Implementation of surface hopping molecular dynamics using semiempirical methods

The development of the QM/MM interface and its application for the on-the-fly QM/MM nonadiabatic dynamics in JADE package: Theory, implementation, and applications

Understanding the nonadiabatic dynamics of complex systems is a challenging task in computational photochemistry. Herein, we present an efficient and user-friendly quantum mechanics/molecular mechanics (QM/MM) interface to run on-the-fly nonadiabatic dynamics. Currently, this interface consists of an independent set of codes designed for general-purpose use. Herein, we demonstrate the ability and feasibility of the QM/MM interface by integrating it with our long-term developed JADE package. Tailored to handle nonadiabatic processes in various complex systems, especially condensed phases and protein environments, we delve into the theories, implementations, and applications of on-the-fly QM/MM nonadiabatic dynamics. The QM/MM approach is established within the framework of the additive QM/MM scheme, employing electrostatic embedding, link-atom inclusion, and charge-redistribution schemes to treat the QM/MM boundary. Trajectory surface-hopping dynamics are facilitated using the fewest switches algorithm, encompassing classical and quantum treatments for nuclear and electronic motions, respectively. Finally, we report simulations of nonadiabatic dynamics for two typical systems: azomethane in water and the retinal chromophore PSB3 in a protein environment. Our results not only illustrate the power of the QM/MM program but also reveal the important roles of environmental factors in nonadiabatic processes.

Unveiling the chemical kinetics of aminomethanol (NH2CH2OH): insights into O . H and O2 photo-oxidation reactions and formamide dominance

Aminomethanol is released into the atmosphere through various sources, including biomass burning. In this study, we have expounded the chemical kinetics of aminomethanol in the reaction pathways initiated by the hydroxyl radical (O ˙ H) with the aid of ab initio//density functional theory (DFT) i.e., coupled-cluster theory (CCSD(T))//hybrid-DFT (M06-2X/6-311++G (3df, 3pd). We have explored various possible directions of theO ˙ H radical on aminomethanol, as well as the formation of distinct pre-reactive complexes. Our computational findings reveal that the H transfer necessitates activation energies ranging from 4.1 to 6.5 kcal/mol from the -CH2 group, 3.5-6.5 kcal/mol from the -NH2 group and 7-9.3 kcal/mol from the -OH group of three rotational conformers. The H transfer from -CH2, -NH2 and -OH exhibits an estimated total rate constant (k OH) of approximately 1.97 × 10-11 cm3 molecule-1 s-1 at 300 K. The branching fraction analysis indicates a pronounced dominance of C-centered NH2C ˙ HOH radicals with a favorability of 77%, surpassing the N-centeredN ˙ HCH2OH (20%) and O-centered NH2CH2O ˙ (3%) radicals. Moreover, our investigation delves into the oxidation of the prominently favored carbon-centered NH2C ˙ HOH radical through its interaction with atmospheric oxygen molecules. Intriguingly, our findings reveal that formamide (NH2CHO) emerges as the predominant product in the NH2C ˙ HOH + 3O2 reaction, eclipsing alternative outcomes such as amino formic acid (NH2COOH) and formimidic acid (HN = C(H)-OH). At atmospheric conditions pertinent to the troposphere, the branching fraction value for the formation of formamide is about 99%, coupled with a rate constant of 5.5 × 10-12 cm3 molecule-1 s-1. Finally, we have scrutinized the detrimental impact of formamide on the atmosphere. Interaction of formamide with atmospheric hydroxyl radicals could give rise to the production of potentially perilous compounds such as HNCO. Further, unreactedN ˙ HCH2OH radicals may initiate the formation of carcinogenic nitrosamines when reacting with trace N-oxides (namely, NO and NO2). This, in turn, escalates the environmental risk factors.

FSSH-2: Fewest Switches Surface Hopping with Robust Switching Probability

This study introduces the FSSH-2 scheme, a redefined and numerically stable adiabatic Fewest Switches Surface Hopping (FSSH) method for mixed quantum-classical dynamics. It reformulates the standard FSSH hopping probability without using nonadiabatic coupling vectors and allows for numerical time integration with larger step sizes. The advantages of FSSH-2 are demonstrated by numerical experiments for five different model systems in one and two spatial dimensions with up to three electronic states.

New insights into the photocyclization reaction of a popular diarylethene switch: a nonadiabatic molecular dynamics study

Diarylethene (DAE) molecular switches have continued to attract the attention of researchers for over 20 years. Their remarkable photophysical properties endow them with countless applications in photonics and molecular technologies. However, despite extensive experimental and theoretical research, the mechanism of DAE photoswitching is not yet fully rationalized. In this work, we investigate the ring closure dynamics of a popular DAE switch, 1,2-bis(3-methyl-5-phenyl-2 thienyl)perfluorocyclopentene (PT), using nonadiabatic molecular dynamics (NAMD) simulations. Employing the fewest switches surface hopping protocol, along with the semi-empirical multireference ODM2/MRCI-SD method, we investigate possible reaction pathways for this photoprocess, as well as their timescales and resulting photoproducts. Furthermore, using a dynamic configuration-space sampling procedure, we elucidate the role of triplet states in the photocyclization of PT, supporting available experimental data for the closely related DMPT molecule, which indicate an ultrafast intersystem crossing (ISC) transition competing with the singlet-driven photoswitching reaction. Our findings not only corroborate experimental studies on DAE switches, but also provide new mechanistic insights into the potential use in the rational design of DAE switches tailored for specific technological applications.

