Generalized exciton with a noninteger particle and hole charge as an excitation order

The conventional concept of the exciton quasiparticle with its particle and hole of unit charges is based on a one-electron band-structure paradigm. We propose a concept of the generalized exciton (GE) with noninteger hole and particle charges, which reflects the true mixed character of molecular electronic excitations and which absorbs the conventional concept of exciton as its limiting case. The sum of the GE hole and particle charge distributions represents the difference between the electron densities of considered excited and ground many-electron states. A universal classification of excited states according to the magnitude of the GE particle (or absolute hole) charge is proposed. In this classification, the GE charge serves as the excitation order (EO) reflecting the relative proximity of an excitation to a single or a double excitation. The proposed GE-EO concept is illustrated with the EOs and with the GE particle and hole distributions obtained for the prototype linear hydrogen chains H_n (n = 4, 6, 12) as well as for the boron hydride and 1,3-butadiene molecules.