Collective electronically excited states of a uniform chain of atoms

Electronically excited states of finite uniform chains of atoms were considered taking into account the influence of the continuous energy spectrum. Traditional quantum-chemical methods for calculating two-electron transitions between neighboring chain atoms were combined with the asymptotic theory of interactions between excited atoms and neutral particles and the mathematical apparatus of the theory of multiple scattering for taking into account intercenter transitions in an ensemble of interacting centers. Recurrence equations for describing energy zones containing symmetrical and antisymmetric excited state levels of chains with an arbitrary length were obtained. Depending on system parameters, different modes of the distribution of the electron density of collective excited states were possible. At a certain ratio between level shifts and exchange integral values, excited states with a uniform electron density distribution over all chain nodes could form for certain solutions. This was a fortuitous circumstance caused by the influence of the continuous spectrum. Such states appeared at small principal quantum number n values, they were similar to one-electron excitations of the type of Frenkel excitons, when an electron was localized near its Coulomb center. These conditions were rapidly disturbed as n increased, and one-electron excitations of a linear molecule were formed in the system (that is, limiting excitations of the type of Wannier-Mott excitons did not form).