Nonadiabatic dynamics with trajectory surface hopping method: Dynamics with surface hopping

Nonadiabatic Couplings Can Speed Up Quantum Tunneling Transition Path Times

Quantum tunneling is known to play an important role in the dynamics of systems with nonadiabatic couplings. However, until recently, the time-domain properties of nonadiabatic scattering have been severely under-explored. Using numerically exact quantum methods, we study the impact that nonadiabatic couplings have on the time it takes to tunnel through a barrier. We find that the Wigner phase time is the appropriate measure to use when determining the tunneling flight time also when considering nonadiabatic systems. The central result of the present study is that in an avoided crossing system in one dimension, the nonadiabatic couplings speed up the tunneling event, relative to the adiabatic case in which all nonadiabatic coupling is ignored. This has implications for both the study of quantum tunneling times and for the field of nonadiabatic scattering and chemistry.

Revealing and Tuning the Photophysics of C=N Containing Photothermal Molecules: Excited State Dynamics Simulations

Molecular photothermal conversion materials are recently attracting increasing attention for phototherapy applications. Herein we investigate the excitation and de-excitation processes of a photothermal molecule (C1TI) that is among the recently developed class of small-molecule-based photothermal imines with superb photothermal conversion efficiencies (PTCEs) up to 90% and a molecule (M2) that is constructed by replacing the amino group of C1TI with an H atom, via excited-state dynamics simulations based on the time-dependent density functional theory (TD-DFT). The simulations reveal fast (<150 fs of average time) nonradiative decays of the lowest excited singlet (S1) state to a conical intersection (CI) with the ground (S0) state in high yields (C1TI: 93.9% and M2: 87.1%). The fast decays, driven by C=N bond rotation to a perpendicular structural configuration, are found to be barrierless. The slight structural difference between C1TI and M2 leads to drastically different S0-S1 energy surfaces, especially M2 features a relatively much lower CI (0.8 eV in energy) and much more decay energy (1.0 eV) to approach the CI. This work provides insights into the de-excitation mechanisms and the performance tuning of C=N enabled photothermal materials.

Strong Field Double Ionization of Formaldehyde Investigated Using Momentum Resolved Covariance Imaging and Trajectory Surface Hopping

We use covariance velocity map imaging of fragment ions from the strong field double ionization of formaldehyde in conjunction with trajectory surface hopping calculations to determine the ionization yields to different singlet and triplet states of the dication. The calculated kinetic energy release for trajectories initiated on different electronic states is compared with the experimental values based on momentum resolved covariance measurements. We determine the state resolved double ionization yields as a function of laser intensity and pulse duration down to 6 fs (two optical cycles).

Modulating the Photocyclization Reactivity of Diarylethenes through Changes in the Excited-State Aromaticity of the π-Linker

Quantum chemical calculations are performed to explore if the reactivity of diarylethene switches toward photocyclization can be controlled by the excited-state aromaticity of their bridging π-linker. Using an archetypal diarylethene with a non-aromatic π-linker as a reference, completely different outcomes are found when the π-linker is allowed to become either aromatic (no reaction) or antiaromatic (fast reaction) upon photoexcitation. The results demonstrate a possibility to use the excited-state aromaticity concept for actual modulation of photochemical reactivity.

Nuclear Gradient Expressions for Molecular Cavity Quantum ElectrodynamicsSimulations using Mixed Quantum-Classical Methods

We derive a rigorous nuclear gradient for a molecule-cavity hybrid system using the Quantum Electrodynamics Hamiltonian. We treat the electronic-photonic DOFs as the quantum subsystem, and the nuclei as the classical subsystem. Using the adiabatic basis for the electronic DOF and the Fock basis for the photonic DOF, and requiring the total energy conservation of this mixed quantum-classical system, we derived the rigorous nuclear gradient for the molecule-cavity hybrid system, which is naturally connected to the approximate gradient under the Jaynes-Cummings approximation. The nuclear gradient expression can be readily used in any mixed quantum-classical simulations and will allow one to perform the non-adiabatic on-the-fly simulation of polariton quantum dynamics. The theoretical developments in this work could significantly benefit the polariton quantum dynamics community with a rigorous nuclear gradient of the molecule-cavity hybrid system and have a broad impact on the future non-adiabatic simulations of polariton quantum dynamics.

