Simulating the Coupled Structural-Electronic Dynamics of Photoexcited Lead Iodide Perovskites

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.

Learning Decoherence Time Formulas for Surface Hopping from Quantum Dynamics

Surface hopping simulations have achieved great success in many different fields, but their reliability has long been limited by the overcoherence problem. We here present a general machine learning assisted approach to identify optimal decoherence time formulas for surface hopping using exact quantum dynamics as references. In order to avoid computationally expensive force calculations, we use the nuclear kinetic energy and the adiabatic energy difference to iteratively generate the descriptor space. Through multilayer screening of the candidate descriptors and discrete optimization of the relevant parameters, we obtain new energy-based decoherence time formulas. As benchmarked in thousands of diverse multilevel systems and six standard scattering models, surface hopping with our new decoherence time formulas nearly reproduces the exact quantum dynamics while maintaining high efficiency. Thereby, our approach provides a promising avenue for systematically improving the accuracy of surface hopping simulations in complex systems from quantum dynamics data.

Nanoscale and Real-Time Nuclear-Electronic Dynamics Simulation Study of Charge Transfer at the Donor-Acceptor Interface in Organic Photovoltaics

Charge-transfer (CT) processes in donor-acceptor interfaces of organic photovoltaics have been challenging targets for computational chemistry owing to their nanoscale and ultrafast nature. Herein, we report real-time nuclear-electronic dynamics simulations of CT processes in a nanometer-scale donor-acceptor interface model composed of a donor poly(3-hexylthiophene-2,5-diyl) crystal and an acceptor [6,6]-phenyl-C₆₁-butyric acid methyl ester aggregate. The simulations were realized using our original reduced-scaling computational technique, namely, patchwork-approximation-based Ehrenfest dynamics. The results illustrated the CT pathway with atomic resolution, thereby rationalizing the observed excitation-energy dependence of the quantity of CT. Further, nuclear motion, which is affected by the electronic dynamics, was observed to play a significant role in the CT process by modulating molecular orbital energies. The present study suggests that microscopic CT processes strongly depend on local structures of disordered donor-acceptor interfaces as well as coupling between nuclear and electronic dynamics.

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.

Infrared and Near-Infrared Spectrometry of Anatase and Rutile Particles Bandgap Excited in Liquid

Chemical conversion of materials is completed in milliseconds or seconds by assembling atoms over semiconductor photocatalysts. Bandgap-excited electrons and holes reactive on this time scale are key to efficient atom assembly to yield the desired products. In this study, attenuated total reflection of infrared and near-infrared light was applied to characterize and quantify the electronic absorption of TiO2 photocatalysts excited in liquid. Nanoparticles of rutile or anatase were placed on a diamond prism, covered with liquid, and irradiated by steady UV light through the prism. Electrons excited in rutile particles (JRC-TIO-6) formed small polarons characterized by a symmetric absorption band spread over 10000-700 cm-1 with a maximum at 6000 cm-1. Electrons in anatase particles (JRC-TIO-7) created large polarons and produced an asymmetric absorption band that gradually strengthened at wavenumbers below 5000 cm-1 and sharply weakened at 1000 cm-1. The absorption spectrum of large electron polarons in TIO-7 was compared with the absorption reported in a Sr-doped NaTaO3 photocatalyst, and it was suggested that excited electrons were accommodated as large polarons in NaTaO3 photocatalysts efficient for artificial photosynthesis. UV-light power dependence of the absorption bands was observed in N2-exposed decane liquid to deduce electron-hole recombination kinetics. With light power density P > 200 W m-2 (TIO-6) and 2000 W m-2 (TIO-7), the polaron absorptions were enhanced with absorbance being proportional to P1/2. The observed 1/2-order power law suggested recombination of multiple electrons and holes randomly moving in each particle. Upon excitation with smaller P, the power-law order increased to unity. The unity-order power law was interpreted with recombination of an electron and a hole that were excited by the same photon. In addition, an average lifetime of 1 ms was estimated with electron polarons in TIO-6 when weakly excited at P = 20 W m-2 to simulate solar-light irradiation.

Nonadiabatic Molecular Dynamics with Extended Density Functional Tight-Binding: Application to Nanocrystals and Periodic Solids

In this work, we report a new methodology for nonadiabatic molecular dynamics calculations within the extended tight-binding (xTB) framework. We demonstrate the applicability of the developed approach to finite and periodic systems with thousands of atoms by modeling "hot" electron relaxation dynamics in silicon nanocrystals and electron-hole recombination in both a graphitic carbon nitride monolayer and a titanium-based metal-organic framework (MOF). This work reports the nonadiabatic dynamic simulations in the largest Si nanocrystals studied so far by the xTB framework, with diameters up to 3.5 nm. For silicon nanocrystals, we find a non-monotonic dependence of "hot" electron relaxation rates on the nanocrystal size, in agreement with available experimental reports. We rationalize this relationship by a combination of decreasing nonadiabatic couplings related to system size and the increase of available coherent transfer pathways in systems with higher densities of states. We emphasize the importance of proper treatment of coherences for obtaining such non-monotonic dependences. We characterize the electron-hole recombination dynamics in the graphitic carbon nitride monolayer and the Ti-containing MOF. We demonstrate the importance of spin-adaptation and proper sampling of surface hopping trajectories in modeling such processes. We also assess several trajectory surface hopping schemes and highlight their distinct qualitative behavior in modeling the excited-state dynamics in superexchange-like models depending on how they handle coherences between nearly parallel states.

