On-the-fly simulation of time-resolved fluorescence spectra and anisotropy.

We combine on-the-fly trajectory surface hopping simulations and the doorway-window representation of nonlinear optical response functions to create an efficient protocol for the evaluation of time- and frequency-resolved fluorescence (TFRF) spectra and anisotropies of the realistic polyatomic systems. This approach gives the effective description of the proper (e.g., experimental) pulse envelopes, laser field polarizations, and the proper orientational averaging of TFRF signals directly from the well-established on-the-fly nonadiabatic dynamic simulations without extra computational cost. To discuss the implementation details of the developed protocol, we chose cis-azobenzene as a prototype to simulate the time evolution of the TFRF spectra governed by its nonadiabatic dynamics. The results show that the TFRF is determined by the interplay of several key factors, i.e., decays of excited-state populations, evolution of the transition dipole moments along with the dynamic propagation, and scaling factor of the TFRF signals associated with the cube of emission frequency. This work not only provides an efficient and effective approach to simulate the TFRF and anisotropies of realistic polyatomic systems but also discusses the important relationship between the TFRF signals and the underlining nonadiabatic dynamics.

Studies of nonadiabatic dynamics in the singlet fission processes of pentacene dimer via tensor network method.

Singlet fission (SF) is a very significant photophysical phenomenon and possesses potential applications. In this work, we try to give a rather detailed theoretical investigation of the SF process in the stacked polyacene dimer by combining the high-level quantum chemistry calculations and the quantum dynamics simulations based on the tensor network method. Starting with the construction of the linear vibronic coupling model, we explore the pure electronic dynamics and the vibronic dynamics in the SF processes. The role of vibrational modes in nonadiabatic dynamics is addressed. The results show that the super-exchange mechanism mediated by the charge-transfer state is found in both pure electronic dynamics and the nonadiabatic dynamics. Particularly the vibrational modes with the frequencies resonance with the adiabatic energy gap play very import roles in the SF dynamics. This work not only provides a deep and detailed understanding of the SF process but also verifies the efficiency of the tensor network method with the train structure that can serve as the reference dynamics method to explore the dynamics behaviors of complex systems.

Automated Exploration of Reaction Networks and Mechanisms Based on Metadynamics Nanoreactor Simulations.

We developed an automated approach to construct a complex reaction network and explore the reaction mechanisms for numerous reactant molecules by integrating several theoretical approaches. Nanoreactor-type molecular dynamics was used to generate possible chemical reactions, in which the metadynamics was used to overcome the reaction barriers, and the semiempirical GFN2-xTB method was used to reduce the computational cost. Reaction events were identified from trajectories using the hidden Markov model based on the evolution of the molecular connectivity. This provided the starting points for further transition-state searches at the electronic structure levels of density functional theory to obtain the reaction mechanism. Finally, the entire reaction network containing multiple pathways was built. The feasibility and efficiency of the automated construction of the reaction network were investigated using the HCHO and NH3 biomolecular reaction and the reaction network for a multispecies system comprising dozens of HCN and H2O molecules. The results indicated that the proposed approach provides a valuable and effective tool for the automated exploration of the reaction networks.

Influence of Mode-Specific Excitation on the Nonadiabatic Dynamics of Methyl Nitrate (CH3ONO2).

The impact of mode-specific vibrational excitations on initial-preparation conditions was studied by examining the excited-state population decay rates in the nonadiabatic dynamics of methyl nitrate (CH3ONO2). In particular, exciting a few specific modes by adding a single quantum of energy clearly decelerated the nonadiabatic dynamics population decay rates. The underlying reason for this slower population decay was explained by analyzing the profiles of the excited-state potential energy surfaces in the Franck-Condon regions and the topology of the S1/S0 conical intersection. This study not only provides physical insights into the key mechanisms controlling nonadiabatic dynamics but also shows the possibility of controlling nonadiabatic dynamics via mode-specific vibrational excitations.

Simultaneously improving the efficiencies of photo- and thermal isomerization of an oxindole-based light-driven molecular rotary motor by a structural redesign.