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.

Photochemical and thermochemical pathways to S2 and polysulfur formation in the atmosphere of Venus

Polysulfur species have been proposed to be the unknown near-UV absorber in the atmosphere of Venus. Recent work argues that photolysis of one of the (SO)₂ isomers, cis-OSSO, directly yields S₂ with a branching ratio of about 10%. If correct, this pathway dominates polysulfur formation by several orders of magnitude, and by addition reactions yields significant quantities of S₃, S₄, and S₈. We report here the results of high-level ab-initio quantum-chemistry computations that demonstrate that S₂ is not a product in cis-OSSO photolysis. Instead, we establish a novel mechanism in which S₂ is formed in a two-step process. Firstly, the intermediate S₂O is produced by the coupling between the S and Cl atmospheric chemistries (in particular, SO reaction with ClS) and in a lesser extension by O-abstraction reactions from cis-OSSO. Secondly, S₂O reacts with SO. This modified chemistry yields S₂ and subsequent polysulfur abundances comparable to the photolytic cis-OSSO mechanism through a more plausible pathway. Ab initio quantification of the photodissociations at play fills a critical data void in current atmospheric models of Venus.

Polysulfur compounds have been ascribed as the unknown near-UV absorbers in Venusian atmosphere and play a key role in the sulfur chemical cycle of this planet. Here, authors establish their production from (SO)₂ on the grounds of quantifications of photochemical and thermal pathways involved in the sulfur chemical cycle of the planet.

Electron-phonon relaxation at the Au/WSe2 interface is significantly accelerated by a Ti adhesion layer: time-domain ab initio analysis

Thermal transport at nanoscale metal-semiconductor interfaces via electron-phonon coupling is crucial for applications of modern microelectronic, electro-optic and thermoelectric devices. To enhance the device performance, the heat flow can be regulated by modifying the interfacial atomic interactions. We use ab initio time-dependent density functional theory combined with non-adiabatic molecular dynamics to study how the hot electron and hole relaxation rates change on incorporating a thin Ti adhesion layer at the Au/WSe₂ interface. The excited charge carrier relaxation is much faster in Au/Ti/WSe₂ due to the enhanced electron-phonon coupling, rationalized by the following reasons: (1) Ti atoms are lighter than Au, W and Se atoms and move faster. (2) Ti has a significant contribution to the electronic properties in the relevant energy range. (3) Ti interacts strongly with WSe₂ and promotes its bond-scissoring which causes Fermi-level pinning, making WSe₂ contribute to electronic properties around the Fermi level. The changes in the relaxation rates are more pronounced for excited electrons compared to holes because both relative and absolute Ti contributions to the electronic properties are larger above than below the Fermi level. The results provide guidance for improving the design of novel and robust materials by optimizing the heat dissipation at metal-semiconductor interfaces.

Automatized protocol and interface to simulate QM/MM time-resolved transient absorption at TD-DFT level with COBRAMM

We present a series of new implementations that we recently introduced in COBRAMM, the open-source academic software developed in our group. The goal of these implementations is to offer an automatized workflow and interface to simulate time-resolved transient absorption (TA) spectra of medium-to-big chromophore embedded in a complex environment. Therefore, the excited states absorption and the stimulated emission are simulated along nonadiabatic dynamics performed with trajectory surface hopping. The possibility of treating systems from medium to big size is given by the use of time-dependent density functional theory (TD-DFT) and the presence of the environment is taken into account employing a hybrid quantum mechanics/molecular mechanics (QM/MM) scheme. The full implementation includes a series of auxiliary scripts to properly setup the QM/MM system, the calculation of the wavefunction overlap along the dynamics for the propagation, the evaluation of the transition dipole moment at linear response TD-DFT level, and scripts to setup, run and analyze the TA from an ensemble of trajectories. Altogether, we believe that our implementation will open the door to the easily simulate the time-resolved TA of systems so far computationally inaccessible.