A CASSCF/MRCI trajectory surface hopping simulation of the photochemical dynamics and the gas phase ultrafast electron diffraction patterns of cyclobutanone

We present the simulation of the photochemical dynamics of cyclobutanone induced by the excitation of the 3 s Rydberg state. For this purpose, we apply the complete active space self-consistent field method together with the spin-orbit multireference configuration interaction singles treatment, combined with the trajectory surface hopping for the inclusion of nonadiabatic effects. The simulations were performed in the spin-adiabatic representation, including nine electronic states derived from three singlet and two triplet spin-diabatic states. Our simulations reproduce the two previously observed primary dissociation channels: the C2 pathway yielding C2H4 + CH2CO and the C3 pathway producing c-C3H6 + CO. In addition, two secondary products, CH2 + CO from the C2 pathway and C3H6 from the C3 pathway, both of them previously reported, are also observed in our simulation. We determine the ratio of the C3:C2 products to be about 2.8. Our findings show that most of the trajectories reach their electronic ground state within 200 fs, with dissociation events finished after 300 fs. We also identify the minimum energy conical intersections that are responsible for the relaxation and provide an analysis of the photochemical reaction mechanism based on multidimensional scaling. Furthermore, we demonstrate a minimal impact of triplet states on the photodissociation mechanism within the observed timescale. In order to provide a direct link to experiments, we simulate the gas phase ultrafast electron diffraction patterns and connect their features to the underlying structural dynamics.

Modeling pH-Dependent Biomolecular Photochemistry

The tuning mechanism of pH can be extremely challenging to model computationally in complex biological systems, especially with respect to the photochemical properties. This article reports a protocol aimed at modeling pH-dependent photodynamics using a combination of constant-pH molecular dynamics and semiclassical nonadiabatic molecular dynamics simulations. With retinal photoisomerization in Anabaena sensory rhodopsin (ASR) as a testbed, we show that our protocol produces pH-dependent photochemical properties, such as the isomerization quantum yield or decay rates. We decompose our results into single-titrated residue contributions, identifying some key tuning amino acids. Additionally, we assess the validity of the single protonation state picture to represent the system at a given pH and propose the most populated protein charge state as a compromise between cost and accuracy.

Theory and modeling of light-matter interactions in chemistry: current and future

Light-matter interaction not only plays an instrumental role in characterizing materials' properties via various spectroscopic techniques but also provides a general strategy to manipulate material properties via the design of novel nanostructures. This perspective summarizes recent theoretical advances in modeling light-matter interactions in chemistry, mainly focusing on plasmon and polariton chemistry. The former utilizes the highly localized photon, plasmonic hot electrons, and local heat to drive chemical reactions. In contrast, polariton chemistry modifies the potential energy curvatures of bare electronic systems, and hence their chemistry, via forming light-matter hybrid states, so-called polaritons. The perspective starts with the basic background of light-matter interactions, molecular quantum electrodynamics theory, and the challenges of modeling light-matter interactions in chemistry. Then, the recent advances in modeling plasmon and polariton chemistry are described, and future directions toward multiscale simulations of light-matter interaction-mediated chemistry are discussed.

LVC/MM: A Hybrid Linear Vibronic Coupling/Molecular Mechanics Model with Distributed Multipole-Based Electrostatic Embedding for Highly Efficient Surface Hopping Dynamics in Solution

We present a theoretical framework for a hybrid linear vibronic coupling model electrostatically embedded into a molecular mechanics environment, termed the linear vibronic coupling/molecular mechanics (LVC/MM) method, for the surface hopping including arbitrary coupling (SHARC) molecular dynamics package. Electrostatic embedding is realized through the computation of interactions between environment point charges and distributed multipole expansions (DMEs, up to quadrupoles) that represent each electronic state and transition densities in the diabatic basis. The DME parameters are obtained through a restrained electrostatic potential (RESP) fit, which we extended to yield higher-order multipoles. We also implemented in SHARC a scheme for achieving roto-translational invariance of LVC models as well as a general quantum mechanics/molecular mechanics (QM/MM) interface, an OpenMM interface, and restraining potentials for simulating liquid droplets. Using thioformaldehyde in water as a test case, we demonstrate that LVC/MM can accurately reproduce the solvation structure and energetics of rigid solutes, with errors on the order of 1-2 kcal/mol compared to a BP86/MM reference. The implementation in SHARC is shown to be very efficient, enabling the simulation of trajectories on the nanosecond time scale in a matter of days.

NeI2 Photofragmentation Dynamics Through Quasiclassical and Semiclassical Studies

The triatomic system NeI2 is studied under the consideration that the diatom is found in an excited electronic state (B). The vibrational levels (v=13, …, 23) are considered within two well-known theoretical procedures: quasi-classical trajectories (QCT), where the classical equations of motion for nuclei are solved on a single potential energy surface (PES), and the trajectory surface hopping (TSH) method, where the same are solved in a bunch of crossed vibrational PES (diabatic representation). The trajectory surface hopping fewest switches (TSHFS) is implemented to minimize the number of hoppings, thus allowing the calculations of hopping probability between the different PES's, and the kinetic mechanism to track the dissociation path. From these calculations, several observables such as, the lifetimes, vibrational and rotational energies (I2 ), dissociation channels, are obtained. Our results are compared with previous experimental and theoretical work.