We designed a novel highly efficient light-driven molecular rotary motor theoretically by using electronic structure calculations and nonadiabatic dynamics simulations, and it showed excellent performance for both photo- and thermal isomerization processes simultaneously. By the small structural modification based on 3-(2,7-dimethyl-2,3-dihydro-1H-inden-1-ylidene)-1-methylindolin-2-one (DDIYM) synthesized by Feringa et al. recently, an oxindole-based light-driven molecular rotary motor, 3-(1,5-dimethyl-4,5-dihydrocyclopenta[b]pyrrol-6(1H)-ylidene)-1-methylindolin-2-one (DDPYM), is proposed, which displays a significant electronic push-pull character and weak steric hindrance for double-bond isomerization. The newly designed motor DDPYM shows a remarkable improvement of the quantum yield for both EP → ZM and ZP → EM photoisomerization processes, compared to the original motor DDIYM. Furthermore, the rotary motion in photoisomerization processes of DDPYM behaves more like a pure axial rotational motion approximately, while that of DDIYM is an obvious precessional motion. The weakness of the steric hindrance reduces the energy barriers of the thermal helix EM → EP and ZM → ZP inversion steps, and would accelerate two ground-state isomerization steps significantly. Our results confirm the feasibility of simultaneously improving the efficiencies of photo- and thermal isomerization of oxindole-based light-driven molecular rotary motors and this design idea sheds light on the future development of more efficient molecular motors.

Trajectory Propagation of Symmetrical Quasi-classical Dynamics with Meyer-Miller Mapping Hamiltonian Using Machine Learning.

The long short-term memory recurrent neural network (LSTM-RNN) approach is applied to realize the trajectory-based nonadiabatic dynamics within the framework of the symmetrical quasi-classical dynamics method based on the Meyer-Miller mapping Hamiltonian (MM-SQC). After construction, the LSTM-RNN model allows us to propagate the entire trajectory evolutions of all involved degrees of freedoms (DOFs) from initial conditions. The proposed idea is proven to be reliable and accurate in the simulations of the dynamics of several site-exciton electron-phonon coupling models and three Tully's scattering models. It indicates that the LSTM-RNN model perfectly captures the dynamical information on the trajectory evolution in the MM-SQC dynamics. Our work proposes a novel machine learning approach in the simulation of trajectory-based nonadiabatic dynamic of complex systems with a large number of DOFs.

The impact of different geometrical restrictions on the nonadiabatic photoisomerization of biliverdin chromophores.

The photoisomerization mechanism of the chromophore of bacterial biliverdin (BV) phytochromes is explored via nonadiabatic dynamics simulation by using the on-the-fly trajectory surface-hopping method at the semi-empirical OM2/MRCI level. Particularly, the current study focuses on the influence of geometrical constrains on the nonadiabatic photoisomerization dynamics of the BV chromophore. Here a rather simplified approach is employed in the nonadiabatic dynamics to capture the features of geometrical constrains, which adds mechanical restrictions to the specific moieties of the BV chromophore. This simplified method provides a rather quick approach to examine the influence of geometrical restrictions on photoisomerization. As expected, different constrains bring distinctive influences on the photoisomerization mechanism of the BV chromophore, giving either strong or minor modification of both involved reaction channels and excited-state lifetimes after the constrains are added in different ring moieties. These observations not only contribute to the primary understanding of the role of the spatial restriction caused by biological environments in photoinduced dynamics of the BV chromophore, but also provide useful ideas for the artificial regulation of the photoisomerization reaction channels of phytochrome proteins.

Automatic Evolution of Machine-Learning-Based Quantum Dynamics with Uncertainty Analysis.

