Photoinduced relaxation dynamics of nitrogen-capped silicon nanoclusters: a TD-DFT study

Machine learning accelerated nonadiabatic dynamics simulations of materials with excitonic effects

This study presents an efficient methodology for simulating nonadiabatic dynamics of complex materials with excitonic effects by integrating machine learning (ML) models with simplified Tamm-Dancoff approximation (sTDA) calculations. By leveraging ML models, we accurately predict ground-state wavefunctions using unconverged Kohn-Sham (KS) Hamiltonians. These ML-predicted KS Hamiltonians are then employed for sTDA-based excited-state calculations (sTDA/ML). The results demonstrate that excited-state energies, time-derivative nonadiabatic couplings, and absorption spectra from sTDA/ML calculations are accurate enough compared with those from conventional density functional theory based sTDA (sTDA/DFT) calculations. Furthermore, sTDA/ML-based nonadiabatic molecular dynamics simulations on two different materials systems, namely chloro-substituted silicon quantum dot and monolayer black phosphorus, achieve more than 100 times speedup than the conventional linear response time-dependent DFT simulations. This work highlights the potential of ML-accelerated nonadiabatic dynamics simulations for studying the complicated photoinduced dynamics of large materials systems, offering significant computational savings without compromising accuracy.

Conformational and Solvent Effects on the Photoinduced Electron Transfer Dynamics of a Zinc Phthalocyanine-Benzoperylenetriimide Conjugate: A Nonadiabatic Dynamics Simulation

Herein, we employed a combination of static electronic structure calculations and nonadiabatic dynamics simulations at linear-response time dependent density functional theory (LR-TDDFT) level with the optimally tuned range-separated hybrid (OT-RSH) functional to explore the ultrafast photoinduced dynamics of a zinc phthalocyanine-benzoperylenetriimide (ZnPc-BPTI) conjugate. Due to the flexibility of the linker, we identified two major conformations: the stacked conformation (ZnPc-BPTI-1) and the extended conformation (ZnPc-BPTI-2). Since the charge transfer states are much lower than the lowest local excitation in ZnPc-BPTI-1, which is contrary to ZnPc-BPTI-2, the ultrafast electron transfer (~3.6 ps) is only observed in the nonadiabatic simulations of ZnPc-BPTI-1 upon local excitation around the absorption maximum of ZnPc. However, when considering the solvent effects in benzonitrile: the lowest S1 states are both charge transfer states from ZnPc to BPTI for different conformers. Subsequent nonadiabatic dynamics simulations indicate that both conformers experience ultrafast electron transfer in benzonitrile with two time constants of 90 [100] fs and 1.40 [1.43] ps. Our present work not only agrees well with previous experimental study, but also points out the important role of conformational changes and solvent effects in regulating the photodynamics of organic donor-acceptor conjugates.

Photoinduced Nonadiabatic Dynamics of a Single-Walled Carbon Nanotube-Porphyrin Complex

Single-walled carbon nanotubes (SWCNTs) have gained a lot of attention in the past few decades due to their promising optoelectronic properties. In addition, SWCNTs can form complexes that have good chemical stability and transport properties with other optical functional materials through noncovalent interactions. Elucidating the detailed mechanism of these complexes is of great significance for improving their optoelectronic properties. Nevertheless, simulating the photoinduced dynamics of these complexes accurately is rather challenging since they usually contain hundreds of atoms. To save computational efforts, most of the previous works have ignored the excitonic effects by employing nonadiabatic carrier (electron and hole) dynamics simulations. To properly consider the influence of excitonic effects on the photoinduced ultrafast processes of the SWCNT-tetraphenyl porphyrin (H2TPP) complex and to further improve the computational efficiency, we developed the nonadiabatic molecular dynamics (NAMD) method based on the extended tight binding-based simplified Tamm-Dancoff approximation (sTDA-xTB), which is applied to study the ultrafast photoinduced dynamics of the noncovalent SWCNT-porphyrin complex. In combination with statically electronic structure calculations, the present work successfully reveals the detailed microscopic mechanism of the ultrafast excitation energy transfer process of the complex. Upon local excitation on the H2TPP molecule, an ultrafast energy transfer process occurs from H2TPP (SWCNT-H2TPP*) to SWCNT (SWCNT*-H2TPP) within 10 fs. Then, two slower processes corresponding to the energy transfer from H2TPP to SWCNT and hole transfer from H2TPP to SWCNT take place in the 1 ps time scale. The sTDA-xTB-based electronic structure calculation and NAMD simulation results not only match the previous experimental observations from static and transient spectra but also provide more insights into the detailed information on the complex's photoinduced dynamics. Therefore, the sTDA-xTB-based NAMD method is a powerful theoretical tool for studying the ultrafast photoinduced dynamics in large extended systems with a large number of electronically excited states, which could be helpful for the subsequent design of SWCNT-based functional materials.