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.

Ab initio nonadiabatic molecular dynamics of charge carriers in metal halide perovskites

Photoinduced nonequilibrium processes in nanoscale materials play key roles in photovoltaic and photocatalytic applications. This review summarizes recent theoretical investigations of excited state dynamics in metal halide perovskites (MHPs), carried out using a state-of-the-art methodology combining nonadiabatic molecular dynamics with real-time time-dependent density functional theory. The simulations allow one to study evolution of charge carriers at the ab initio level and in the time-domain, in direct connection with time-resolved spectroscopy experiments. Eliminating the need for the common approximations, such as harmonic phonons, a choice of the reaction coordinate, weak electron-phonon coupling, a particular kinetic mechanism, and perturbative calculation of rate constants, we model full-dimensional quantum dynamics of electrons coupled to semiclassical vibrations. We study realistic aspects of material composition and structure and their influence on various nonequilibrium processes, including nonradiative trapping and relaxation of charge carriers, hot carrier cooling and luminescence, Auger-type charge-charge scattering, multiple excitons generation and recombination, charge and energy transfer between donor and acceptor materials, and charge recombination inside individual materials and across donor/acceptor interfaces. These phenomena are illustrated with representative materials and interfaces. Focus is placed on response to external perturbations, formation of point defects and their passivation, mixed stoichiometries, dopants, grain boundaries, and interfaces of MHPs with charge transport layers, and quantum confinement. In addition to bulk materials, perovskite quantum dots and 2D perovskites with different layer and spacer cation structures, edge passivation, and dielectric screening are discussed. The atomistic insights into excited state dynamics under realistic conditions provide the fundamental understanding needed for design of advanced solar energy and optoelectronic devices.

Crystal Symmetry and Static Electron Correlation Greatly Accelerate Nonradiative Dynamics in Lead Halide Perovskites

Using a recently developed many-body nonadiabatic molecular dynamics (NA-MD) framework for large condensed matter systems, we study the phonon-driven nonradiative relaxation of excess electronic excitation energy in cubic and tetragonal phases of the lead halide perovskite CsPbI₃. We find that the many-body treatment of the electronic excited states significantly changes the structure of the excited states' coupling, promotes a stronger nonadiabatic coupling of states, and ultimately accelerates the relaxation dynamics relative to the single-particle description of excited states. The acceleration of the nonadiabatic dynamics correlates with the degree of configurational mixing, which is controlled by the crystal symmetry. The higher-symmetry cubic phase of CsPbI₃ exhibits stronger configuration mixing than does the tetragonal phase and subsequently yields faster nonradiative dynamics. Overall, using a many-body treatment of excited states and accounting for decoherence dynamics are important for closing the gap between the computationally derived and experimentally measured nonradiative excitation energy relaxation rates.

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

Nonradiative relaxation of excited molecules is central to many crucial issues in photochemistry. Condensed phases are typical contexts in which such problems are considered, and the nonradiative relaxation dynamics are expected to be significantly affected by interactions with the environment, for example, a solvent. We developed a nonadiabatic molecular dynamics simulation technique that can treat the nonradiative relaxation and explicitly include the environment in the calculations without a heavy computational burden. Specifically, we combined trajectory surface hopping with Tully's fewest-switches algorithm, a tight-binding approximated version of spin-flip time-dependent density-functional theory, and divide-and-conquer (DC) spatial fragmentation scheme. Numerical results showed that this method can treat systems with thousands of atoms within reasonable computational resources, and the error arising from DC fragmentation is negligibly small. Using this method, we obtained molecular insights into the solvent dependence of the photoexcited-state dynamics of trans-azobenzene, which demonstrate the importance of the environment for condensed-phase nonradiative relaxation.

Fast Nonadiabatic Molecular Dynamics via Spin-Flip Time-Dependent Density-Functional Tight-Binding Approach: Application to Nonradiative Relaxation of Tetraphenylethylene with Locked Aromatic Rings

Nonadiabatic dynamics around conical intersections between ground and excited states are crucial to understand excited-state phenomena in complex chemical systems. With this background in mind, we present an approach combining fewest-switches trajectory surface hopping and spin-flip (SF) time-dependent (TD) density-functional tight binding (DFTB), which is a simplified version of SF-TD density functional theory (DFT) with semiempirical parametrizations, for computationally efficient nonadiabatic molecular dynamics simulations. The estimated computational time of the SF-TD-DFTB approach is several orders of magnitude lower than that of SF-TD-DFT. In addition, the proposed method reproduces the time scales and quantum yields in photoisomerization reactions of azobenzene at a level comparable with conventional ab initio approaches, demonstrating reasonable accuracy. Finally, we report a practical application of the developed technique to explore the nonradiative relaxation processes of tetraphenylethylene and its derivative with torsionally locked aromatic rings and discuss the effect of locking the rings on the excited-state lifetime.