The machine learning approaches are applied in the dynamical simulation of open quantum systems. The long short-term memory recurrent neural network (LSTM-RNN) models are used to simulate the long-time quantum dynamics, which are built based on the key information of the short-time evolution. We employ various hyperparameter optimization methods, including simulated annealing, Bayesian optimization with tree-structured parzen estimator, and random search, to achieve the automatic construction and adjustment of the LSTM-RNN models. The implementation details of three hyperparameter optimization methods are examined, and among them, the simulated annealing approach is strongly recommended due to its excellent performance. The uncertainties of the machine learning models are comprehensively analyzed by the combination of bootstrap sampling and Monte Carlo dropout approaches, which give the prediction confidence of the LSTM-RNN models in the simulation of the open quantum dynamics. This work builds an effective machine learning approach to simulate the dynamics evolution of open quantum systems. In addition, the current study provides an efficient protocol to build optimal neural networks and estimate the trustiness of the machine learning models.

Effect of Temperature on Photoisomerization Dynamics of a Newly Designed Two-Stroke Light-Driven Molecular Rotary Motor.

The working mechanism of conventional light-driven molecular rotary motors, especially Feringa-type motors, contains two photoisomerization steps and two thermal helix inversion steps. Due to the existence of a thermal helix inversion step, both the ability to work at lower temperatures and the rotation speed are limited. In this work, a two-stroke light-driven molecular rotary motor, 2-(1,5-dimethyl-4,5-dihydrocyclopenta[b]pyrrol-6(1H)-ylidene)-1,2-dihydro-3H-pyrrol-3-one (DDPY), is proposed, which is capable of performing unidirectional and repetitive rotation by only two photoisomerization (EP→ZP and ZP→EP) steps. With trajectory surface-hopping simulation at the semi-empirical OM2/MRCI level, the EP→ZP and ZP→EP nonadiabatic dynamics of DDPY were systematically studied at different temperatures. Both EP→ZP and ZP→EP photoisomerizations are on an ultrafast timescale (ca. 200-300 fs). The decay mode of EP→ZP photoisomerization is approximately bi-exponential, while that of ZP→EP photoisomerization is found to be periodic. For EP and ZP isomers of DDPY, after the S0→S1 excitation, the dynamical processes of nonadiabatic decay are both followed by twisting about the central C=C double bond and the pyramidalization of the C atom at the stator-axle linkage. The effect of temperature on the nonadiabatic dynamics of EP→ZP and ZP→EP photoisomerizations of DDPY has been systematically investigated. The average lifetimes of the S1 excited state and quantum yields for both EP→ZP and ZP→EP photoisomerization are almost temperature-independent, while the corresponding unidirectionality of rotation is significantly increased (e.g., 74% for EP→ZP and 72% for ZP→EP at 300 K vs 100% for EP→ZP and 94% for ZP→EP at 50 K) with lowering the temperature.

The principal component analysis of the ring deformation in the nonadiabatic surface hopping dynamics.

The analysis of the leading active molecular motions in the on-the-fly trajectory surface hopping simulation provides the essential information to understand the geometric evolution in nonadiabatic dynamics. When the ring deformation is involved, the identification of the key active coordinates becomes challenging. A "hierarchical" protocol based on the dimensionality reduction and clustering approaches is proposed for the automatic analysis of the ring deformation in the nonadiabatic molecular dynamics. The representative system keto isocytosine is taken as the prototype to illustrate this protocol. The results indicate that the current hierarchical analysis protocol is a powerful way to clearly clarify both the major and minor active molecular motions of the ring distortion in nonadiabatic dynamics.

Design and Nonadiabatic Photoisomerization Dynamics Study of a Three-Stroke Light-Driven Molecular Rotary Motor.

Working cycle of conventional light-driven molecular rotary motors (LDMRMs), especially Feringa-type motors, usually have four steps, two photoisomerization steps, and two thermal helix inversion (THI) steps. THI steps hinder the ability of the motor to operate at lower temperatures and limit the rotation speed of LDMRMs. A three-stroke LDMRM, 2-(2,7-dimethyl-2,3-dihydro-1H-inden-1-ylidene)-1,2-dihydro-3H-pyrrol-3-one (DDIY), is proposed, which is capable of completing an unidirectional rotation by two photoisomerization steps and one thermal helix inversion step at room temperature. On the basis of trajectory surface-hopping simulation at the semi-empirical OM2/MRCI level, the EP→ZP and ZP→EM nonadiabatic photoisomerization dynamics of DDIY were systematically analyzed. Quantum yields of EP→ZP and ZP→EM photoisomerization of DDIY are ca. 34% and 18%, respectively. Both EP→ZP and ZP→EM photoisomerization processes occur on an ultrafast time scale (ca. 100-300 fs). This three-stroke LDMRM may stimulate further research for the development of new families of more efficient LDMRMs.

