Nonadiabatic Dynamics of Charge Transfer and Singlet Fission at the Pentacene/C60 Interface

Ultrafast Hot Exciton Nonadiabatic Excited-State Dynamics in Green Fluorescent Protein Chromophore Analogue

The ultrafast high-energy nonadiabatic excited-state dynamics of the benzylidenedimethylimidazolinone chromophore dimer has been investigated using an electronic structure method coupled with on-the-fly quantitative wave function analysis to gain insight into the photophysics of hot excitons in biological systems. The dynamical simulation provides a rationalization of the behavior of the exciton in a dimer after the photoabsorption of light to higher-energy states. The results suggest that hot exciton localization within the manifold of excited states is caused by the hindrance of torsional rotation due to imidazolinone (I) or phenolate (P) bonds i.e., ΦI- or ΦP-dihedral rotation, in the monomeric units of a dimer. This hindrance arises due to weak π-π stacking interaction in the dimer, resulting in an energetically uphill excited-state barrier for ΦI- and ΦP-twisted rotation, impeding the isomerization process in the chromophore. Thus, this study highlights the potential impact of the weak π-π interaction in regulating the photodynamics of the green fluorescent protein chromophore derivatives.

Non-adiabatic dynamics of photoexcited cyclobutanone: Predicting structural measurements from trajectory surface hopping with XMS-CASPT2 simulations

Over the years, theoretical calculations and scalable computer simulations have complemented ultrafast experiments, as they offer the advantage of overcoming experimental restrictions and having access to the whole dynamics. This synergy between theory and experiment promises to yield a deeper understanding of photochemical processes, offering valuable insights into the behavior of complex systems at the molecular level. However, the ability of theoretical models to predict ultrafast experimental outcomes has remained largely unexplored. In this work, we aim to predict the electron diffraction signals of an upcoming ultrafast photochemical experiment using high-level electronic structure calculations and non-adiabatic dynamics simulations. In particular, we perform trajectory surface hopping with extended multi-state complete active space with second order perturbation simulations for understanding the photodissociation of cyclobutanone (CB) upon excitation at 200 nm. Spin-orbit couplings are considered for investigating the role of triplet states. Our simulations capture the bond cleavage after ultrafast relaxation from the 3s Rydberg state, leading to the formation of the previously observed primary photoproducts: CO + cyclopropane/propene (C3 products), ketene, and ethene (C2 products). The ratio of the C3:C2 products is found to be about 1:1. Within 700 fs, the majority of trajectories transition to their electronic ground state, with a small fraction conserving the initial cyclobutanone ring structure. We found a minimal influence of triplet states during the early stages of the dynamics, with their significance increasing at later times. We simulate MeV-ultrafast electron diffraction (UED) patterns from our trajectory results, linking the observed features with specific photoproducts and the underlying structural dynamics. Our analysis reveals highly intense features in the UED signals corresponding to the photochemical processes of CB. These features offer valuable insights into the experimental monitoring of ring opening dynamics and the formation of C3 and C2 photoproducts.

Nonadiabatic molecular dynamics with subsystem density functional theory: application to crystalline pentacene

In this work, we report the development and assessment of the nonadiabatic molecular dynamics approach with the electronic structure calculations based on the linearly scaling subsystem density functional method. The approach is implemented in an open-source embedded Quantum Espresso/Libra software specially designed for nonadiabatic dynamics simulations in extended systems. As proof of the applicability of this method to large condensed-matter systems, we examine the dynamics of nonradiative relaxation of excess excitation energy in pentacene crystals with the simulation supercells containing more than 600 atoms. We find that increased structural disorder observed in larger supercell models induces larger nonadiabatic couplings of electronic states and accelerates the relaxation dynamics of excited states. We conduct a comparative analysis of several quantum-classical trajectory surface hopping schemes, including two new methods proposed in this work (revised decoherence-induced surface hopping and instantaneous decoherence at frustrated hops). Most of the tested schemes suggest fast energy relaxation occurring with the timescales in the 0.7-2.0 ps range, but they significantly overestimate the ground state recovery rates. Only the modified simplified decay of mixing approach yields a notably slower relaxation timescales of 8-14 ps, with a significantly inhibited ground state recovery.

