Correction: Benchmark and performance of long-range corrected time-dependent density functional tight binding (LC-TD-DFTB) on rhodopsins and light-harvesting complexes.

Correction for 'Benchmark and performance of long-range corrected time-dependent density functional tight binding (LC-TD-DFTB) on rhodopsins and light-harvesting complexes' by Beatrix M. Bold et al., Phys. Chem. Chem. Phys., 2020, 22, 10500-10518, https://doi.org/10.1039/C9CP05753F.

Analytical Time-Dependent Long-Range Corrected Density Functional Tight Binding (TD-LC-DFTB) Gradients in DFTB+: Implementation and Benchmark for Excited-State Geometries and Transition Energies.

The absorption and emission of light is a ubiquitous process in chemical and biological processes, making a theoretical description inevitable for understanding and predicting such properties. Although ab initio and DFT methods are capable of describing excited states with good accuracy in many cases, the investigation of dynamical processes and the need to sample the phase space in complex systems often requires methods with reduced computational costs but still sufficient accuracy. In the present work, we report the derivation and implementation of analytical nuclear gradients for time-dependent long-range corrected density functional tight binding (TD-LC-DFTB) in the DFTB+ program. The accuracy of the TD-LC-DFTB potential-energy surfaces is benchmarked for excited-state geometries and adiabatic as well as vertical transition energies. The benchmark set consists of more than 100 organic molecules taken as subsets from available benchmark sets. The reported method yields a mean deviation of 0.31 eV for adiabatic excitation energies with respect to CC2. In order to study more subtle effects, seminumerical second derivatives based on the analytical gradients are employed to simulate vibrationally resolved UV/vis spectra. This extensive test exhibits few problematic cases, which can be traced back to the parametrization of the repulsive potential.

Benchmark and performance of long-range corrected time-dependent density functional tight binding (LC-TD-DFTB) on rhodopsins and light-harvesting complexes.

The chromophores of rhodopsins (Rh) and light-harvesting (LH) complexes still represent a major challenge for a quantum chemical description due to their size and complex electronic structure. Since gradient corrected and hybrid density functional approaches have been shown to fail for these systems, only range-separated functionals seem to be a promising alternative to the more time consuming post-Hartree-Fock approaches. For extended sampling of optical properties, however, even more approximate approaches are required. Recently, a long-range corrected (LC) functional has been implemented into the efficient density functional tight binding (DFTB) method, allowing to sample the excited states properties of chromophores embedded into proteins using quantum mechanical/molecular mechanical (QM/MM) with the time-dependent (TD) DFTB approach. In the present study, we assess the accuracy of LC-TD-DFT and LC-TD-DFTB for rhodopsins (bacteriorhodopsin (bR) and pharaonis phoborhodopsin (ppR)) and LH complexes (light-harvesting complex II (LH2) and Fenna-Matthews-Olson (FMO) complex). This benchmark study shows the improved description of the color tuning parameters compared to standard DFT functionals. In general, LC-TD-DFTB can exhibit a similar performance as the corresponding LC functionals, allowing a reliable description of excited states properties at significantly reduced cost. The two chromophores investigated here pose complementary challenges: while huge sensitivity to external field perturbation (color tuning) and charge transfer excitations are characteristic for the retinal chromophore, the multi-chromophoric character of the LH complexes emphasizes a correct description of inter-chromophore couplings, giving less importance to color tuning. None of the investigated functionals masters both systems simultaneously with satisfactory accuracy. LC-TD-DFTB, at the current stage, although showing a systematic improvement compared to TD-DFTB cannot be recommended for studying color tuning in retinal proteins, similar to some of the LC-DFT functionals, because the response to external fields is still too weak. For sampling of LH-spectra, however, LC-TD-DFTB is a viable tool, allowing to efficiently sample absorption energies, as shown for three different LH complexes. As the calculations indicate, geometry optimization may overestimate the importance of local minima, which may be averaged over when using trajectories. Fast quantum chemical approaches therefore may allow for a direct sampling of spectra in the near future.

Generalized Density-Functional Tight-Binding Repulsive Potentials from Unsupervised Machine Learning.

We combine the approximate density-functional tight-binding (DFTB) method with unsupervised machine learning. This allows us to improve transferability and accuracy, make use of large quantum chemical data sets for the parametrization, and efficiently automatize the parametrization process of DFTB. For this purpose, generalized pair-potentials are introduced, where the chemical environment is included during the learning process, leading to more specific effective two-body potentials. We train on energies and forces of equilibrium and nonequilibrium structures of 2100 molecules, and test on ∼130 000 organic molecules containing O, N, C, H, and F atoms. Atomization energies of the reference method can be reproduced within an error of ∼2.6 kcal/mol, indicating drastic improvement over standard DFTB.

