An Efficient Exciton Coupling Scheme Based on Simplified Time-Dependent Density Functional Theory

A very efficient and broadly applicable exciton coupling (ExC) approach based on simplified time-dependent density functional theory (sTD-DFT) is presented. Starting from this parent method, nonoverlapping fragments and neglect of interfragment charge transfer excitations are assumed to arrive at the ExC procedure. This leads to an ExC Hamiltonian that provides equivalent electronic absorption and circular dichroism spectra as the parent sTD-DFT method for largely separated fragments. The ExC approach easily accelerates the computation of such spectra of molecular aggregates by about 2 orders of magnitude compared to sTD-DFT. The latter itself is already faster by about 4-5 orders of magnitude compared to regular TD-DFT. We demonstrate the performance of the approach for excitation spectra of organic molecular clusters. Given that the fragment electronic structure in the ExC-sTD-DFT approach is solved independently, computation of spectra for systems with ∼10,000 atoms can be performed within minutes of computation time. Furthermore, the role of electrostatic embedding in the independent fragments is investigated. For the purposes covered in this work, the embedding can be simplified by employing a dielectric continuum, thus greatly reducing the overall computational complexity. This approach may be used in screening photophysical properties of large molecular aggregates and soft matter materials. We present the derivation and implementation for the Tamm-Dancoff-approximated and the random-phase-approximation eigenvalue problems. Benchmarks compared to the parent sTD-DFT methods are shown for absorption and electronic circular dichroism spectra.