  Herein, we present a new method to efficiently calculate electronically
excited states in large molecular assemblies, consisting of hundreds of
molecules. For this purpose, we combine the long-range corrected tight-binding
density-functional fragment molecular orbital method (FMO-LC-DFTB) with an
excitonic Hamiltonian, which is constructed in the basis of locally excited and
charge-transfer configuration state functions calculated for embedded monomers
and dimers and accounts explicitly for the electronic coupling between all
types of excitons. We first evaluate both the accuracy and efficiency of our
fragmentation approach for molecular dimers and aggregates by comparing with
the full LC-TD-DFTB method. The comparison of the calculated spectra of an
anthracene cluster shows a very good agreement between our method and the
LC-TD-DFTB reference. The effective computational scaling of our method has
been explored for anthracene clusters and for perylene bisimide aggregates. We
demonstrate the applicability of our method by the calculation of the excited
state properties of pentacene crystal models consisting of up to 319 molecules.
Furthermore, the participation ratio of the monomer fragments to the excited
states is analyzed by the calculation of natural transition orbital (NTO)
participation numbers, which are verified by the hole and particle density for
a chosen pentacene cluster. The use of our FMO-LC-TDDFTB method will allow for
future studies of excitonic dynamics and charge transport to be performed on
complex molecular systems consisting of thousands of atoms.
