FMO-LC-TDDFTB method for excited states of large molecular assemblies in the strong light-matter coupling regime

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.