Nonadiabatic Coupling in Trajectory Surface Hopping: Accurate Time Derivative Couplings by the Curvature-Driven Approximation

Trajectory surface hopping (TSH) is a widely used mixed quantum-classical dynamics method that is used to simulate molecular dynamics with multiple electronic states. In TSH, time-derivative coupling is employed to propagate the electronic coefficients and in that way to determine when the electronic state on which the nuclear trajectory is propagated switches. In this work, we discuss nonadiabatic TSH dynamics algorithms employing the curvature-driven approximation and overlap-based time derivative couplings, and we report test calculations on six photochemical reactions where we compare the results to one another and to calculations employing analytic nonadiabatic coupling vectors. We correct previous published results thanks to a bug found in the software. We also provide additional, more detailed studies of the time-derivative couplings. Our results show good agreement between curvature-driven algorithms and overlap-based algorithms.

Nonadiabatic Derivative Couplings Calculated Using Information of Potential Energy Surfaces without Wavefunctions: Ab Initio and Machine Learning Implementations

In this work, we implemented an approximate algorithm for calculating nonadiabatic coupling matrix elements (NACMEs) of a polyatomic system with ab initio methods and machine learning (ML) models. Utilizing this algorithm, one can calculate NACMEs using only the information of potential energy surfaces (PESs), i.e., energies, and gradients as well as Hessian matrix elements. We used a realistic system, namely CH₂NH, to compare NACMEs calculated by this approximate PES-based algorithm and the accurate wavefunction-based algorithm. Our results show that this approximate PES-based algorithm can give very accurate results comparable to the wavefunction-based algorithm except at energetically degenerate points, i.e., conical intersections. We also tested a machine learning (ML)-trained model with this approximate PES-based algorithm, which also supplied similarly accurate NACMEs but more efficiently. The advantage of this PES-based algorithm is its significant potential to combine with electronic structure methods that do not implement wavefunction-based algorithms, low-scaling energy-based fragment methods, etc., and in particular efficient ML models, to compute NACMEs. The present work could encourage further research on nonadiabatic processes of large systems simulated by ab initio nonadiabatic dynamics simulation methods in which NACMEs are always required.

On-the-Fly Nonadiabatic Dynamics Simulations of Single-Walled Carbon Nanotubes with Covalent Defects

Single-walled carbon nanotubes (SWCNTs) with covalent surface defects have been explored recently due to their promise for use in single-photon telecommunication emission and in spintronic applications. The all-atom dynamic evolution of electrostatically bound excitons (the primary electronic excitations) in these systems has only been loosely explored from a theoretical perspective due to the size limitations of these large systems (>500 atoms). In this work, we present computational modeling of nonradiative relaxation in a variety of SWCNT chiralities with single-defect functionalizations. Our excited-state dynamics modeling uses a trajectory surface hopping algorithm accounting for excitonic effects with a configuration interaction approach. We find a strong chirality and defect-composition dependence on the population relaxation (varying over 50-500 fs) between the primary nanotube band gap excitation E₁₁ and the defect-associated, single-photon-emitting E₁₁* state. These simulations give direct insight into the relaxation between the band-edge states and the localized excitonic state, in competition with dynamic trapping/detrapping processes observed in experiment. Engineering fast population decay into the quasi-two-level subsystem with weak coupling to higher-energy states increases the effectiveness and controllability of these quantum light emitters.

Nonadiabatic Forward Flux Sampling for Excited-State Rare Events

We present a rare event sampling scheme applicable to coupled electronic excited states. In particular, we extend the forward flux sampling (FFS) method for rare event sampling to a nonadiabatic version (NAFFS) that uses the trajectory surface hopping (TSH) method for nonadiabatic dynamics. NAFFS is applied to two dynamically relevant excited-state models that feature an avoided crossing and a conical intersection with tunable parameters. We investigate how nonadiabatic couplings, temperature, and reaction barriers affect transition rate constants in regimes that cannot be otherwise obtained with plain, traditional TSH. The comparison with reference brute-force TSH simulations for limiting cases of rareness shows that NAFFS can be several orders of magnitude cheaper than conventional TSH and thus represents a conceptually novel tool to extend excited-state dynamics to time scales that are able to capture rare nonadiabatic events.