Parametrization and Benchmark of Long-Range Corrected DFTB2 for Organic Molecules.

We present the parametrization and benchmark of long-range corrected second-order density functional tight binding (DFTB), LC-DFTB2, for organic and biological molecules. The LC-DFTB2 model not only improves fundamental orbital energy gaps but also ameliorates the DFT self-interaction error and overpolarization problem, and further improves charge-transfer excited states significantly. Electronic parameters for the construction of the DFTB2 Hamiltonian as well as repulsive potentials were optimized for molecules containing C, H, N, and O chemical elements. We use a semiautomatic parametrization scheme based on a genetic algorithm. With the new parameters, LC-DFTB2 describes geometries and vibrational frequencies of organic molecules similarly well as third-order DFTB3/3OB, the de facto standard parametrization based on a GGA functional. LC-DFTB2 performs well also for atomization and reaction energies, however, slightly less satisfactorily than DFTB3/3OB.

Time-Dependent Extension of the Long-Range Corrected Density Functional Based Tight-Binding Method.

We present a consistent linear response formulation of the density functional based tight-binding method for long-range corrected exchange-correlation functionals (LC-DFTB). Besides a detailed account of derivation and implementation of the method, we also test the new scheme on a variety of systems considered to be problematic for conventional local/semilocal time-dependent density functional theory (TD-DFT). To this class belong the optical properties of polyacenes and nucleobases, as well as charge transfer excited states in molecular dimers. We find that the approximate LC-DFTB method exhibits the same general trends and similar accuracy as range-separated DFT methods at significantly reduced computational cost. The scheme should be especially useful in the determination of the electronic excited states of very large molecules, for which conventional TD-DFT is supposed to fail due to a multitude of artificial low energy states.

Simulation of Singlet Exciton Diffusion in Bulk Organic Materials.

We present a scheme for nonadiabatic direct dynamics simulation of Frenkel exciton diffusion in bulk molecular systems. The fluctuations of exciton couplings caused by the molecular motion can crucially influence exciton transport in such materials. This effect can be conveniently taken into account by computing the exciton couplings along molecular dynamics trajectories, as shown recently. In this work, we combine Molecular Dynamics simulations with a Frenkel Hamiltonian into a combined quantum-mechanical/molecular mechanics approach in order to allow for a simultaneous propagation of nuclear and electronic degrees of freedom using nonadiabatic dynamics propagation schemes. To reach the necessary time and length scales, we use classical force-fields and the semiempirical time-dependent density functional tight-binding method in combination with a fragmentation of the electronic structure. Fewest-switches surface-hopping, with adaptions to handle trivial crossings, and the Boltzmann-corrected Ehrenfest method are used to follow the excitonic quantum dynamics according to the classical evolution of the nuclei. As an application, we present the simulation of singlet exciton diffusion in crystalline anthracene, which allows us to address strengths and shortcomings of the presented methodology in detail.

Simulation of Temperature-Dependent Charge Transport in Organic Semiconductors with Various Degrees of Disorder.

Different trends in the temperature dependence of the mobility can be observed in organic semiconductors, which constitutes a serious challenge for theoretical approaches. In this work, we apply an atomistic bottom-up simulation for the calculation of temperature-dependent mobilities of a broad selection of materials, ranging from single crystal to amorphous solid. We evaluate how well the method is able to distinguish temperature dependences of different materials and how the findings relate to experimental observations. The applied method is able to cover the full range of temperature dependencies from activated transport in amorphous materials to band-like transport in crystals. In well-characterized materials, we find good agreement with the experiment and a band-like temperature dependence. In less-ordered materials, we find discrepancies from the experiment that indicated that experimentally studied materials possess a higher degree of disorder than do the simulated defect-free morphologies.

Multi-Scale Approach to Non-Adiabatic Charge Transport in High-Mobility Organic Semiconductors.

A linear scaling QM/MM model for studying charge transport in high-mobility molecular semiconductors is presented and applied to an anthracene single crystal and a hexabenzocoronene derivative in its liquid crystalline phase. The model includes both intra- and intermolecular electron-phonon couplings, long-range interactions with the environment, and corrections to the self-interaction error of density functional theory. By performing Ehrenfest simulations of the cationic system, hole mobilities are derived and compared to the experiment. A detailed picture of the charge carrier dynamics is given, and the performance of our method is discussed.