Intramolecular singlet fission: Quantum dynamical simulations including the effect of the laser field

In the previous work [Reddy et al., J. Chem. Phys. 151, 044307 (2019)], we have analyzed the dynamics of the intramolecular singlet fission process in a series of prototypical pentacene-based dimers, where the pentacene monomers are covalently bonded to a phenylene linker in ortho, meta, and para positions. The results obtained were qualitatively consistent with the experimental data available, showing an ultrafast population of the multiexcitonic state that mainly takes place via a mediated (superexchange-like) mechanism involving charge transfer and doubly excited states. Our results also highlighted the instrumental role of molecular vibrations in the process as a sizable population of the multiexcitonic state could only be obtained through vibronic coupling. Here, we extend these studies and investigate the effect of the laser field on the dynamics of intramolecular singlet fission by explicitly including the coupling to the laser field in our model. In this manner, and by selectively tuning the laser field to the different low-lying absorption bands of the systems investigated, we analyze the wavelength dependence of the intramolecular singlet fission process. In addition, we have also analyzed how the nature of the initially photoexcited electronic state (either localized or delocalized) affects its dynamics. Altogether, our results provide new insights into the design of intramolecular singlet fission-active molecules.

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.

Theoretical investigation of distal charge separation in a perylenediimide trimer

An exciton-phonon (ex-ph) model based on our recently developed block interaction product basis framework is introduced to simulate the distal charge separation (CS) process in aggregated perylenediimide (PDI) trimer incorporating the quantum dynamic method, i.e., the time-dependent density matrix renormalization group. The electronic Hamiltonian in the ex-ph model is represented by nine constructed diabatic states, which include three local excited (LE) states and six charge transfer (CT) states from both the neighboring and distal chromophores. These diabatic states are automatically generated from the direct products of the leading localized neutral or ionic states of each chromophore's reduced density matrix, which are obtained from ab initio quantum chemical calculation of the subsystem consisting of the targeted chromophore and its nearest neighbors, thus considering the interaction of the adjacent environment. In order to quantum-dynamically simulate the distal CS process with massive coupled vibrational modes in molecular aggregates, we used our recently proposed hierarchical mapping approach to renormalize these modes and truncate those vibrational modes that are not effectively coupled with electronic states accordingly. The simulation result demonstrates that the formation of the distal CS process undergoes an intermediate state of adjacent CT, i.e., starts from the LE states, passes through an adjacent CT state to generate the intermediates (∼200 fs), and then formalizes the targeted distal CS via further charge transference (∼1 ps). This finding agrees well with the results observed in the experiment, indicating that our scheme is capable of quantitatively investigating the CS process in a realistic aggregated PDI trimer and can also be potentially applied to exploring CS and other photoinduced processes in larger systems.

Machine-Learned Kohn-Sham Hamiltonian Mapping for Nonadiabatic Molecular Dynamics

In this work, we report a simple, efficient, and scalable machine-learning (ML) approach for mapping non-self-consistent Kohn-Sham Hamiltonians constructed with one kind of density functional to the nearly self-consistent Hamiltonians constructed with another kind of density functional. This approach is designed as a fast surrogate Hamiltonian calculator for use in long nonadiabatic dynamics simulations of large atomistic systems. In this approach, the input and output features are Hamiltonian matrices computed from different levels of theory. We demonstrate that the developed ML-based Hamiltonian mapping method (1) speeds up the calculations by several orders of magnitude, (2) is conceptually simpler than alternative ML approaches, (3) is applicable to different systems and sizes and can be used for mapping Hamiltonians constructed with arbitrary density functionals, (4) requires a modest training data, learns fast, and generates molecular orbitals and their energies with the accuracy nearly matching that of conventional calculations, and (5) when applied to nonadiabatic dynamics simulation of excitation energy relaxation in large systems yields the corresponding time scales within the margin of error of the conventional calculations. Using this approach, we explore the excitation energy relaxation in C60 fullerene and Si75H64 quantum dot structures and derive qualitative and quantitative insights into dynamics in these systems.

