Trajectory Surface Hopping Approach to Condensed-Phase Nonradiative Relaxation Dynamics Using Divide-and-Conquer Spin-Flip Time-Dependent Density-Functional Tight Binding

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

We introduce a novel methodology for simulating the excited-state dynamics of extensive molecular aggregates in the framework of the long-range corrected time-dependent density-functional tight-binding fragment molecular orbital method (FMO-LC-TDDFTB) combined with the mean-field Ehrenfest method. The electronic structure of the system is described in a quasi-diabatic basis composed of locally excited and charge-transfer states of all fragments. In order to carry out nonadiabatic molecular dynamics simulations, we derive and implement the excited-state gradients of the locally excited and charge-transfer states. Subsequently, the accuracy of the analytical excited-state gradients is evaluated. The applicability to the simulation of exciton transport in organic semiconductors is illustrated on a large cluster of anthracene molecules. Additionally, nonadiabatic molecular dynamics simulations of a model system of benzothieno-benzothiophene molecules highlight the method's utility in studying charge-transfer dynamics in organic materials. Our new methodology will facilitate the investigation of excitonic transfer in extensive biological systems, nanomaterials, and other complex molecular systems consisting of thousands of atoms.

Implementation of Nonadiabatic Molecular Dynamics for Intersystem Crossing Based on a Time-Dependent Density-Functional Tight-Binding Method

Intersystem crossing (ISC) and internal conversion (IC) are types of nonadiabatic transitions that play important roles in a wide range of fields, including photochemistry, photophysics, and photobiology. The nonadiabatic molecular dynamics (NA-MD) method is a powerful tool for computational simulations of dynamic phenomena involving nonadiabatic transitions. In this study, we implemented the NA-MD method, which treats ISC and IC on an equal footing, where the electronic structure is treated at the level of the time-dependent (TD) density-functional tight-binding (DFTB) method, a low-cost semiempirical analog of TD density functional theory (DFT). In particular, the spin-orbit coupling calculation algorithm was implemented in the TD-DFTB framework, and the results showed trends similar to those obtained using TD-DFT. In addition, the NA-MD method successfully reproduced ultrafast ISC of 2-nitronaphthalene.

Excitation configuration analysis for divide-and-conquer excited-state calculation method using dynamical polarizability

The authors previously developed a divide-and-conquer (DC)-based non-local excited-state calculation method for large systems using dynamical polarizability [Nakai and Yoshikawa, J. Chem. Phys. 146, 124123 (2017)]. This method evaluates the excitation energies and oscillator strengths using information on the dynamical polarizability poles. This article proposes a novel analysis of the previously developed method to obtain further configuration information on excited states, including excitation and de-excitation coefficients of each excitation configuration. Numerical applications to simple molecules, such as ethylene, hydrogen molecule, ammonia, and pyridazine, confirmed that the proposed analysis could accurately reproduce the excitation and de-excitation coefficients. The combination with the DC scheme enables both the local and non-local excited states of large systems with an excited nature to be treated.

Evaluation of tight-binding DFT performance for the description of organic photochromes properties

Photochromic molecules are widely studied and developed for their many potential applications. To optimize the required properties through theoretical models, a considerable chemical space is to be explored, and their environment in devices is to be accounted for.. To this end, cheap and reliable computational methods can be powerful tools to steer synthetic developments. As ab initio methods remain costly for extensive studies (in terms of the size of the system and/or number of molecules), semiempirical methods such as density functional tight-binding (TB) could offer a good compromise between accuracy computational cost. However, these approaches necessitate benchmarking on the families of compounds of interest. Thus, the aim of the present study is to evaluate the accuracy of several key features calculated with TB methods (DFTB2, DFTB3, GFN2-xTB, and LC-DFTB2) for three sets of photochromic organic molecules: azobenzene (AZO), norbornadiene/quadricyclane (NBD/QC), and dithienylethene (DTE) derivatives. The features considered here are the optimized geometries, the difference in energy between the two isomers (ΔE), and of the energies of the first relevant excited states. All the TB results are compared to those obtained with DFT methods and state-of-the-art electronic structure calculation methods: DLPNO-CCSD(T) for ground states and DLPNO-STEOM-CCSD for excited states. Our results show that, overall, DFTB3 is the TB method leading to the best results for the geometries and the ΔE values and can be used alone for these purposes for NBD/QC and DTE derivatives. Single point calculations at the r2SCAN-3c level using TB geometries allow circumventing the deficiencies of the TB methods in the AZO series. For electronic transition calculations, the range separated LC-DFTB2 method is the most accurate TB method tested for AZO and NBD/QC derivatives, in close agreement with the reference.

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

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 it 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 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.

Divide-and-Conquer Linear-Scaling Quantum Chemical Computations

Fragmentation and embedding schemes are of great importance when applying quantum-chemical calculations to more complex and attractive targets. The divide-and-conquer (DC)-based quantum-chemical model is a fragmentation scheme that can be connected to embedding schemes. This feature article explains several DC-based schemes developed by the authors over the last two decades, which was inspired by the pioneering study of DC self-consistent field (SCF) method by Yang and Lee (J. Chem. Phys. 1995, 103, 5674-5678). First, the theoretical aspects of the DC-based SCF, electron correlation, excited-state, and nuclear orbital methods are described, followed by the two-component relativistic theory, quantum-mechanical molecular dynamics simulation, and the introduction of three programs, including DC-based schemes. Illustrative applications confirmed the accuracy and feasibility of the DC-based schemes.

How Good Is the Vibronic Hamiltonian Repetition Approach for Long-Time Nonadiabatic Molecular Dynamics?

Multiple applied studies of slow nonadiabatic processes in nanoscale and condensed matter systems have adopted the "repetition" approximation in which long trajectories for such simulations are obtained by concatenating shorter trajectories, directly available from ab initio calculations, many times. Here, we comprehensively assess this approximation using model Hamiltonians with parameters covering a wide range of regimes. We find that state transition time scales may strongly depend on the length of the repeated data, although the convergence is not monotonic and may be slow. The repetition approach may under- or overestimate the time scales by a factor of ≤7-8, does not directly depend on the dispersion of energy gap and nonadiabatic coupling (NAC) frequencies, but may depend on the magnitude of the NACs. We suggest that the repetition-based nonadiabatic dynamics may be inaccurate in simulations with very small NACs, where intrinsic transition times are on the order of ≥100 ps.

Scalable Ehrenfest Molecular Dynamics Exploiting the Locality of Density-Functional Tight-Binding Hamiltonian

To explore the science behind excited-state dynamics in high-complexity chemical systems, a scalable nonadiabatic molecular dynamics (MD) technique is indispensable. In this study, by treating the electronic degrees of freedom at the density-functional tight-binding level, we developed and implemented a reduced scaling and multinode-parallelizable Ehrenfest MD method. To achieve this goal, we introduced a concept called patchwork approximation (PA), where the effective Hamiltonian for real-time propagation of the electronic density matrix is partitioned into a set of local parts. Numerical results for giant icosahedral fullerenes, which comprise up to 6000 atoms, suggest that the scaling of the present PA-based method is less than quadratic, which yields a significant advantage over the conventional cubic scaling method in terms of computational time. The acceleration by the parallelization on multiple nodes was also assessed. Furthermore, the electronic and structural dynamics resulting from the perturbation by the external electric field were accurately reproduced with the PA, even when the electronic excitation was spatially delocalized.