Vertical Excitation Energies and Lifetimes of the Two Lowest Singlet Excited States of Cytosine, 5-Aza-cytosine, and the Triazine Family: Quantum Mechanics-Molecular Mechanics Studies

A swarm of semi-classical quantum mechanics/molecular mechanics molecular-dynamics simulations where OM2/MNDO is combined with the Gromacs program for consideration of explicit water is performed, solving the time-dependent Schrödinger equation in each step of the trajectories together with the Tully's fewest switches algorithm. Within this stochastic treatment, time dependent probabilities of the three lowest electronic states are determined. The fact that nucleobases are quickly deactivated is confirmed in the cytosine case where our best lifetime estimation is τ₁=0.82 ps for the model with 100 water molecules with the SPCE force field and a time step of 0.1 fs. Lifetimes of the remaining molecules are visibly longer: 5-azacytosine, 2,4-diamino-1,3,5-triazine (DT), and 2,4,6-triamino-1,3,5-triazine (TT) molecules have an S₁ → S₀ de-excitation time of slightly above 10 ps. The lifetimes of the triazine family increases with the increasing number of exocyclic amino groups, that is, s-triazine < 2-amino-1,3,5-triazine < DT < TT. This can be explained by a higher mobility of the carbon-bonded hydrogen atoms in comparison with heavier amino groups since their movement is slowed down due to a substantially higher mass than hydrogen atoms, which can easier reach the out-of-plane positions required in the conical intersection structures. Moreover, bulkier NH₂ ligands suffer due to greater friction caused by the surrounding water environment. These mechanical aspects caused a change in the explored lifetime dependences in comparison with our previous gas-phase study.

Nonadiabatic Coupling in Trajectory Surface Hopping: How Approximations Impact Excited-State Reaction Dynamics

Photochemical reactions are widely modeled using the popular trajectory surface hopping (TSH) method, an affordable mixed quantum-classical approximation to the full quantum dynamics of the system. TSH is able to account for nonadiabatic effects using an ensemble of trajectories, which are propagated on a single potential energy surface at a time and which can hop from one electronic state to another. The occurrences and locations of these hops are typically determined using the nonadiabatic coupling between electronic states, which can be assessed in a number of ways. In this work, we benchmark the impact of some approximations to the coupling term on the TSH dynamics for several typical isomerization and ring-opening reactions. We have identified that two of the schemes tested, the popular local diabatization scheme and a scheme based on biorthonormal wave function overlap implemented in the OpenMOLCAS code as part of this work, reproduce at a much reduced cost the dynamics obtained using the explicitly calculated nonadiabatic coupling vectors. The other two schemes tested can give different results, and in some cases, even entirely incorrect dynamics. Of these two, the scheme based on configuration interaction vectors gives unpredictable failures, while the other scheme based on the Baeck-An approximation systematically overestimates hopping to the ground state as compared to the reference approaches.

Nonadiabatic Dynamics in a Continuous Circularly Polarized Laser Field with Floquet Phase-Space Surface Hopping

Nonadiabatic chemical reactions involving continuous circularly polarized light (cw CPL) have not attracted as much attention as dynamics in unpolarized/linearly polarized light. However, including circularly (in contrast to linearly) polarized light allows one to effectively introduce a complex-valued time-dependent Hamiltonian, which offers a new path for control or exploration through the introduction of Berry forces. Here, we investigate several inexpensive semiclassical approaches for modeling such nonadiabatic dynamics in the presence of a time-dependent complex-valued Hamiltonian, beginning with a straightforward instantaneous adiabatic fewest-switches surface hopping (IA-FSSH) approach (where the electronic states depend on position and time), continuing to a standard Floquet fewest switches surface hopping (F-FSSH) approach (where the electronic states depend on position and frequency), and ending with an exotic Floquet phase-space surface hopping (F-PSSH) approach (where the electronic states depend on position, frequency, and momentum). Using a set of model systems with time-dependent complex-valued Hamiltonians, we show that the Floquet phase-space adiabats are the optimal choice of basis as far as accounting for Berry phase effects and delivering accuracy. Thus, the F-PSSH algorithm sets the stage for future modeling of nonadiabatic dynamics under strong externally pumped circular polarization.

Investigation of plasmon relaxation mechanisms using nonadiabatic molecular dynamics

Hot carriers generated from the decay of plasmon excitation can be harvested to drive a wide range of physical or chemical processes. However, their generation efficiency is limited by the concomitant phonon-induced relaxation processes by which the energy in excited carriers is transformed into heat. However, simulations of dynamics of nanoscale clusters are challenging due to the computational complexity involved. Here, we adopt our newly developed Trajectory Surface Hopping (TSH) nonadiabatic molecular dynamics algorithm to simulate plasmon relaxation in Au20 clusters, taking the atomistic details into account. The electronic properties are treated within the Linear Response Time-Dependent Tight-binding Density Functional Theory (LR-TDDFTB) framework. The relaxation of plasmon due to coupling to phonon modes in Au20 beyond the Born–Oppenheimer approximation is described by the TSH algorithm. The numerically efficient LR-TDDFTB method allows us to address a dense manifold of excited states to ensure the inclusion of plasmon excitation. Starting from the photoexcited plasmon states in Au20 cluster, we find that the time constant for relaxation from plasmon excited states to the lowest excited states is about 2.7 ps, mainly resulting from a stepwise decay process caused by low-frequency phonons of the Au20 cluster. Furthermore, our simulations show that the lifetime of the phonon-induced plasmon dephasing process is ∼10.4 fs and that such a swift process can be attributed to the strong nonadiabatic effect in small clusters. Our simulations demonstrate a detailed description of the dynamic processes in nanoclusters, including plasmon excitation, hot carrier generation from plasmon excitation dephasing, and the subsequent phonon-induced relaxation process.