Highly efficient implementation of analytic nonadiabatic derivative couplings within the pseudospectral method

A pseudospectral implementation of nonadiabatic derivative couplings in the Tamm-Dancoff approximation is reported, and the accuracy and efficiency of the pseudospectral nonadiabatic derivative couplings are studied. Our results demonstrate that the pseudospectral method provides mean absolute errors of 0.2%-1.9%, while providing a significant speedup. Benchmark calculations on fullerenes (Cn, n up to 100) using B3LYP achieved 10- to 15-fold, 8- to 17-fold, and 43- to 75-fold speedups for 6-31G**, 6-31++G**, and cc-pVTZ basis sets, respectively, when compared to the conventional spectral method.

Recovering Marcus Theory Rates and Beyond without the Need for Decoherence Corrections: The Mapping Approach to Surface Hopping

It is well-known that fewest-switches surface hopping (FSSH) fails to correctly capture the quadratic scaling of rate constants with diabatic coupling in the weak-coupling limit, as expected from Fermi's golden rule and Marcus theory. To address this deficiency, the most widely used approach is to introduce a "decoherence correction", which removes the inconsistency between the wave function coefficients and the active state. Here we investigate the behavior of a new nonadiabatic trajectory method, called the mapping approach to surface hopping (MASH), on systems that exhibit an incoherent rate behavior. Unlike FSSH, MASH hops between active surfaces deterministically and can never have an inconsistency between the wave function coefficients and the active state. We show that MASH not only can describe rates for intermediate and strong diabatic coupling but also can accurately reproduce the results of Marcus theory in the golden-rule limit, without the need for a decoherence correction. MASH is therefore a significant improvement over FSSH in the simulation of nonadiabatic reactions.

Detailed balance in mixed quantum-classical mapping approaches

The violation of detailed balance poses a serious problem for the majority of current quasiclassical methods for simulating nonadiabatic dynamics. In order to analyze the severity of the problem, we predict the long-time limits of the electronic populations according to various quasiclassical mapping approaches by applying arguments from classical ergodic theory. Our analysis confirms that regions of the mapping space that correspond to negative populations, which most mapping approaches introduce in order to go beyond the Ehrenfest approximation, pose the most serious issue for reproducing the correct thermalization behavior. This is because inverted potentials, which arise from negative electronic populations entering the nuclear force, can result in trajectories unphysically accelerating off to infinity. The recently developed mapping approach to surface hopping (MASH) provides a simple way of avoiding inverted potentials while retaining an accurate description of the dynamics. We prove that MASH, unlike any other quasiclassical approach, is guaranteed to describe the exact thermalization behavior of all quantum-classical systems, confirming it as one of the most promising methods for simulating nonadiabatic dynamics in real condensed-phase systems.

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.

Convergence of Time-Derivative Nonadiabatic Couplings in Plane-Wave DFT Calculations

Accurate prediction of charge carrier relaxation rates is essential to design molecules and materials with the desired photochemical properties for applications like photocatalysis and solar energy conversion. Nonadiabatic molecular dynamics allows one to simulate the relaxation process of excited charge carriers. Plane-wave density functional theory (DFT) calculations make the time-derivative nonadiabatic couplings (TNACs) simple to compute because the basis is independent of the atomic positions. However, the effect of the kinetic energy cutoff for the plane-wave basis on the accuracy of the dynamics has not been studied. Here, we examine the effect of the kinetic energy cutoff on the TNACs and decay time scales for the prototypical model system of tetracene. These calculations show that the choice of kinetic energy cutoff can change the relaxation time by up to 30%. The relaxation times of states that have small TNACs to other states or are far from degenerate are more sensitive to the kinetic energy cutoff than those of states with large TNACs or near degeneracies. A kinetic energy cutoff of 60 Ry is sufficient for all states to reach semiquantitative agreement (absolute error <10%) with the decay times of our 110 Ry reference data, and a cutoff of 80 Ry is required for all states to reach quantitative agreement (absolute error <2%).