Automatic Approach to Explore the Multireaction Mechanism for Medium-Sized Bimolecular Reactions via Collision Dynamics Simulations and Transition State Searches.

We develop a broadly applicable computational method for the automatic exploration of the bimolecular multireaction mechanism. The current methodology mainly involves the high-energy Born-Oppenheimer molecular dynamics (BOMD) simulation and the successive reaction pathway construction. Several computational tricks are introduced, which include the selection of the reactive regions based on the electronic structure calculations and the employment of the virtual collision dynamics simulations with the monitoring of the atomic distance before the BOMD simulation. These prescreening steps largely reduce the number of trajectories in the BOMD simulations and significantly save the computational cost. The hidden Markov model combined with the modified atomic connectivity matrix is used for the detection of reaction events in each BOMD trajectory. Starting from several geometries close to the reaction events, the further intermediate optimization and transition state searches are conducted. The proposed method allows us to build the complicated multireaction mechanism of medium-sized bimolecular systems automatically. Here, we examine the feasibility and efficiency of the current method by its performance in searching the mechanisms of two prototype reactions in environmental science, which are the penicillin G anion + H2O and penicillin G anion + OH radical reactions. The result indicates that the proposed theoretical method is a powerful protocol for the automatic search of the bimolecular reaction mechanisms for medium-sized compounds.

Ultrafast Internal Conversion Dynamics through the on-the-Fly Simulation of Transient Absorption Pump-Probe Spectra with Different Electronic Structure Methods.

An on-the-fly surface-hopping simulation protocol is developed for the evaluation of transient absorption (TA) pump-probe (PP) signals of molecular systems exhibiting internal conversion to the electronic ground state. We study the nonadiabatic dynamics of azomethane and the associating TA PP spectra at three levels of the electronic-structure theory, OM2/MRCI, SA-CASSCF, and XMS-CASPT2. The impact of these methods on the population dynamics and time-resolved TA PP signals is substantially different. This difference is attributed to the strong non-Condon effects that must be taken into account for the proper understanding and interpretation of time-resolved TA PP signals of nonadiabatic polyatomic systems. This shows that the combination of the dynamical and spectral simulations definitely provides more accurate and detailed information on the microscopic mechanisms of photophysical and photochemical processes. Hence the simulation of time-resolved spectroscopic signals provides another important dimension to examine the accuracy of quantum chemistry methods.

Hydrolytic transformation mechanism of tetracycline antibiotics: Reaction kinetics, products identification and determination in WWTPs.

Antibiotic residues and antibiotic resistance have been widely reported in aquatic environments. Hydrolysis of antibiotics is one of the important environmental processes. Here we investigated the hydrolytic transformation of four tetracycline antibiotics i.e. tetracycline (TC), chlortetracycline (CTC), oxytetracycline (OTC) and doxycycline (DC) under different environmental conditions, and determined their parents and transformation products in the wastewater treatment plants (WWTPs). The results showed that the hydrolysis of the four tetracyclines followed first-order reaction kinetics, and the acid-catalyzed hydrolysis rates were significantly lower than the base-catalyzed and neutral pH hydrolysis rates. The effect of temperature on tetracycline hydrolysis was quantified by Arrhenius equation, with Ea values ranged from 42.0 kJ mol-1 to 77.0 kJ mol-1 at pH 7.0. In total, nine, six, eight and nine transformation products at three different pH conditions were identified for TC, CTC, OTC and DC, respectively. The main hydrolysis pathways involved the epimerization/isomerization, and dehydration. According to the mass balance analysis, 4-epi-tetracycline and iso-chlortetracycline were the main hydrolytic products for TC and CTC, respectively. The 2 tetracyclines and 4 hydrolysis products were found in the sludge samples in two WWTPs, with concentrations from 15.8 ng/g to 1418 ng/g. Preliminary toxicity evaluation for the tetracyclines and their hydrolysis products showed that some hydrolysis products had higher predicted toxicity than their parent compounds. These results suggest that the hydrolysis products of tetracycline antibiotics should also be included in environmental monitoring and risk assessment.