Sampling effects in quantum mechanical/molecular mechanics trajectory surface hopping non-adiabatic dynamics

The impact of different initial conditions in non-adiabatic trajectory surface hopping dynamics within a hybrid quantum mechanical/molecular mechanics scheme is investigated. The influence of a quantum sampling, based on a Wigner distribution, a fully thermal sampling, based on classical molecular dynamics, and a quantum sampled system, but thermally equilibrated with the environment, is investigated on the relaxation dynamics of solvated fulvene after light irradiation. We find that the decay from the first singlet excited state to the ground state shows high dependency on the initial condition and simulation parameters. The three sampling methods lead to different distributions of initial geometries and momenta, which then affect the fate of the excited state dynamics. We evaluated both the effect of sampling geometries and momenta, analysing how the ultrafast decay of fulvene changes accordingly. The results are expected to be of interest to decide how to initialize non-adiabatic dynamics in the presence of the environment. This article is part of the theme issue 'Chemistry without the Born-Oppenheimer approximation'.

Stereodynamics-Controlled Product Branching in the Nonadiabatic H + NaD → Na(3s, 3p) + HD Reaction at Low Temperatures

Nonadiabatic processes play an important role at energies near or higher than conical intersection of adiabatic potential energy surfaces in chemical reactions. In this work, dynamics of the nonadiabatic H + NaD reaction at low temperatures are studied by using the quantum wave packet method based on an improved L-shaped grid. The nonadiabatic H + NaD reaction has two exothermic reaction channels: Na(3s) + HD and Na(3p) + HD; the latter can only occur via nonadiabatic transition. The dynamics results show that the product branching of the H + NaD reaction at collision energies ranging from 20 to 80 cm^-1 is controlled by stereodynamics. The Na(3s) and Na(3p) reaction channels occur through collinear collision and side-on collision, respectively. When the collision energy is lower than 20 cm^-1, the resonance-mediated reaction mechanism is dominant in both the Na(3s) and Na(3p) reaction channels.

Describing the photo-isomerization of a retinal chromophore model with coupled and quantum trajectories

The exact factorization of the electron-nuclear wavefunction is applied to the study of the photo- isomerization of a retinal chromophore model. We describe such an ultrafast nonadiabatic process by analyzing the time-dependent potentials of the theory and by mimicking nuclear dynamics with quantum and coupled trajectories. The time-dependent vector and scalar potentials are the signature of the exact factorization, as they guide nuclear dynamics by encoding the complete electronic dynamics and including excited-state effects. Analysis of the potentials is, thus, essential - when possible - to predict the time-dependent behavior of the system of interest. In this work, we employ the exact time-dependent potentials, available for the numerically-exactly solvable model used here, to propagate quantum nuclear trajectories representing the isomerization reaction of the retinal chromophore. The quantum trajectories are the best possible trajectory-based description of the reaction when using the exact-factorization formalism, and thus allow us to assess the performance of the coupled-trajectory, fully approximate, schemes derived from the exact-factorization equations.

Conformer-Specific Dissociation Dynamics in Dimethyl Methylphosphonate Radical Cation

The dynamics of the dimethyl methylphosphonate (DMMP) radical cation after production by strong field adiabatic ionization have been investigated. Pump-probe experiments using strong field 1300 nm pulses to adiabatically ionize DMMP and a 800 nm non-ionizing probe induce coherent oscillations of the parent ion yield with a period of about 45 fs. The yields of two fragments, PO2C2H7+ and PO2CH4+, oscillate approximately out of phase with the parent ion, but with a slight phase shift relative to each other. We use electronic structure theory and nonadiabatic surface hopping dynamics to understand the underlying dynamics. The results show that while the cation oscillates on the ground state along the P=O bond stretch coordinate, the probe excites population to higher electronic states that can lead to fragments PO2C2H7+ and PO2CH4+. The computational results combined with the experimental observations indicate that the two conformers of DMMP that are populated under experimental conditions exhibit different dynamics after being excited to the higher electronic states of the cation leading to different dissociation products. These results highlight the potential usefulness of these pump-probe measurements as a tool to study conformer-specific dynamics in molecules of biological interest.

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

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

Incorporating Berry Force Effects into the Fewest Switches Surface-Hopping Algorithm: Intersystem Crossing and the Case of Electronic Degeneracy

We present a preliminary surface-hopping approach for modeling intersystem crossing (ISC) dynamics between four electronic states: one singlet and one (triply degenerate) triplet. In order to incorporate all Berry force effects, the algorithm requires that, when moving along an adiabatic surface associated with the triplet manifold, one must also keep track of a quasi-diabatic index (akin to a "m_s" quantum number) for each trajectory. For a simple model problem, we find that a great deal of new physics can be captured by our algorithm, setting the stage for larger, more realistic (or perhaps even ab initio) simulations in the future.

