Calculating excitonic interactions using transition currents with application to PTCDA

We consider assemblies of molecules where the electronic wavefunctions of different molecules do not overlap. Typically, the interaction Hamiltonian between two molecules is then described by their Coulomb interaction, and matrix-elements between products of single-molecule energy eigenstates are calculated using the corresponding (transition) charge densities. In the present work, we compare this approach with one based on (transition) current densities. As an example, we perform calculations for 3,4,9,10-perylenetetracarboxylicacid-dianhydride (PTCDA) molecules in different arrangements. We find that for exact molecular wavefunctions, both methods agree, but there are marked differences for the wavefunctions that we obtained from electronic-structure theory. The main difference can be attributed to the error in the molecular transition energy and results in an arrangement-independent ratio between the interactions calculated with the two approaches. At small separations between the molecules, additional deviations occur, which we trace back to the quality of the molecular electronic wavefunctions. Within both approaches, we calculate interactions for the arrangement of PTCDA on KCl and NaCl surfaces and compare to the ones obtained using the point-dipole approximation. Finally, we provide a simple algorithm that allows fast and accurate calculations of the involved integrals.