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.

Transition Path Flight Times and Nonadiabatic Electronic Transitions

Transition path flight times are studied for scattering on two electronic surfaces with a single crossing. These flight times reveal nontrivial quantum effects such as resonance lifetimes and nonclassical passage times and reveal that nonadiabatic effects often increase flight times. The flight times are computed using numerically exact time propagation and compared with results obtained from the Fewest Switches Surface Hopping (FSSH) method. Comparison of the two methods shows that the FSSH method is reliable for transition path times only when the scattering is classically allowed on the relevant adiabatic surfaces. However, where quantum effects such as tunneling and resonances dominate, the FSSH method is not adequate to accurately predict the correct times and transition probabilities. These results highlight limitations in methods which do not account for quantum interference effects, and suggest that measuring flight times is important for obtaining insights from the time-domain into quantum effects in nonadiabatic scattering.

Nonadiabatic Molecular Dynamics Simulations Based on Time-Dependent Density Functional Tight-Binding Method

Nonadiabatic excited-state molecular dynamics underpin many photophysical and photochemical phenomena, such as exciton dynamics, charge separation and transport. In this work, we present an efficient nonadiabatic molecular dynamic (NAMD) simulation method based on time-dependent density functional tight-binding (TDDFTB) theory. Specifically, the adiabatic electronic structure, an essential NAMD input, is described at the TDDFTB level. The nonadiabatic effects originating from the coupled motions of electrons and nuclei are treated by the trajectory surface hopping algorithm. To improve the computational efficiency, nonadiabatic couplings between excited states within the TDDFTB method are derived and implemented using an analytical approach. Further, the time-dependent nonadiabatic coupling scalars are calculated based on the overlap between molecular orbitals rather than the Slater determinants to speed up the simulations. In addition, the electronic decoherence scheme and a state reassigned unavoided crossings algorithm, which has been implemented in the NEXMD software, are used to improve the accuracy of the simulated dynamics and handle trivial unavoided crossings. Finally, the photoinduced nonadiabatic dynamics of a benzene molecule are simulated to demonstrate our implementation. The results for excited state NAMD simulations of benzene molecule based on TDDFTB method compare well that obtained with numerically expensive time-dependent density functional theory. The proposed methodology provides an attractive theoretical simulation tool for predicting the photophysical and photochemical properties of complex materials.

Surface hopping dynamics in periodic solid-state materials with a linear vibronic coupling model

We report a surface hopping approach in which the implemented linear vibronic coupling Hamiltonian is constructed and the electronic wavefunction is propagated in the reciprocal space. The parameters of the linear vibronic coupling model, including onsite energies, phonon frequencies, and electron-phonon couplings, are calculated with density-functional theory and density-functional perturbation theory and interpolated in fine sampling points of the Brillouin zone with maximally localized Wannier functions. Using this approach, we studied the relaxation dynamics of the photo-excited hot carrier in a one-dimensional periodic carbon chain. The results show that the completeness of the number of Hilbert space k points and the number of phonon q points plays an important role in the hot carrier relaxation processes. By calculating the relaxation times of hot carriers under different reciprocal space sampling and extrapolating with the stretched-compressed exponential function, the relaxation times of hot electrons and holes in the quasi-continuous energy band are obtained. By considering the feedback effect in the hopping processes and analyzing the time-dependent phonon energy in different normal modes, we found that the long-wave longitudinal optical phonons play a major role in the relaxation dynamics of hot electrons and holes. We, therefore, provided herein an efficient and accurate approach for modeling the photophysical processes in periodic solid-state material systems.

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.

All-Atom Nonadiabatic Dynamics Simulation of Hybrid Graphene Nanoribbons Based on Wannier Analysis and Machine Learning

Trajectory surface hopping combined with ab initio electronic structure calculations is a popular and powerful approach for on-the-fly nonadiabatic dynamics simulations. For large systems, however, this remains a significant challenge because of the unaffordable computational cost of large-scale electronic structure calculations. Here, we present an efficient divide-and-conquer approach to construct the system Hamiltonian based on Wannier analysis and machine learning. In detail, the large system under investigation is first decomposed into small building blocks, and then all possible segments formed by building blocks within a cutoff distance are found out. Ab initio molecular dynamics is carried out to generate a sequence of geometries for each equivalent segment with periodicity. The Hamiltonian matrices in the maximum localized Wannier function (MLWF) basis are obtained for all geometries and utilized to train artificial neural networks (ANNs) for the structure-dependent Hamiltonian elements. Taking advantage of the orthogonality and spatial locality of MLWFs, the one-electron Hamiltonian of a large system at arbitrary geometry can be directly constructed by the trained ANNs. As demonstrations, we study charge transport in a zigzag graphene nanoribbon (GNR), a coved GNR, and a series of hybrid GNRs with a state-of-the-art surface hopping method. The interplay between delocalized and localized states is found to determine the electron dynamics in hybrid GNRs. Our approach has successfully studied GNRs with >10 000 atoms, paving the way for efficient and reliable all-atom nonadiabatic dynamics simulation of general systems.

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.