Photoinduced Dynamics of a Single-Walled Carbon Nanotube with a sp3 Defect: The Importance of Excitonic Effects

Herein, we employed linear-response time-dependent functional theory nonadiabatic dynamic simulations to explore the photoinduced exciton dynamics of a chiral single-walled carbon nanotube CNT(6,5) covalently doped with a 4-nitrobenzyl group (CNT65-NO2). The results indicate that the introduction of a sp3 defect leads to the splitting of the degenerate VBM/VBM-1 and CBM/CBM+1 states. Both the VBM upshift and the CBM downshift are responsible for the experimentally observed redshifted E11* trapping state. The simulations reveal that the photoinduced exciton relaxation dynamics completes within 500 fs, which is consistent with the experimental work. On the other hand, we also conducted the nonadiabatic carrier (electron and hole) dynamic simulations, which completely ignore the excitonic effects. The comparison demonstrates that excitonic effects are indispensable. Deep analyses show that such effects induce several dark states, which play an important role in regulating the photoinduced dynamics of CNT65-NO2. The present work demonstrates the importance of including excitonic effects in simulating photoinduced processes of carbon nanotubes. In addition, it not only rationalizes previous experiments but also provides valuable insights that will help in the future rational design of novel covalently doped carbon nanotubes with superior photoluminescent properties.

Nonadiabatic Dynamics Simulations for Photoinduced Processes in Molecules and Semiconductors: Methodologies and Applications

Nonadiabatic dynamics (NAMD) simulations have become powerful tools for elucidating complicated photoinduced processes in various systems from molecules to semiconductor materials. In this review, we present an overview of our recent research on photophysics of molecular systems and periodic semiconductor materials with the aid of ab initio NAMD simulation methods implemented in the generalized trajectory surface-hopping (GTSH) package. Both theoretical backgrounds and applications of the developed NAMD methods are presented in detail. For molecular systems, the linear-response time-dependent density functional theory (LR-TDDFT) method is primarily used to model electronic structures in NAMD simulations owing to its balanced efficiency and accuracy. Moreover, the efficient algorithms for calculating nonadiabatic coupling terms (NACTs) and spin-orbit couplings (SOCs) have been coded into the package to increase the simulation efficiency. In combination with various analysis techniques, we can explore the mechanistic details of the photoinduced dynamics of a range of molecular systems, including charge separation and energy transfer processes in organic donor-acceptor structures, ultrafast intersystem crossing (ISC) processes in transition metal complexes (TMCs), and exciton dynamics in molecular aggregates. For semiconductor materials, we developed the NAMD methods for simulating the photoinduced carrier dynamics within the framework of the Kohn-Sham density functional theory (KS-DFT), in which SOC effects are explicitly accounted for using the two-component, noncollinear DFT method. Using this method, we have investigated the photoinduced carrier dynamics at the interface of a variety of van der Waals (vdW) heterojunctions, such as two-dimensional transition metal dichalcogenides (TMDs), carbon nanotubes (CNTs), and perovskites-related systems. Recently, we extended the LR-TDDFT-based NAMD method for semiconductor materials, allowing us to study the excitonic effects in the photoinduced energy transfer process. These results demonstrate that the NAMD simulations are powerful tools for exploring the photodynamics of molecular systems and semiconductor materials. In future studies, the NAMD simulation methods can be employed to elucidate experimental phenomena and reveal microscopic details as well as rationally design novel photofunctional materials with desired properties.