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.

Investigating the factors that influence sacrificial hydrogen evolution activity for three structurally-related molecular photocatalysts: thermodynamic driving force, excited-state dynamics, and surface interaction with cocatalysts

The design of molecular organic photocatalysts for reactions such as water splitting requires consideration of factors that go beyond electronic band gap and thermodynamic driving forces. Here, we carried out a theoretical investigation of three molecular photocatalysts (1-3) that are structurally similar but that show different hydrogen evolution activities (25, 23 & 0 μmol h^-1 for 1-3, respectively). We used density functional theory (DFT) and time-dependent DFT calculations to evaluate the molecules' optoelectronic properties, such as ionization potential, electron affinity, and exciton potentials, as well as the interaction between the molecular photocatalysts and an idealized platinum cocatalyst surface. The 'static' picture thus obtained was augmented by probing the nonadiabatic dynamics of the molecules beyond the Born-Oppenheimer approximation, revealing a different picture of exciton recombination and relaxation for molecule 3. Our results suggest that slow exciton recombination, fast relaxation to the lowest-energy excited state, and a shorter charge transfer distance between the photocatalyst and the metal cocatalyst are important features that contribute to the photocatalytic hydrogen evolution activity of 1 and 2, and may partly rationalize the observed inactivity of 3, in addition to its lower light absorption profile.

Symmetrical Linkage in Porphyrin Nanoring Suppressed the Electron-Hole Recombination Demonstrated by Nonadiabatic Molecular Dynamics

Macromolecular porphyrin nanorings are receiving significant attention because of their excellent optoelectronic properties. However, their efficiencies as potential solar materials are significantly affected by nonradiative charge recombination. To understand the recombination mechanism by alternating structural parameters and using tight-binding nonadiabatic molecular dynamics, we demonstrate that charge recombination depends strongly on the mode of the linker in the porphyrin nanoring. The nanoring having all-butadiyne-linkage (pristine-P8) inhibits carrier relaxation. In contrast, a partially fused nanoring (fused-P8) expedites the rate of quantum transition. An extension of the lifetime by a factor of 4 is due to the larger optical gap in pristine-P8 that reduces the NA coupling by decreasing the overlap between band edge states. Additionally, an intense phonon peak in the low-frequency region and rapid coherence loss within the electronic subsystem favors prolonging the carrier lifetime. This study provides an atomistic realization for the design of macromolecular porphyrin nanorings for the potential use in photovoltaic materials.

Model of Charge Transfer Collisions between C60 and Slow Ions

A semi-classical model describing the charge transfer collisions of C60 fullerene with different slow ions has been developed to explain available experimental data. This data reveals multiple Breit-Wigner like peaks in the cross sections, with subsequent peaks of reactive cross sections decreasing in magnitude. Calculations of charge transfer probabilities, quasi-resonant cross sections and cross sections for reactive collisions have been performed using semi-empirical interaction potentials between fullerenes and ion projectiles. All computations have been carried out with realistic wave functions for C60's valence electrons derived from the simplified jellium model. The quality of these electron wave functions have been successfully verified by comparing theoretical calculations and experimental data on the small angle cross sections of resonant C60+C60+ collisions. Using the semi-empirical potentials to describe resonant scattering phenomena in C60 collisions with ions and Landau-Zener charge transfer theory, we calculated theoretical cross sections for various C60 charge transfer and fragmentation reactions which agree with experiments.

Multilayer Subsystem Surface Hopping Method for Large-Scale Nonadiabatic Dynamics Simulation with Hundreds of Thousands of States

We present a multilayer subsystem surface hopping (MSSH) method to deal with nonadiabatic dynamics in large-scale systems. A small subsystem instead of the full system is adopted for surface hopping and is updated on-the-fly to achieve a reliable description of important adiabatic states and the wave function evolution. Additional subsystems for molecular dynamics and statistical description are introduced to further improve the simulation reliability. The global flux hopping probabilities with optimal state assignments are utilized to treat the complex surface crossings. As demonstrated in a series of one- and two-dimensional Holstein models with up to hundreds of thousands of states, MSSH shows weak parameter dependence in all investigated systems. Especially, the computational costs are reduced by 2-6 orders of magnitude compared to traditional surface hopping simulations in full systems, and size-independent results are achieved with a large time-step size of 2-5 fs. The new method is compatible with different decoherence correction strategies and achieves a much better balance between efficiency and reliability, thus promising for applications in general charge and exciton dynamics simulations.

