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.