Solvent effects on the photoinduced charge separation dynamics of directly linked zinc phthalocyanine-perylenediimide dyads: a nonadiabatic dynamics simulation with an optimally tuned screened range-separated hybrid functional

Herein, we have employed a combination of the optimally tuned screened range-separated hybrid (OT-SRSH) functional, the polarizable continuum model (PCM), and nonadiabatic dynamics (NAMD) simulations to investigate the photoinduced dynamics of directly linked donor-acceptor dyads formed using zinc phthalocyanine (ZnPc) and perylenediimide (PDI), in which ZnPc is the donor while PDI is the acceptor. Our simulations aim to analyze the behavior of these dyads upon local excitation of the ZnPc moiety in the gas phase and in benzonitrile. Our findings indicate that the presence of a solvent can significantly influence the excited state dynamics of ZnPc-PDI dyads. Specifically, the polar solvent benzonitrile effectively lowers the vertical excitation energies of the charge transfer (CT) state from ZnPc to PDI. As a result, the energetic order of the locally excited (LE) states of ZnPc and the CT states is reversed compared to the gas phase. Consequently, the photoinduced electron transfer (PET) dynamics from ZnPc to PDI, which is absent in the gas phase, takes place in benzonitrile with a time constant of 10.4 ps. Importantly, our present work not only qualitatively agrees with experimental results but also provides in-depth insights into the underlying mechanisms responsible for the photoinduced dynamics of ZnPc-PDI. Moreover, this study emphasizes the importance of appropriately considering solvent effects in NAMD simulation of organic donor-acceptor systems, taking into account the distinct excited state dynamics observed in the gas phase and benzonitrile. Furthermore, the combination of the OT-SRSH functional, the PCM solvent model, and nonadiabatic dynamics simulations shows promise as a strategy for investigating the complex excited state dynamics of organic donor-acceptor systems in solvents. These findings will be valuable for the future design of novel organic donor-acceptor structures with improved performance.

Non-negligible roles of charge transfer excitons in ultrafast excitation energy transfer dynamics of a double-walled carbon nanotube

Herein, we employed a developed linear response time dependent density functional theory-based nonadiabatic dynamics simulation method that explicitly takes into account the excitonic effects to investigate photoinduced excitation energy transfer dynamics of a double-walled carbon nanotube (CNT) model with different excitation energies. The E₁₁ excitation of the outer CNT will generate a local excitation (LE) |out*〉 exciton due to its low energy, which does not induce any charge separation. In contrast, the E₁₁ excitation of the inner CNT can generate four kinds of excitons with the LE exciton |in*〉 dominates. In the 500-fs dynamics simulation, the LE exciton |in*〉 and charge transfer (CT) excitons |out^-in⁺〉 and |out⁺in^-〉 are all gradually converted to the |out*〉 exciton, corresponding to a photoinduced excitation energy transfer, which is consistent with experimental studies. Finally, when the excitation energy is close to the E₂₂ state of the outer CNT (∼1.05 eV), a mixed population of different excitons, with the |out*〉 exciton dominated, is generated. Then, photoinduced energy transfer from the outer to inner CNTs occurs in the first 50 fs, which is followed by an inner to outer excitation energy transfer that is completed in 400 fs. The present work not only sheds important light on the mechanistic details of wavelength-dependent excitation energy transfer of a double-walled CNT model but also demonstrates the roles and importance of CT excitons in photoinduced excitation energy transfer. It also emphasized that explicitly including the excitonic effects in electronic structure calculations and nonadiabatic dynamics simulations is significant for correct understanding/rational design of optoelectronic properties of periodically extended systems.

Generalized Ab Initio Nonadiabatic Dynamics Simulation Methods from Molecular to Extended Systems

Nonadiabatic dynamics simulation has become a powerful tool to describe nonadiabatic effects involved in photophysical processes and photochemical reactions. In the past decade, our group has developed generalized trajectory-based ab initio surface-hopping (GTSH) dynamics simulation methods, which can be used to describe a series of nonadiabatic processes, such as internal conversion, intersystem crossing, excitation energy transfer and charge transfer of molecular systems, and photoinduced nonadiabatic carrier dynamics of extended systems with and without spin-orbit couplings. In this contribution, we will first give a brief introduction to our recently developed methods and related numerical implementations at different computational levels. Later, we will present some of our latest applications in realistic systems, which cover organic molecules, biological proteins, organometallic compounds, periodic organic and inorganic materials, etc. Final discussion is given to challenges and outlooks of ab initio nonadiabatic dynamics simulations.