Excitation Energy Transfer between bodipy Dyes in a Symmetric Molecular Excitonic Seesaw

We examine the redistribution of energy between electronic and vibrational degrees of freedom that takes place between a π-conjugated oligomer, a phenylene-butadiynylene, and two identical boron-dipyrromethene (bodipy) end-caps using femtosecond transient absorption spectroscopy, single-molecule spectroscopy, and nonadiabatic excited-state molecular dynamics (NEXMD) modeling techniques. The molecular structure represents an excitonic seesaw in that the excitation energy on the oligomer backbone can migrate to either one end-cap or the other, but not to both. The NEXMD simulations closely reproduce the characteristic time scale for redistribution of electronic and vibrational energy of 2.2 ps and uncover the vibrational modes contributing to the intramolecular relaxation. The calculations indicate that the dihedral angle between the bodipy dye and the oligomer change upon excitation of the oligomer. Single-molecule experiments reveal a difference in photoluminescence lifetime of the bodipy dyes depending on whether they are excited by direct absorption or by redistribution of energy from the backbone. This difference in lifetime may be attributed to the difference in dihedral angle. The simulations also suggest that a strong coupling can occur between the two end-caps, giving rise to a reversible shuttling of excitation energy between them. Strong coupling should lead to a pronounced loss in polarization memory of the fluorescence since the oligomer backbone tends to be slightly distorted and the two bodipy transition dipoles have different orientations. A sensitive single-molecule technique is presented to test for such coupling. However, although redistribution of electronic and vibrational energy between the end-caps can occur, it appears to be unidirectional and irreversible, suggesting that an additional localization mechanism is at play which is, as yet, not fully accounted for in the simulations.

On application of deep learning to simplified quantum-classical dynamics in electronically excited states

Deep learning (DL) is applied to simulate non-adiabatic molecular dynamics of phenanthrene, using the time-dependent density functional based tight binding (TD-DFTB) approach for excited states combined with mixed quantum–classical propagation. Reference calculations rely on Tully’s fewest-switches surface hopping (FSSH) algorithm coupled to TD-DFTB, which provides electronic relaxation dynamics in fair agreement with various available experimental results. Aiming at describing the coupled electron-nuclei dynamics in large molecular systems, we then examine the combination of DL for excited-state potential energy surfaces (PESs) with a simplified trajectory surface hopping propagation based on the Belyaev–Lebedev (BL) scheme. We start to assess the accuracy of the TD-DFTB approach upon comparison of the optical spectrum with experimental and higher-level theoretical results. Using the recently developed SchNetPack (Schütt et al 2019 J. Chem. Theory Comput. 15 448–55) for DL applications, we train several models and evaluate their performance in predicting excited-state energies and forces. Then, the main focus is given to the analysis of the electronic population of low-lying excited states computed with the aforementioned methods. We determine the relaxation timescales and compare them with experimental data. Our results show that DL demonstrates its ability to describe the excited-state PESs. When coupled to the simplified BL scheme considered in this study, it provides reliable description of the electronic relaxation in phenanthrene as compared with either the experimental data or the higher-level FSSH/TD-DFTB theoretical results. Furthermore, the DL performance allows high-throughput analysis at a negligible cost.

Machine Learning for Electronically Excited States of Molecules

Electronically excited states of molecules are at the heart of photochemistry, photophysics, as well as photobiology and also play a role in material science. Their theoretical description requires highly accurate quantum chemical calculations, which are computationally expensive. In this review, we focus on not only how machine learning is employed to speed up such excited-state simulations but also how this branch of artificial intelligence can be used to advance this exciting research field in all its aspects. Discussed applications of machine learning for excited states include excited-state dynamics simulations, static calculations of absorption spectra, as well as many others. In order to put these studies into context, we discuss the promises and pitfalls of the involved machine learning techniques. Since the latter are mostly based on quantum chemistry calculations, we also provide a short introduction into excited-state electronic structure methods and approaches for nonadiabatic dynamics simulations and describe tricks and problems when using them in machine learning for excited states of molecules.

Machine Learning for Electronically Excited States of Molecules

Electronically excited states of molecules are at the heart of photochemistry, photophysics, as well as photobiology and also play a role in material science. Their theoretical description requires highly accurate quantum chemical calculations, which are computationally expensive. In this review, we focus on not only how machine learning is employed to speed up such excited-state simulations but also how this branch of artificial intelligence can be used to advance this exciting research field in all its aspects. Discussed applications of machine learning for excited states include excited-state dynamics simulations, static calculations of absorption spectra, as well as many others. In order to put these studies into context, we discuss the promises and pitfalls of the involved machine learning techniques. Since the latter are mostly based on quantum chemistry calculations, we also provide a short introduction into excited-state electronic structure methods and approaches for nonadiabatic dynamics simulations and describe tricks and problems when using them in machine learning for excited states of molecules.

Nonadiabatic Molecular Dynamics Study of the Relaxation Pathways of Photoexcited Cyclooctatetraene

In the current study, we present nonadiabatic (NAMD) and adiabatic molecular dynamics simulations of the transition-state dynamics of photoexcited cyclooctatetraene (COT). The equilibrium-state structure and absorption spectra are analyzed using the semiempirical Austin Model 1 potential. The NAMD simulations are obtained by a surface-hopping algorithm. We analyzed in detail an active excited to ground state relaxation pathway accompanied by an S₂/S₃(D_2d) → S₁(D_8h) → S₀(D_4h) → S₀(D_2d) double-bond shifting mechanism. The simulated excitation lifetime is in good agreement with experiment. The first excited singlet state S₁ plays a crucial role in the photochemistry. The obtained critical molecular conformations, energy barrier, and transition-state lifetime results will provide a basis for further investigations of the bond-order inversion and photoswitching process of COT.

