  We present a new methodology to calculate the strong light-matter coupling
between photonic modes in microcavities and large molecular aggregates that
consist of hundreds of molecular fragments. To this end, we combine our
fragment molecular orbital long-range corrected time-dependent density
functional tight-binding methodology with a generalized Tavis-Cummings
Hamiltonian. We employ an excitonic Hamiltonian, which is built from a
quasi-diabatic basis that is constructed from locally excited and
charge-transfer states of all molecular fragments. In order to calculate
polaritonic states, we extend our quasi-diabatic basis to include photonic
states of a microcavity and derive and implement the couplings between the
locally excited states and the cavity states and built a Tavis-Cummings
Hamiltonian that incorporates the intermolecular excitonic couplings.
Subsequently, we demonstrate the capability of our methodology by simulating
the influence of the electric field polarization on the polaritonic spectra for
a tetracene aggregate of 125 monomers. Furthermore, we investigate the
dependence of the splitting of the upper and lower polaritonic branches on the
system size by comparing the spectra of three different tetracene clusters. In
addition, we investigate the polariton dispersion of a large tetracene
aggregate for electric field polarizations in the x, y and z direction. Our new
methodology can facilitate the future study of exciton dynamics in complex
molecular systems, which consist of up to hundreds of molecules, that are
influenced by strong light-matter coupling to microcavities.