Excited State Dynamics in Dual-Defects Modified Graphitic Carbon Nitride

Significant efforts are focused on defect-engineering of metal-free graphitic carbon nitride (g-C₃N₄) to amplify its efficacy. A conceptually new multidefect-modified g-C₃N₄ having simultaneously two or more defects has attracted strong attention for its enhanced photocatalytic properties. We model and compare the excited state dynamics in g-C₃N₄ with (i) nitrogen defects (N vacancy and CN group) and (ii) dual defects (N vacancy, CN group, and O doping) and show that the nonradiative recombination of charge carriers in these systems follows the Shockley-Read-Hall mechanism. The nitrogen defects create three midgap states that trap charges and act as recombination centers. The dual-defect modified systems exhibit superior properties compared with pristine g-C₃N₄ because the defects facilitate rapid charge separation and extend the spectrum of absorbed light. The system doped with O shows better performance due to enhanced carrier lifetime and higher oxidation potential caused by a downshifted valence band. The study provides guidance for rational design of stable and efficient photocatalytic materials.

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.

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.

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.

Effect of varying the TD-lc-DFTB range-separation parameter on charge and energy transfer in a model pentacene/buckminsterfullerene heterojunction

Atomistic modeling of energy and charge transfer at the heterojunction of organic solar cells is an active field with many remaining outstanding questions owing, in part, to the difficulties in performing reliable photodynamics calculations on very large systems. One approach to being able to overcome these difficulties is to design and apply an appropriate simplified method. Density-functional tight binding (DFTB) has become a popular form of approximate density-functional theory based on a minimal valence basis set and neglect of all but two center integrals. We report the results of our tests of a recent long-range correction (lc) [A. Humeniuk and R. Mitrić, J. Chem. Phys. 143, 134120 (2015)] for time-dependent (TD) lc-DFTB by carrying out TD-lc-DFTB fewest switches surface hopping calculations of energy and charge transfer times using the relatively new DFTBABY [A. Humeniuk and R. Mitrić, Comput. Phys. Commun. 221, 174 (2017)] program. An advantage of this method is the ability to run enough trajectories to get meaningful ensemble averages. Our interest in the present work is less in determining exact energy and charge transfer rates than in understanding how the results of these calculations vary with the value of the range-separation parameter (R_lc = 1/μ) for a model organic solar cell heterojunction consisting of a gas-phase van der Waals complex P/F made up of a single pentacene (P) molecule together with a single buckminsterfullerene (F) molecule. The default value of R_lc = 3.03 a₀ is found to be much too small as neither energy nor charge transfer is observed until R_lc ≈ 10 a₀. Tests at a single geometry show that the best agreement with high-quality ab initio spectra is obtained in the limit of no lc (i.e., very large R_lc). A plot of energy and charge transfer rates as a function of R_lc is provided, which suggests that a value of R_lc ≈ 15 a₀ yields the typical literature (condensed-phase) charge transfer time of about 100 fs. However, energy and charge transfer times become as high as ∼300 fs for R_lc ≈ 25 a₀. A closer examination of the charge transfer process P^*/F → P⁺/F^- shows that the initial electron transfer is accompanied by a partial delocalization of the P hole onto F, which then relocalizes back onto P, consistent with a polaron-like picture in which the nuclei relax to stabilize the resultant redistribution of charges.

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.