Solvent effects on excited-state relaxation dynamics of paddle-wheel BODIPY-Hexaoxatriphenylene conjugates: Insights from non-adiabatic dynamics simulations

Understanding the excited state dynamics of donor-acceptor (D-A) complexes is of fundamental importance both experimentally and theoretically. Herein, we have first explored the photoinduced dynamics of a recently synthesized paddle-wheel BODIPY-hexaoxatriphenylene (BODIPY is the abbreviation for BF2-chelated dipyrromethenes) conjugates D-A complexes with the combination of both electronic structure calculations and non-adiabatic dynamics simulations. On the basis of computational results, we concluded that the BODIPY-hexaoxatriphenylene (BH) conjugates will be promoted to the local excited (LE) states of the BODIPY fragments upon excitation, which is followed by the ultrafast exciton transfer from LE state to charge transfer (CT). Instead of the photoinduced electron transfer process proposed in previous experimental work, such a exciton transfer process is accompanied with the photoinduced hole transfer from BODIPY to hexaoxatriphenylene. Additionally, solvent effects are found to play an important role in the photoinduced dynamics. Specifically, the hole transfer dynamics is accelerated by the acetonitrile solvent, which can be ascribed to significant influences of the solvents on the charge transfer states, i.e. the energy gaps between LE and CT excitons are reduced greatly and the non-adiabatic couplings are increased in the meantime. Our present work not only provides valuable insights into the underlying photoinduced mechanism of BH, but also can be helpful for the future design of novel donor-acceptor conjugates with better optoelectronic performance.

Ultrafast charge transfer in a nonfullerene all-small-molecule organic solar cell: a nonadiabatic dynamics simulation with optimally tuned range-separated functional

The combination of nonadiabatic dynamics simulation and optimally tuned range-separated functional might be a powerful tool for elucidating the ultrafast charge transfer in nonfullerene all-small-molecule organic solar cells.

Ultrafast Exciton Delocalization and Localization Dynamics of a Perylene Bisimide Quadruple π-­Stack: A Nonadiabatic Dynamics Simulation

Unraveling the photogenerated exciton dynamics of π­stacked molecular aggregates is of great importance for both fundamental studies and industrial applications. Among various π­stacked molecular aggregates, perylene tetracarboxylic acid bisimides (PBI)...

Rational design of monolayer transition metal dichalcogenide@fullerene van der Waals photovoltaic heterojunctions with time-domain density functional theory simulations

van der Waals heterojunctions formed by transition metal dichalcogenides (TMDs) and fullerenes are promising candidates for novel photovoltaic devices due to the excellent optoelectronic properties of both TMDs and fullerenes. However, relevant experimental and theoretical investigations remain scarce to the best of our knowledge. Herein, we have first employed static density functional theory (DFT) calculations in combination with time-domain density functional theory (TDDFT) based nonadiabatic dynamics simulations to rationally evaluate the photovoltaic performances of four TMD@fullerene heterostructures, i.e. WSe₂@C₆₀, WSe₂@C₇₀, MoTe₂@C₆₀ and MoTe₂@C₇₀, respectively. Our simulation results indicate that the C₇₀-based heterostructures overall have better photoinduced electron transfer efficiencies than their C₆₀-based counterparts, among which the performance of the WSe₂@C₇₀ heterostructure is the best and the electron transfer from WSe₂ to C₇₀ almost accomplishes within 1 ps. In addition, the large build-in potential of about 0.75 eV of WSe₂@C₇₀ is beneficial for the charge separation processes. Our present work not only selects the van der Waals TMD@fullerene heterojunctions that might have excellent photovoltaic properties, but also paves the way for the rational design of novel heterojunctions with better optoelectronic performances with DFT and TDDFT simulations in the future.

Chemical Bonding as a New Avenue for Controlling Excited-State Properties and Excitation Energy-Transfer Processes in Zinc Phthalocyanine-Fullerene Dyads

Whether chemical bonding can regulate the excited-state and optoelectronic properties of donor-acceptor dyads has been largely elusive. In this work, we used electronic structure and nonadiabatic dynamics methods to explore the excited-state properties of covalently bonded zinc phthalocyanine (ZnPc)-fullerene (C₆₀ ) dyads with a 6-6 (or 5-6) bonding configuration in which ZnPc is bonded to two carbon atoms shared by the two hexagonal rings (or a pentagonal and a hexagonal ring) in C₆₀ . In both cases, the locally excited (LE) states on ZnPc are spectroscopically bright. However, their different chemical bonding differentiates the electronic interactions between ZnPc and C₆₀ . In the 5-6 bonding configuration, the LE states on ZnPc are much higher in energy than the LE states on C₆₀ . Thus, the excitation energy transfer from ZnPc to C₆₀ is thermodynamically favorable. On the other hand, in the 6-6 bonding configuration, such a process is inhibited because the LE states on ZnPc are the lowest ones. More detailed mechanisms are elucidated from nonadiabatic dynamics simulations. In the 6-6 bonding configuration, no excitation energy transfer was observed. In contrast, in the 5-6 bonding configuration, several LE and charge-transfer (CT) excitons were shown to participate in the energy-transfer process. Further analysis reveals that the photoinduced energy transfer is mediated by a CT exciton, such that electron- and hole-transfer processes take place in a concerted but asynchronous manner in the excitation energy transfer. It is also found that high-level electronic structure methods including exciton effects are indispensable to accurately describe photoinduced energy- and electron-transfer processes. Furthermore, this work opens up new avenues for regulating the excited-state properties of molecular donor-acceptor dyads by means of chemical bonding.