On-the-Fly Symmetrical Quasi-Classical Dynamics with Meyer-Miller Mapping Hamiltonian for the Treatment of Nonadiabatic Dynamics at Conical Intersections

The on-the-fly version of the symmetrical quasi-classical dynamics method based on the Meyer-Miller mapping Hamiltonian (SQC/MM) is implemented to study the nonadiabatic dynamics at conical intersections of polyatomic systems. The current on-the-fly implementation of the SQC/MM method is based on the adiabatic representation and the dressed momentum. To include the zero-point energy (ZPE) correction of the electronic mapping variables, we employ both the γ-adjusted and γ-fixed approaches. Nonadiabatic dynamics of the methaniminium cation (CH₂NH₂⁺) and azomethane are simulated using the on-the-fly SQC/MM method. For CH₂NH₂⁺, both ZPE correction approaches give reasonable and consistent results. However, for azomethane, the γ-adjusted version of the SQC/MM dynamics behaves much better than the γ-fixed version. Further analysis indicates that it is always recommended to use the γ-adjusted SQC/MM dynamics in the on-the-fly simulation of photoinduced dynamics of polyatomic systems, particularly when the excited state is well separated from the ground state in the Franck-Condon region. This work indicates that the on-the-fly SQC/MM method is a powerful simulation protocol to deal with the nonadiabatic dynamics of realistic polyatomic systems.

Velocity Adjustment in Surface Hopping: Ethylene as a Case Study of the Maximum Error Caused by Direction Choice

The most common surface hopping dynamics algorithms require velocity adjustment after hopping to ensure total-energy conservation. Based on the semiclassical analysis, this adjustment must be made parallel to the nonadiabatic coupling vector's direction. Nevertheless, this direction is not always known, and the common practice has been to adjust the velocity in either the linear momentum or velocity directions. This paper benchmarks surface hopping dynamics of photoexcited ethylene with velocity adjustment in several directions, including those of the nonadiabatic coupling vector, the momentum, and the energy gradient difference. It is shown that differences in time constants and structural evolution fall within the statistical uncertainty of the method considering up to 500 trajectories in each dynamics set, rendering the three approaches statistically equivalent. For larger ensembles beyond 1000 trajectories, significant differences between the results arise, limiting the validity of adjustment in alternative directions. Other possible adjustment directions (velocity, single-state gradients, angular momentum) are evaluated as well. Given the small size of ethylene, the results reported in this paper should be considered an upper limit for the error caused by the choice of the velocity-adjustment direction on surface hopping dynamics.

Ultrafast nonradiative deactivation of photoexcited 8-oxo-hypoxanthine: a nonadiabatic molecular dynamics study

In the scientific endeavor to understand the chemical origins of life, the photochemistry of the smallest life building blocks, nucleobases, has been a constant object of focus and intense research. Here, we report the results of the first theoretical study on the photo-properties of an 8-oxo-hypoxanthine molecule, the chromophore of 8-oxo-inosine, which is relevant to the recently proposed, prebiotically plausible synthetic routes to the formation of purine- and pyrimidine-nucleotides. With ab initio and semi-empirical OM2/MRCI quantum-chemistry calculations, we predict a strong photostability of the 8-oxo-hypoxanthine system and see the origin of this effect in ultrafast nonradiative relaxation through puckering of the 6-membered heterocyclic ring.

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.

A Simple Solution to Trivial Crossings: A Stochastic State Tracking Approach

We present a new state tracking algorithm based on a stochastic state reassignment that reflects the quantum mechanical interpretation of the state time-overlaps. We assess the new method with a range of model Hamiltonians and demonstrate that it yields the results generally consistent with the deterministic min-cost algorithm. However, the stochastic state tracking algorithm reduces magnitudes of the state population fluctuations as the quantum system evolves toward its equilibrium. The new algorithm facilitates the thermalization of quantum state populations and suppresses the population revivals and oscillations near the equilibrium in many-state systems. The new stochastic algorithm has a favorable computational scaling, is easy to implement due to its conceptual transparency, and treats various types of state identity changes (trivial or avoided crossings and any intermediate cases) on equal footing.

Time-Derivative Couplings for Self-Consistent Electronically Nonadiabatic Dynamics

Electronically nonadiabatic dynamics methods based on a self-consistent potential, such as semiclassical Ehrenfest and coherent switching with decay of mixing, have a number of advantages but are computationally slower than approximations based on an unaveraged potential because they require evaluation of all components of the nonadiabatic coupling vector. Here we introduce a new approximation to the self-consistent potential that does not have this computational drawback. The new approximation uses time-derivative couplings evaluated by overlap integrals of electronic wave functions to approximate the nonadiabatic coupling terms in the equations of motion. We present a numerical test of the method for ethylene that shows there is little loss of accuracy in the ensemble-averaged results. This new approximation to the self-consistent potential makes direct dynamics calculations with self-consistent potentials more efficient for complex systems and makes them practically affordable for some cases where the cost was previously too high.