Visible Light-Driven Micromotor with Incident-Angle-Controlled Motion and Dynamic Collective Behavior

Light-driven micromotor has become one of the research focuses in the past decade, and its motion behavior is usually controlled by light intensity, polarization, and light wavelength. Herein, the light incident angle is utilized to control the motion behavior of silica/Au/pentacene (SiO₂/Au/PEN) spherical Janus micromotor. Under tilted irradiation, a single micromotor shows positive phototactic moving behavior without the addition of external chemical fuels, which relies on the photocatalytic reactions and the self-electrophoresis mechanism. Interestingly, when the incident light is tuned to the vertical angle, the SiO₂/Au/PEN micromotor stops moving. Similarly, a number of SiO₂/Au/PEN micromotors exhibit the same "on-off" motion change, which is dependent on the light incident angle. More interestingly, the "on-off" motion of the SiO₂/Au/PEN microparticles under vertical light irradiation results in the formation of the agglomeration with position and size precisely controlled by light. In addition, the resulting aggregation exhibits light-controlled dynamic migration behavior. The incident angle control thus opens up new opportunities for the motion control of the micromotors for diverse applications.

Ab initio quantum dynamics of charge carriers in graphitic carbon nitride nanosheets

Graphitic carbon nitride (g-C₃N₄), a metal-free and visible light responsive photocatalyst, has garnered much attention due to its wide range of applications. In order to elucidate the role of dimensionality on the properties of photo-generated charge carriers, we apply nonadiabatic (NA) molecular dynamics combined with time-domain density functional theory to investigate nonradiative relaxation of hot electrons and holes, and electron-hole recombination in monolayer and bulk g-C₃N₄. The nonradiative charge recombination occurs on a nanosecond timescale and is faster in bulk than the nanosheet, in agreement with the experiment. The difference arises due to the smaller energy gap and participation of additional vibrations in the bulk system. The long carrier lifetimes are favored by small NA coupling and rapid phonon-induced loss of quantum coherence between the excited and ground electronic states. Decoherence is fast because g-C₃N₄ is soft and undergoes large scale vibrations. The NA coupling is small since electrons and holes are localized on different atoms, and the electron-hole overlap is relatively small. Phonon-driven relaxation of hot electrons and holes takes 100-200 fs and is slightly slower at higher initial energies due to participation of fewer vibrational modes. This feature of two-dimensional g-C₃N₄ contrasts traditional three-dimensional semiconductors, which exhibit faster relaxation at higher energies due to larger density of states, and can be used to extract hot carriers to perform useful functions. The ab initio quantum dynamics simulations present a comprehensive picture of the photo-induced charge carrier dynamics in g-C₃N₄, guiding design of photovoltaic and photocatalytic devices.

Ultrafast Electron Transfer Before Singlet Fission and Slow Triplet State Electron Transfer in Pentacene Single Crystal/C60 Heterostructure

The singlet fission (SF) process converts one high-energy singlet exciton to two low-energy triplet excitons after absorbing one photon. Organic photovoltaic devices based on the SF process have shown great potential in solar energy conversion to exceed Shockley-Queisser limit. The key to SF photovoltaic devices requires efficient electron transfer (ET) from triplet exciton after SF, which is yet to be thoroughly investigated. Here, we performed thorough photophysical studies in 6,13-Bis(triisopropylsilylethynyl)pentacene (TIPS-pentacene)/C₆₀ heterostructures using TIPS-pentacene microsize single crystal as a well-defined model system. We show the SF process in TIPS-pentacene single crystal occurs by a two-step process, with triplet pair intermediates forming in 75 fs and then dissociating to non-interacting triplets in 1.6 ps. The SF process in single crystal is comparable to that in polycrystalline film. Importantly, we observe a considerable fraction of singlet excitons is quenched by ultrafast (<75 fs) interfacial ET prior to fission and no ET from triplet excitons in 1.5 ns time window. We confirm that the absence of ET is not limited by exciton diffusion but due to very slow (≫1.5 ns) interfacial ET from triplet exciton. The observations contradict expected singlet and triplet ET behaviors based on a simple two-state Marcus ET model and suggest long-range interfacial ET from delocalized photoexcitation. The ultrafast ET from singlet exciton before SF and slow ET from triplet exciton call for reconsideration and careful design of efficient SF photovoltaic devices.