Ultrafast channel I and channel II charge generation processes at a nonfullerene donor-acceptor PTB7:PDI interface is crucial for its excellent photovoltaic performance

Nonfullerene organic solar cells have received much attention in recent years due to their low cost, high absorption coefficient and excellent synthetic flexibility. However, the microscopic photoinduced dynamics at corresponding donor-acceptor interfaces remains unclear. In this work, we have firstly employed state-of-the-art TDDFT-based nonadiabatic dynamics simulations in combination with static electronic structure calculations to explore the ultrafast photoinduced dynamics at a typical nonfullerene donor-acceptor PTB7:PDI interface using a minimal model system (172 atoms). Upon excitation with specific wavelength of light, both PTB7 and PDI can be locally excited to generate |PTB7* and |PDI* excitons due to their high absorption ability and significant overlap in absorption spectrum. After that, these localized excitons gradually convert to charge transfer exciton |PTB7+PDI-, while another |PTB7-PDI+ charge transfer exciton is not involved in the whole process. Along with the exciton conversion, electron transfer from PTB7 to PDI (channel I charge generation) and the hole transfer from PDI to PTB7 (channel II charge generation) occurs simultaneously with time constants of 643 fs and 549 fs respectively. In the same time, D index that measures the centroid distance of electron and hole increases from 1.0 Å to 4.0 Å, which clearly reflects a charge transfer process at the interface. Our present work provides solid evidence that both channel I and channel II charge generation processes play important roles at PTB7:PDI interface, which could be helpful for the design of novel nonfullerene solar cells with better photovoltaic performance.

Modeling nonadiabatic dynamics in condensed matter materials: some recent advances and applications

This review focuses on recent developments in the field of nonadiabatic molecular dynamics (NA-MD), with particular attention given to condensed-matter systems. NA-MD simulations for small molecular systems can be performed using high-level electronic structure (ES) calculations, methods accounting for the quantization of nuclear motion, and using fewer approximations in the dynamical methodology itself. Modeling condensed-matter systems imposes many limitations on various aspects of NA-MD computations, requiring approximations at various levels of theory-from the ES, to the ways in which the coupling of electrons and nuclei are accounted for. Nonetheless, the approximate treatment of NA-MD in condensed-phase materials has gained a spin lately in many applied studies. A number of advancements of the methodology and computational tools have been undertaken, including general-purpose methods, as well as those tailored to nanoscale and condensed matter systems. This review summarizes such methodological and software developments, puts them into the broader context of existing approaches, and highlights some of the challenges that remain to be solved.

Nonadiabatic dynamics simulations on internal conversion and intersystem crossing processes in gold(i) compounds

The position at which the second gold(i)-phosphine group is attached was experimentally found to play a noticeable role in intersystem crossing rates of gold(i) naphthalene derivatives. However, the physical origin is ambiguous. Herein we have employed generalized trajectory-based surface-hopping dynamics simulations to simulate the excited-state relaxation dynamics of these gold(i) naphthalene compounds including both the intersystem crossing process from the initially populated first excited singlet states S₁ to triplet manifolds and internal conversion processes within these triplet states. Our predicted intersystem crossing rates are consistent with experiments very well. On the basis of the present results, we have found that (1) ultrafast and subpicosecond intersystem crossing processes are mainly caused by small energy gaps and large spin-orbit couplings between S₁ and T_n; (2) adding the second gold(i)-phosphine group does not increase spin-orbit couplings between S₁ and T_n but decrease their values remarkably, which implies that heavy-atom effects are state-specific, not state-universal; (3) the position at which the second gold(i)-phosphine group is attached has a remarkable influence on the electronic structures of S₁ and T_n and their relative energies, which affect energy gaps and spin-orbit couplings between S₁ and T_n and eventually modulate intersystem crossing rates from S₁ to T_n. These new insights are very useful for the design of gold-containing compounds with excellent photoluminescence properties. Finally, this work also exemplifies that different isomers of a compound could have distinct excited-state relaxation dynamics.