Excited States of a Linear Molecular Chain Containing an Impurity

A one-dimensional model of coupled molecules containing an impurity is proposed and properties of its excited states are examined for the purpose of understanding excitation energy localization and delocalization in radiation chemistry. The model consists of a linear array of equally spaced identical molecules and an impurity molecule and is characterized by Coulomb and resonance integrals, viz. , matrix elements of the Hamiltonian of the total system between the wave functions corresponding to localized excitation. The eigen energies of the excited states of this model are shown to form a band with a particular level separated downward from the bottom and/or another one upwards from the top of the band. Another model containing a displaced molecule in a chain of otherwise equally spaced identical molecules is also studied and shown to possess the same type of level scheme. The separation of the bottom or the top level from the band edge is calculated for particular cases where the coupling between the wave functions corresponding to localized excitation is of dipole-dipole or quadrupole-quadrupole type. Implications of the results to radiation chemistry are discussed.