Structural rigidity accelerates quantum decoherence and extends carrier lifetime in porphyrin nanoballs: a time domain atomistic simulation

Nonradiative electron-hole (e-h) recombination is the primary source of energy loss in photovoltaic cells and inevitably, it competes with the charge transfer process, leading to poor device performance. Therefore, much attention has to be paid for delaying such processes; increasing the excitonic lifetime may be a solution for this. Using the real-time, density functional tight-binding theory (DFTB) combined with nonadiabatic molecular dynamics (NAMD) simulations, we demonstrate the exciton relaxation phenomena of different metal-centered porphyrin nanoballs, which are supposed to be very important for the light-harvesting process. It has been revealed that the carrier recombination rate gradually decreases with the increase in the molecular stiffness by introducing metal-coordinating templating agents into the nanoball. Our simulation demonstrates that the lower atomic fluctuations lead to poorer electron-phonon nonadiabatic coupling in association with weak phonon modes and these as a whole are responsible for shorter quantum coherence and hence delayed recombination events. Our analysis is in good agreement with the recent experimental observation. By replacing the Zn metal center with a heavier Cd atom, a similar trend is observed; however, the rate slows down abruptly. The present simulation study provides the fundamental mechanism in detail behind the undesired energy loss during exciton recombination and suggests a rational design of impressive nanosystems for future device fabrication.

Non-adiabatic Excited-State Molecular Dynamics: Theory and Applications for Modeling Photophysics in Extended Molecular Materials

Optically active molecular materials, such as organic conjugated polymers and biological systems, are characterized by strong coupling between electronic and vibrational degrees of freedom. Typically, simulations must go beyond the Born-Oppenheimer approximation to account for non-adiabatic coupling between excited states. Indeed, non-adiabatic dynamics is commonly associated with exciton dynamics and photophysics involving charge and energy transfer, as well as exciton dissociation and charge recombination. Understanding the photoinduced dynamics in such materials is vital to providing an accurate description of exciton formation, evolution, and decay. This interdisciplinary field has matured significantly over the past decades. Formulation of new theoretical frameworks, development of more efficient and accurate computational algorithms, and evolution of high-performance computer hardware has extended these simulations to very large molecular systems with hundreds of atoms, including numerous studies of organic semiconductors and biomolecules. In this Review, we will describe recent theoretical advances including treatment of electronic decoherence in surface-hopping methods, the role of solvent effects, trivial unavoided crossings, analysis of data based on transition densities, and efficient computational implementations of these numerical methods. We also emphasize newly developed semiclassical approaches, based on the Gaussian approximation, which retain phase and width information to account for significant decoherence and interference effects while maintaining the high efficiency of surface-hopping approaches. The above developments have been employed to successfully describe photophysics in a variety of molecular materials.

A Photowelding Strategy for Conductivity Restoration in Flexible Circuits

Light-driven micropumps, which are based on electro-osmosis with the electric field generated by photocatalytic reactions, are among most attractive research topics in chemical micromotors. Until now, research in this field has mainly been focused on the directional motion or collective behavior of microparticles, which lack practical applications. In this study, we have developed a photowelding strategy for repeated photoinduced conductivity recovery of cracked flexible circuits. We immersed the circuit in a suspension of conductive healing particles and applied photoillumination to the crack; photocatalysis of a predeposited pentacene (PEN) layer triggered electro-osmotic effects to gather conductive particles at the crack, thus leading to conductivity recovery of the circuit. This photowelding strategy is a novel application of light-driven micropumps and photocatalysis for conductivity restoration.

