  The Frenkel exciton Hamiltonian is at the heart of many simulations of
excitation energy transfer in molecular aggregates. It separates the aggregate
into Coulomb-coupled monomers. Here it is shown that the respective parameters,
i.e. monomeric excitation energies and Coulomb couplings between transition
densities, can be efficiently calculated using time-dependent
tight-binding-based density functional theory (TD-DFTB). Specifically, Coulomb
couplings are expressed in terms of self-consistently determined Mulliken
transition charges. The determination of the sign of the coupling requires an
additional super-molecule calculation. The approach is applied to two dimer
systems. First, formaldehyde oxime for which a detailed comparison with
standard DFT using the B3LYP and the PBE functionals is provided. Second, the
Coulomb coupling is explored in dependence on the intermolecular coordinates
for a perylene bisimide dimer. This provides structural evidence for the
previously observed biphasic aggregation behavior of this dye.