NAST: Nonadiabatic Statistical Theory Package for Predicting Kinetics of Spin-Dependent Processes

We present a nonadiabatic statistical theory (NAST) package for predicting kinetics of spin-dependent processes, such as intersystem crossings, spin-forbidden unimolecular reactions, and spin crossovers. The NAST package can calculate the probabilities and rates of transitions between the electronic states of different spin multiplicities. Both the microcanonical (energy-dependent) and canonical (temperature-dependent) rate constants can be obtained. Quantum effects, including tunneling, zero-point vibrational energy, and reaction path interference, can be accounted for. In the limit of an adiabatic unimolecular reaction proceeding on a single electronic state, NAST reduces to the traditional transition state theory. Because NAST requires molecular properties at only a few points on potential energy surfaces, it can be applied to large molecular systems, used with accurate high-level electronic structure methods, and employed to study slow nonadiabatic processes. The essential NAST input data include the nuclear Hessian at the reactant minimum, as well as the nuclear Hessians, energy gradients, and spin-orbit coupling at the minimum energy crossing point (MECP) between two states. The additional computational tools included in the NAST package can be used to extract the required input data from the output files of electronic structure packages, calculate the effective Hessian at the MECP, and fit the reaction coordinate for more advanced NAST calculations. We describe the theory, its implementation, and three examples of application to different molecular systems.

Photoredox Chemistry with Organic Catalysts: Role of Computational Methods

Organic catalysts have the potential to carry out a wide range of otherwise thermally inaccessible reactions via photoredox routes. Early demonstrated successes of organic photoredox catalysts include one-electron CO₂ reduction and H₂ generation via water splitting. Photoredox systems are challenging to study and design owing to the sheer number and diversity of phenomena involved, including light absorption, emission, intersystem crossing, partial or complete charge transfer, and bond breaking or formation. Designing a viable photoredox route therefore requires consideration of a host of factors such as absorption wavelength, solvent, choice of electron donor or acceptor, and so on. Quantum chemistry methods can play a critical role in demystifying photoredox phenomena. Using one-electron CO₂ reduction with phenylene-based chromophores as an illustrative example, this perspective highlights recent developments in quantum chemistry that can advance our understanding of photoredox processes and proposes a way forward for driving the design and discovery of organic catalysts.

Intersystem crossing and internal conversion dynamics with GAIMS-TeraChem: Excited state relaxation in 2-cyclopentenone

Excited states relaxation in complex molecules often involves two types of nonradiative transitions, internal conversion (IC) and intersystem crossing (ISC). In the situations when the timescales of IC and ISC are comparable, an interplay between these two types of transitions can lead to complex nonadiabatic dynamics on multiple electronic states of different characters and spin multiplicities. We demonstrate that the generalized ab initio multiple spawning (GAIMS) method interfaced with the fast graphics processing unit-based TeraChem electronic structure code can be used to model such nonadiabatic dynamics involving both the IC and ISC transitions in molecules of moderate size. We carried out 1500 fs GAIMS simulations leading to the creation of up to 2500 trajectory basis functions to study the excited states relaxation in 2-cyclopentenone. After a vertical excitation from the ground state to the bright S₂ state, the molecule quickly relaxes to the S₁ state via conical intersection. The following relaxation proceeds along two competing pathways: one involves IC to the ground state, and the other is dominated by ISC to the low-lying triplet states. The time constants describing the population transfer between the six lowest singlet and triplet states predicted by the GAIMS dynamics are in good agreement with the characteristic times of IC and ISC obtained from the analysis of the time-resolved photoelectron spectrum.

Nonadiabatic Dynamics with Coupled Trajectories

In this paper, we discuss coupled-trajectory schemes for molecular-dynamics simulations of excited-state processes. New coupled-trajectory strategies to capture decoherence effects, revival of coherence and nonadiabatic interferences in long-time dynamics are proposed, and compared to independent-trajectory schemes. The working framework is provided by the exact factorization of the electron-nuclear wave function, and it exploits ideas emanating from various surface-hopping schemes. The new coupled-trajectory algorithms are tested on a one-dimensional two-state system using different model parameters which allow one to induce different dynamics. The benchmark is provided by the numerically exact solution of the time-dependent Schrödinger equation.