Theoretical studies on triplet-state driven dissociation of formaldehyde by quasi-classical molecular dynamics simulation on machine-learning potential energy surface.

The H-atom dissociation of formaldehyde on the lowest triplet state (T1) is studied by quasi-classical molecular dynamic simulations on the high-dimensional machine-learning potential energy surface (PES) model. An atomic-energy based deep-learning neural network (NN) is used to represent the PES function, and the weighted atom-centered symmetry functions are employed as inputs of the NN model to satisfy the translational, rotational, and permutational symmetries, and to capture the geometry features of each atom and its individual chemical environment. Several standard technical tricks are used in the construction of NN-PES, which includes the application of clustering algorithm in the formation of the training dataset, the examination of the reliability of the NN-PES model by different fitted NN models, and the detection of the out-of-confidence region by the confidence interval of the training dataset. The accuracy of the full-dimensional NN-PES model is examined by two benchmark calculations with respect to ab initio data. Both the NN and electronic-structure calculations give a similar H-atom dissociation reaction pathway on the T1 state in the intrinsic reaction coordinate analysis. The small-scaled trial dynamics simulations based on NN-PES and ab initio PES give highly consistent results. After confirming the accuracy of the NN-PES, a large number of trajectories are calculated in the quasi-classical dynamics, which allows us to get a better understanding of the T1-driven H-atom dissociation dynamics efficiently. Particularly, the dynamics simulations from different initial conditions can be easily simulated with a rather low computational cost. The influence of the mode-specific vibrational excitations on the H-atom dissociation dynamics driven by the T1 state is explored. The results show that the vibrational excitations on symmetric C-H stretching, asymmetric C-H stretching, and C=O stretching motions always enhance the H-atom dissociation probability obviously.

Simulation of Open Quantum Dynamics with Bootstrap-Based Long Short-Term Memory Recurrent Neural Network.

The recurrent neural network with the long short-term memory cell (LSTM-NN) is employed to simulate the long-time dynamics of open quantum systems. The bootstrap method is applied in the LSTM-NN construction and prediction, which provides a Monte Carlo estimation of a forecasting confidence interval. Within this approach, a large number of LSTM-NNs are constructed by resampling time-series sequences that were obtained from the early stage quantum evolution given by numerically exact multilayer multiconfigurational time-dependent Hartree method. The built LSTM-NN ensemble is used for the reliable propagation of the long-time quantum dynamics, and the simulated result is highly consistent with the exact evolution. The forecasting uncertainty that partially reflects the reliability of the LSTM-NN prediction is also given. This demonstrates the bootstrap-based LSTM-NN approach is a practical and powerful tool to propagate the long-time quantum dynamics of open systems with high accuracy and low computational cost.

Investigation of nonadiabatic dynamics in the photolysis of methyl nitrate (CH3ONO2) by on-the-fly surface hopping simulation.

The photolysis mechanism of methyl nitrate (CH3ONO2) was studied using the on-the-fly surface hopping dynamics at the XMS-CASPT2 level. Several critical geometries, including electronic state minima and conical intersections, were obtained, which play essential roles in the nonadiabatic dynamics of CH3ONO2. The ultrafast nonadiabatic decay dynamics to the ground state were simulated, which gives a proper explanation on the broad and structureless absorption spectra of CH3ONO2. The photodissociation channels, including CH3O + NO2, CH3O + NO + O, and others, as well as their branching ratios, were identified. When the dynamics starts from the lowest two electronic states (S1 and S2), the CH3O + NO2 channel is the dominant photolysis pathway, although we observed the minor contributions of other channels. In contrast, when the trajectories start from the third excited state S3, both CH3O + NO2 and CH3O + NO + O channels become important. Here the CH3O-NO2 bond dissociation takes place first, and then for some trajectories, the N-O bond of the NO2 part breaks successively. The quasi-degeneracy of electronic states may exist in the dissociation limits of both CH3O + NO2 and CH3O + NO + O channels. The current work provides valuable information in the understanding of experimental findings of the wavelength-dependent photolysis mechanism of CH3ONO2.

