Polarization energy of a localized charge in a molecular crystal. V. Effect of vacancies

The polarization energy P due to a localized charge, the charge-quadrupole energy W_Q and the changes ΔP and ΔW_Q caused by an unrelaxed vacancy are calculated for the linear polyacene crystals benzene, naphthalene, anthracene, tetracene and pentacene. For tetracene and pentacene extrapolated polarizabilities and quadrupole moments are used. The changes ΔP are all positive and less than 0.1 eV, whereas the changes ΔW_Q reach 0.3 eV and can be of either sign. These differences arise because ΔP and ΔW_Q come from induced and permanent multipoles respectively. Vacancies produce complicated trapping centres of large cross section, with trap depths 0.13-0.21 eV along the series for electrons and 0.03-0.07 eV for holes, plus scattering maxima of 0.14-0.19 eV and 0.23-0.34 eV respectively. Vacancies may thus be more important in carrier transport than previously supposed, while charge-quadrupole contributions are likely to dominate the effects of other crystal imperfections.