Electronic spectroscopy is an indispensable tool for the characterization of the properties of electronic states, from core to valence excitations, including their coupling to vibrational degrees of freedom as well as to a surrounding medium . While linear techniques provide lineshapes of molecular transitions, time-domain nonlinear spectroscopy is capable of unraveling the photophysical and photochemical dynamics hidden under these lineshapes. The development of theoretical tools for simulation and thus understanding spectroscopic data keeps pace with experimental advances. When it comes to larger molecules and supramolecular or pigment-protein complexes important, for example, in the context of catalysis or solar energy conversion research, respectively, density functional theory (DFT) is the method of choice. Even though considerable progress has been made to treat larger systems where chromophores are embedded in some medium, for example, by means of the subsystem approach , eventually it is of advantage to resort to model Hamiltonians whose parametrization is obtained from quantum chemical calculations. In the case of electronic excitation of molecular aggregates and pigment-protein complexes, the Frenkel exciton Hamiltonian (FEH), sometimes also called Frenkel-Davydov Hamiltonian, plays a prominent role . Here the aggregate is decomposed into pairs of interacting monomers. Due to the interaction, the local monomer excitations form delocalized excited states, the so-called Frenkel exciton states. If the Frenkel exciton model applies, these exciton states should be identical to the states that would be obtained by a calculation of excited states of the whole aggregate (supermolecule). While such a supermolecule calculation in general is not possible for arbitrarily large aggregates, the FEH has no such size limitation as it is built up from pairwise interactions. (Eventually, the diagonalization step of the parametrized Hamiltonian becomes the bottleneck.) In addition, it offers the possibility for a straightforward interpretation of the aggregate's electronic properties in terms of FEH parameters such as monomer excitation energies and intermonomer coupling strengths. Further, it can be combined with harmonic models for incorporating the coupling to vibrations (e.g. Huang-Rhys model). This enables one to employ quantum dynamics methods such as the multiconfigurational time-dependent Hartree approach for investigating the vibronic dynamics of the aggregate including hundreds of degrees of freedom and more. Technically, the parametrization of the FEH requires the calculation of the electronically excited states of the monomers and the corresponding transition densities. Based on these transition densities the Coulomb coupling between monomer excitations can be obtained.