Spectral Fingerprint of Excited-State Energy Transfer in Dendrimers through Polarization-Sensitive Transient-Absorption Pump-Probe Signals: On-the-Fly Nonadiabatic Dynamics Simulations.

The time-resolved polarization-sensitive transient-absorption (TA) pump-probe (PP) spectra are simulated using on-the-fly surface-hopping nonadiabatic dynamics and the doorway-window representation of nonlinear spectroscopy. A dendrimer model system composed of two linear phenylene ethynylene units (2-ring and 3-ring) is taken as an example. The ground-state bleach (GSB), stimulated emission (SE), and excited-state absorption (ESA) contributions as well as the total TA PP signals are obtained and carefully analyzed. It is shown that intramolecular excited-state energy transfer from the 2-ring unit to the 3-ring unit can be conveniently identified by employing pump and probe pulses with different polarizations. Our results demonstrate that time-resolved polarization-sensitive TA PP signals provide a powerful tool for the elucidation of excited-state energy-transfer pathways, notably in molecular systems possessing several optically bright nonadiabatically coupled electronic states with different orientations of transition dipole moments.

An efficient implementation of spin-orbit coupling within the framework of semiempirical orthogonalization-corrected methods for ultrafast intersystem crossing dynamics.

We implement spin-orbit coupling (SOC) within the framework of semiempirical orthogonalization-corrected methods (OMx). The excited-state wavefunction is generated from configuration interaction with single excitations (CIS). The SOC Hamiltonian in terms of the one-electron Breit-Pauli operator with effective nuclear charges is adopted in this work. Benchmark calculations show that SOCs evaluated using the OMx/CIS method agree very well with those obtained from time-dependent density functional theory. As a particularly attractive application, we incorporate SOCs between singlet and triplet states into Tully's fewest switches surface hopping algorithm to enable excited-state nonadiabatic dynamics simulations, treating internal conversion and intersystem crossing on an equal footing. This semiempirical dynamics simulation approach is applied to investigate ultrafast intersystem crossing processes in core-substituted naphthalenediimides.

Prediction of the excited-state reaction channels in photo-induced processes of nitrofurantoin using first-principle calculations and dynamics simulations.

The understanding of the photochemistry of antibiotic compounds is important because it gives the direct information on the possible environmental pollution caused by them. Due to their large size, the theoretical studies of their excited-state reactions are rather challenging. In current work, we combined the on-the-fly trajectory surface-hopping dynamics, conical-intersection optimizations and excited-state pathway calculations to study the photochemistry of the trans-isomer of nitrofurantoin, a widely-used drug to treat the urinary tract infections. The dynamics-then-pathway approach was taken. First the trajectory surface hopping dynamics at the state-averaged complete-active-space self-consistent-field (SA-CASSCF) level with small active space and small basis sets were run. Second, the minimum-energy conical-intersection optimizations were performed. Finally the excited pathways from the Frank-Condon region to different reaction channels were built at the multi-state multi-reference second-order perturbation (MS-CASPT2) level with large active space and large basis set. Several possible channels responsible for the photo-induced reaction mechanism of the trans-nitrofurantoin were obtained, including the cleavage of the NO bond of the NO2 moiety, the photoisomerization at the central CN bond, and other internal conversion channels. Our findings give some preliminary explanations on available experimental observations. It is also demonstrates that the current theoretical approach is a powerful tool to explore the excited-state reactions in the photochemistry of media-sized or large-sized drug compounds.