Photoinduced Carrier Dynamics at the Interface of Black Phosphorus and Bismuth Vanadate

Two-dimensional (2D) heterostructures of black phosphorus (BP)/bismuth vanadate (BVO) have attracted much attention due to their potential uses in photocatalytic water splitting. However, the interfacial photoinduced electron- and hole-transfer dynamics are not explored computationally. Herein, we have used density functional theory (DFT) calculations and DFT-based fewest-switches surface-hopping dynamics simulations to investigate the light-driven electron and hole dynamics taking place at the interface of BP and the BVO(010) surface. Our results show that the BP monolayer is adsorbed on BVO(010) via van der Waals interaction. Upon irradiation, the electron transfer takes place from BP to BVO(010) within 500 fs but with two distinct processes. In the first phase, the electron transfer proceeds adiabatically and is mainly driven by atomic motions. In the second phase, the electron transfer decays very slowly. The hole-transfer dynamics from BVO(010) to BP exhibits a similar ultrafast decay in the first stage followed by a slow decay; however, there is a comparable amount of hole trapped in a BP state due to a large energy gap from its higher state. These insights may be useful for the design of novel photocatalytic water-splitting materials.

Dependence of electron transfer dynamics on the number of graphene layers in π-stacked 2D materials: insights from ab initio nonadiabatic molecular dynamics

Recent time-resolved transient absorption studies demonstrated that the rate of photoinduced interfacial charge transfer (CT) from Zn-phthalocyanine (ZnPc) to single-layer graphene (SLG) is faster than to double-layer graphene (DLG), in contrast to the expectation from Fermi's golden rule. We present the first time-domain non-adiabatic molecular dynamics (NA-MD) study of the electron injection process from photoexcited ZnPc molecules into SLG and DLG substrates. Our calculations suggest that CT occurs faster in the ZnPc/SLG system than in the ZnPc/DLG system, with 580 fs and 810 fs being the fastest components of the observed CT timescales, respectively. The computed timescales are in close agreement with those reported in the experiment. The computed CT timescales are determined largely by the magnitudes of the non-adiabatic couplings (NAC), which we find to be 4 meV and 2 meV, for the ZnPc/SLG and ZnPc/DLG systems, respectively. The transitions are driven mainly by the ZnPc out-of-plane bending mode at 1100 cm-1 and an overtone of fundamental modes in graphene at 2450 cm-1. We find that dephasing occurs on the timescale of 20 fs and is similar in both systems, so decoherence does not notably change the qualitative trends in the CT timescales. We highlight the importance of proper energy level alignment for capturing the qualitative trends in the CT dynamics observed in experiment. In addition, we illustrate several methodological points that are important for accurately modeling nonadiabatic dynamics in the ZnPc/FLG systems, such as the choice of surface hopping methodology, the use of phase corrections, NAC scaling, and the inclusion of Hubbard terms in the density functional and molecular dynamics calculations.

Photoinduced Carrier Dynamics at the Interface of Pentacene and Molybdenum Disulfide

Understanding of photoinduced interfacial carrier dynamics in organic-transition metal dichalcogenides heterostructures is very important for the enhancement of their potential photoelectronic conversion efficiencies. In this work we have used density functional theory (DFT) calculations and DFT-based fewest-switches surface-hopping dynamics simulations to explore the photoinduced hole transfer and subsequent nonadiabatic electron-hole recombination dynamics taking place at the interface of pentacene and MoS₂ in pentacene@MoS₂. Upon photoexcitation the electronic transition mainly occurs on the MoS₂ monolayer, which corresponds to moving an electron to the MoS₂ conduction band. As a result, a hole is left in the valence band. This hole state is energetically lower than certain occupied states of the pentacene molecule; thus, the interfacial hole transfer from MoS₂ to pentacene is favorable in energy. In terms of nonadiabatic dynamics simulations, the hole transfer time to the HOMO-1 state of the pentacene is estimated to be about 600 fs; however, the following hole relaxation process from HOMO-1 to HOMO takes much longer time of ca. 15 ps due to the large energy gap between HOMO-1 and HOMO. Moreover, our results also show that the subsequent radiationless recombination process between the hole transferred to the pentacene molecule and the remaining electron on the MoS₂ CBM needs about 10.2 ns. The computational results shed important mechanistic insights on the interfacial carrier dynamics of mixed-dimensional pentacene@MoS₂. These insights could help to design excellent interfaces for organic-TMDs heterostructures.