Photoinduced Double Proton Transfer in the Glyoxal-Methanol Complex Revisited: The Role of the Excited States

Under irradiation in the visible range, the glyoxal-methanol complex in a cryogenic argon matrix undergoes a double proton transfer (DPT) reaction through which the glyoxal molecule isomerizes into hydroxyketene. In this work, we employ electronic structure simulations in order to shed more light on the underlying mechanism. Rewardingly, we find that the lowest singlet excited state (S₁) of the complex acts as a gateway to two previously unknown isomerization pathways, of which one takes place entirely in the singlet manifold and the other also involves the lowest triplet state (T₁). Both of these pathways are fully compatible with the available experimental data, implying that either or both are operative under experimental conditions. In either pathway, the methanol molecule acts as a proton shuttle between the proton-donating and proton-accepting sites of glyoxal, resulting in a dramatic lowering of the potential energy barrier to isomerization with respect to the case of isolated glyoxal. The occurrence of DPT in the singlet manifold is demonstrated directly with the use of nonadiabatic molecular dynamics simulations at the spin-flip time-dependent density functional theory level.

The generality of the GUGA MRCI approach in COLUMBUS for treating complex quantum chemistry

The core part of the program system COLUMBUS allows highly efficient calculations using variational multireference (MR) methods in the framework of configuration interaction with single and double excitations (MR-CISD) and averaged quadratic coupled-cluster calculations (MR-AQCC), based on uncontracted sets of configurations and the graphical unitary group approach (GUGA). The availability of analytic MR-CISD and MR-AQCC energy gradients and analytic nonadiabatic couplings for MR-CISD enables exciting applications including, e.g., investigations of π-conjugated biradicaloid compounds, calculations of multitudes of excited states, development of diabatization procedures, and furnishing the electronic structure information for on-the-fly surface nonadiabatic dynamics. With fully variational uncontracted spin-orbit MRCI, COLUMBUS provides a unique possibility of performing high-level calculations on compounds containing heavy atoms up to lanthanides and actinides. Crucial for carrying out all of these calculations effectively is the availability of an efficient parallel code for the CI step. Configuration spaces of several billion in size now can be treated quite routinely on standard parallel computer clusters. Emerging developments in COLUMBUS, including the all configuration mean energy multiconfiguration self-consistent field method and the graphically contracted function method, promise to allow practically unlimited configuration space dimensions. Spin density based on the GUGA approach, analytic spin-orbit energy gradients, possibilities for local electron correlation MR calculations, development of general interfaces for nonadiabatic dynamics, and MRCI linear vibronic coupling models conclude this overview.

Multireference Electron Correlation Methods: Journeys along Potential Energy Surfaces

Multireference electron correlation methods describe static and dynamical electron correlation in a balanced way and, therefore, can yield accurate and predictive results even when single-reference methods or multiconfigurational self-consistent field theory fails. One of their most prominent applications in quantum chemistry is the exploration of potential energy surfaces. This includes the optimization of molecular geometries, such as equilibrium geometries and conical intersections and on-the-fly photodynamics simulations, both of which depend heavily on the ability of the method to properly explore the potential energy surface. Because such applications require nuclear gradients and derivative couplings, the availability of analytical nuclear gradients greatly enhances the scope of quantum chemical methods. This review focuses on the developments and advances made in the past two decades. A detailed account of the analytical nuclear gradient and derivative coupling theories is presented. Emphasis is given to the software infrastructure that allows one to make use of these methods. Notable applications of multireference electron correlation methods to chemistry, including geometry optimizations and on-the-fly dynamics, are summarized at the end followed by a discussion of future prospects.

Nonadiabatic Dynamics Simulations on Early-Time Photochemistry of Spirobenzopyran

Photoinduced ring-opening, decay, and isomerization of spirobenzopyran have been explored by the OM2/MRCI nonadiabatic dynamics simulations based on Tully's fewest-switches surface hopping scheme. The efficient S₁ to S₀ internal conversion as observed in experiments is attributed to the existence of two efficient excited-state decay pathways. The first one is related to the C-N dissociation, and the second one is done to the C-O dissociation. The C-O dissociation pathway is dominant, and more than 90% trajectories decay to the S₀ state via the C-O bond-fission related S₁/S₀ conical intersections. Near these regions in the S₀ state, trajectories can either return to spirobenzopyran or proceed to various intermediates including merocyanine via a series of bond rotations. Our nonadiabatic dynamics simulations also demonstrate that the hydrogen-out-of-plane (HOOP) motion is important for efficient and ultrafast excited-state deactivation. On the other hand, we have also found that the replacement of methyl groups by hydrogen atoms in spirobenzopyran can artificially introduce different intramolecular hydrogen transfers leading to hydrogen-transferred intermediates. This finding is important for the community and demonstrates that such a kind of structural truncation, sometimes, could be problematic, leading to incorrect photodynamics. Our present work provides valuable insights into the photodynamics of spirobenzopyran, which could be helpful for the design of spiropyran-based photochromic materials.