-potential model for π-electrons in hydrocarbon-systems

This paper presents a study of π-electrons in hydrocarbon chains which could be of interest for biological molecules where the π-electrons play an important role. In single electron models, the many body π-electron Hamiltonian is simplified to a Hamiltonian of independent electrons moving in orbitals to be described as solutions of the 3D-Schroedinger equation of an electron in a potential V(x,y,z) associated with the lattice sites. These orbitals have nodes in the layer plane. It is assumed that V(x,y,z) is the sum of the Slater potentials of the two adjacent charged lattice sites and the contribution of all other sites are neglected. The motion of this electron is considered to be correlated with the motion of the other electrons. In the case of a chain with bonds fixed to equal bond lengths, the most radical simplification still leads to a reasonable description of the wave function of an electron in the potential V(x,y,z), if the electron wave is assumed to extend by about one bond length beyond the centers of the sites at the chain ends. This model is analysed in the case of a cyanine dye with resonating structures and polyenes. (J.S.). 10 refs., 5 figs