Long-range corrected fragment molecular orbital density functional tight-binding method for excited states in large molecular systems

Abstract

Herein, we present a new method to efficiently calculate electronically excited states in large molecular assemblies, consisting of hundreds of molecules. For this purpose, we combine the long-range corrected tight-binding density-functional fragment molecular orbital method (FMO-LC-DFTB) with an excitonic Hamiltonian, which is constructed in the basis of locally excited and charge-transfer configuration state functions calculated for embedded monomers and dimers and accounts explicitly for the electronic coupling between all types of excitons. We first evaluate both the accuracy and efficiency of our fragmentation approach for molecular dimers and aggregates by comparing with the full LC-TD-DFTB method. The comparison of the calculated spectra of an anthracene cluster shows a very good agreement between our method and the LC-TD-DFTB reference. The effective computational scaling of our method has been explored for anthracene clusters and for perylene bisimide aggregates. We demonstrate the applicability of our method by the calculation of the excited state properties of pentacene crystal models consisting of up to 319 molecules. Furthermore, the participation ratio of the monomer fragments to the excited states is analyzed by the calculation of natural transition orbital (NTO) participation numbers, which are verified by the hole and particle density for a chosen pentacene cluster. The use of our FMO-LC-TDDFTB method will allow for future studies of excitonic dynamics and charge transport to be performed on complex molecular systems consisting of thousands of atoms.

Analysis of Site Energies and Excitonic Couplings: The Role of Symmetry and Polarization

“…EOM-CC calculations of chromophores can be performed using the framework of the fragment molecular orbital (FMO) method, − which can also be used for computing excited states. ,,− In FMO, some fragments can be designated as chromophores, and there may be other fragments (e.g., solvent) that are added for describing polarization. Electronic excitations of chromophores can be computed with and without an embedding potential, yielding in either case the site energy ω I of each chromophore I .…”

“…There is a variety of theoretical methods developed for calculating local − and nonlocal − excited states in large molecular systems. There is an ongoing work to model the excitonic coupling ,− and the effect of environment on it. − Fragment-based methods are naturally conducive to handling the excitonic coupling by treating chromophore as fragments.…”

Nonadiabatic Exciton Dynamics and Energy Gradients in the Framework of FMO-LC-TDDFTB

“…The development of semiempirical quantum mechanical (SQM) methodologies has enabled the simulation of molecular dynamics in larger systems with reduced computational demands, owing to the utilization of minimal basis sets and the neglect of differential overlap between atomic basis functions. , Notably, among the spectrum of SQM techniques, the relatively recent emergence of the density-functional tight-binding (DFTB) − method has demonstrated efficacy in simulating processes within the excited-state manifold. − Furthermore, the extension of the DFTB method with the long-range correction has enabled the investigation of charge-transfer excitations . The long-range corrected time-dependent density-functional tight-binding (LC-TDDFTB) method has been integrated into multiple software packages, such as DFTB+, DFTBaby, GAMESS, , and DIALECT, enabling the investigation of excited-state dynamics in molecular systems comprising several hundred atoms. Another semiempirical tight-binding approach is the gfn-xtb methodology of Grimme and co-workers, − which shows excellent results for ground-state molecular properties and dynamics simulations.…”

Analytic Gradient for Time-Dependent Density Functional Theory Combined with the Fragment Molecular Orbital Method

“…The fragment molecular orbital (FMO) method − has been developed for both ground and excited states. The latter can be computed with multiconfigurational self-consistent field (MCSCF), configuration interaction (CI), , GW approximation, time-dependent density functional theory (TDDFT), − and time-dependent density functional tight-binding . FMO has been applied to computing ground − and excited states − of large molecular systems.…”