An algebraic approach to the molecular electronic systems. The dynamical interpretation for the Hückel orbitals in the coset space representation

The coset space treatment of the molecular electronic dynamics is demonstrated in which Hückel orbitals are merely special points in the complicated, multi-dimensional manifolds. The results for the propenyl and cyclo-propenyl systems with degenerate site energies show that for symmetric inter-site couplings, the dynamics is periodic while for asymmetric couplings, it can be irregular or chaotic. Other initial conditions besides the Hückel parameters are considered with results discussed. Though sample calculations are limited to systems of one and two electrons in three orbitals, the conclusions about the chaotic universality in molecular electronic dynamics are drawn.