Knowledge Bank

Surface states in cubic molecular crystals were determined, utilizing the Hamiltonian partition $method.1$ The crystal Hamiltonian was split into an unperturbed term which can be diagonalized, and a perturbation term. The perturbation term involved exciton transfer terms (J-terms) and environmental shift terms (D-terms). The pertinent results are: a) when the absolute value of the D-term exceeds the absolute value of the J-term a localized state splits out of the exciton band; b) two localized states are formed for thin crystals; however, the splitting between the localized states decreases rapidly, as the ratio D/J or the thickness of the crystal increases. The two localized states form a pair of degenerate states in the limit of an infinite crystal; and c) the localization of the exciton on the surface of the crystal is increased with the increase of D/J. The exciton is partially localized on crystal planes adjacent to the surface plane. However this localization falls off rapidly with the increase of distance from the surface plane.