Ž . Synthetic Metals 109 2000 73–77 www.elsevier.comrlocatersynmet Charge-pair states in organic molecular crystals: localized vs. delocalized description Piotr Petelenz ) , Grzegorz Mazur K. Guminski Department of Theoretical Chemistry, Jagiellonian UniÕersity, Ingardena 3, 30-060 Cracow, Poland ´ Received 26 June 1999; accepted 10 September 1999 Abstract The Merrifield model of electronic excitations in a linear molecular crystal is applied to investigate the relation between the bound Ž . electron–hole pairs charge transfer excitons and the corresponding continuum of unbound states. It is demonstrated that, contrary to the conventional explanation, the difference of 0.2–0.3 eV between the electric and optical band gap observed for polyacene crystals is a consequence of charge delocalization rather than lattice relaxation. The results also suggest that in some molecular crystals and polymers, moderate structural disorder may strengthen the photoconductive response instead of suppressing it, which suggests a new strategy in the search for efficient photoconductors. q 2000 Elsevier Science S.A. All rights reserved. Keywords: CT excitons; Exciton binding energy; Electric band gap; Optical band gap; Charge delocalization 1. Introduction While conventional semiconductor theory is deeply rooted in the Bloch Theorem and the delocalized picture of charge carriers, the description of molecular crystals is somewhat ambiguous in this respect. On the one hand, owing to the translational symmetry of the crystal, the Bloch Theorem is still valid, so that the eigenvectors are delocalized, since they have to transform as irreducible representations of the translation group, labeled by quasi- momentum. On the other hand, the weakness of inter- Ž . molecular interactions makes the localized molecular wave functions a convenient basis set and enables one to express the crystal properties in terms of the molecular properties. This is especially useful in microelectrostatic w x calculations 1–4 where molecular polarizabilities are uti- lized to compute the polarization energy of the crystal. The Fourier transformation between the localized and delocalized picture is in itself a straightforward, well-de- fined and therefore harmless procedure. Interpretational inconsistencies arise on the borderline between the results of the calculations, expressed in the localized picture, and Ž experiment, which deals with the actual and therefore ) Corresponding author. Tel.: q 48-12-6336377 ext. 212; fax: q 48-12- 6340515; e-mail: petelenz@trurl.ch.uj.edu.pl . delocalized, by virtue of the Bloch Theorem eigenstates of the crystal. This issue will be studied in the present paper. Another potential source of difficulties arises on the borderline between the bound and unbound electron–hole eigenstates. According to the Bloch Theorem, the motion of the centre of mass of an electron–hole pair is always described by a delocalized wave function, characterized by some value of quasimomentum. This may also apply to the relative motion of the two charges; the corresponding unbound states represent the free charge carriers that give rise, for example, to photoconductivity. However, in addi- tion to this continuum, there exist also bound electron–hole states. While the centre of mass of these states is still delocalized, the relative motion of the charges is quan- tized, and the emerging discrete levels are referred to as excitons. The main difficulty in describing the transition region Ž between the free-carrier continuum and the bound exci- . ton states is of technical nature. In the calculation of exciton levels, one usually introduces a finite basis set, eliminating the coupling between the bound state and the free charge Hilbert subspaces. Consequently, the exciton states that are close to the dissociation limit are poorly described. In particular, there is nothing to prevent their calculated energies from exceeding the energy of a free electron–hole pair with the same value of the centre-of- mass quasimomentum, which is evidently an artefact. The difficulty may be avoided by studying a model where 0379-6779r00r$ - see front matter q 2000 Elsevier Science S.A. All rights reserved. Ž . PII: S0379-6779 99 00200-3