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.

Modern Theoretical Approaches to Modeling the Excited-State Intramolecular Proton Transfer: An Overview

The excited-state intramolecular proton transfer (ESIPT) phenomenon is nowadays widely acknowledged to play a crucial role in many photobiological and photochemical processes. It is an extremely fast transformation, often taking place at sub-100 fs timescales. While its experimental characterization can be highly challenging, a rich manifold of theoretical approaches at different levels is nowadays available to support and guide experimental investigations. In this perspective, we summarize the state-of-the-art quantum-chemical methods, as well as molecular- and quantum-dynamics tools successfully applied in ESIPT process studies, focusing on a critical comparison of their specific properties.

QM/MM Nonadiabatic Dynamics: the SHARC/COBRAMM Approach

We present the SHARC/COBRAMM approach to enable easy and efficient excited-state dynamics simulations at different levels of electronic structure theory in the presence of complex environments using a quantum mechanics/molecular mechanics (QM/MM) setup. SHARC is a trajectory surface-hoping method that can incorporate the simultaneous effects of nonadiabatic and spin-orbit couplings in the excited-state dynamics of molecular systems. COBRAMM allows ground- and excited-state QM/MM calculations using a subtractive scheme, with electrostatic embedding and a hydrogen link-atom approach. The combination of both free and open-source program packages provides a modular and extensive framework to model nonadiabatic processes after light irradiation from the atomistic scale to the nano-scale. As an example, the relaxation of acrolein from S₁ to T₁ in solution is provided.

Interpolating Nonadiabatic Molecular Dynamics Hamiltonian with Artificial Neural Networks

Nonadiabatic (NA) molecular dynamics (MD) allows one to study far-from-equilibrium processes involving excited electronic states coupled to atomic motions. While NAMD involves expensive calculations of excitation energies and NA couplings (NACs), ground-state properties require much less effort and can be obtained with machine learning (ML) at a fraction of the ab initio cost. Application of ML to excited states and NACs is more challenging, due to costly reference methods, many states, and complex geometry dependence. We developed a NAMD methodology that avoids time extrapolation of excitation energies and NACs. Instead, under the classical path approximation that employs a precomputed ground-state trajectory, we use a small fraction (2%) of the geometries to train neural networks and obtain excited-state energies and NACs for the remaining 98% of the geometries by interpolation. Demonstrated with metal halide perovskites that exhibit complex MD, the method provides nearly two orders of computational savings while generating accurate NAMD results.

Perspective on integrating machine learning into computational chemistry and materials science

Machine learning (ML) methods are being used in almost every conceivable area of electronic structure theory and molecular simulation. In particular, ML has become firmly established in the construction of high-dimensional interatomic potentials. Not a day goes by without another proof of principle being published on how ML methods can represent and predict quantum mechanical properties-be they observable, such as molecular polarizabilities, or not, such as atomic charges. As ML is becoming pervasive in electronic structure theory and molecular simulation, we provide an overview of how atomistic computational modeling is being transformed by the incorporation of ML approaches. From the perspective of the practitioner in the field, we assess how common workflows to predict structure, dynamics, and spectroscopy are affected by ML. Finally, we discuss how a tighter and lasting integration of ML methods with computational chemistry and materials science can be achieved and what it will mean for research practice, software development, and postgraduate training.

Short hydrogen bonds enhance nonaromatic protein-related fluorescence

Intrinsic fluorescence of nonaromatic amino acids is a puzzling phenomenon with an enormous potential in biophotonic applications. The physical origins of this effect, however, remain elusive. Herein, we demonstrate how specific hydrogen bond networks can modulate fluorescence. We highlight the key role played by short hydrogen bonds, present in the protein structure, on the ensuing fluorescence. We provide detailed experimental and molecular evidence to explain these unusual nonaromatic optical properties. Our findings should benefit the design of novel optically active biomaterials for applications in biosensing and imaging.

Fluorescence in biological systems is usually associated with the presence of aromatic groups. Here, by employing a combined experimental and computational approach, we show that specific hydrogen bond networks can significantly affect fluorescence. In particular, we reveal that the single amino acid L-glutamine, by undergoing a chemical transformation leading to the formation of a short hydrogen bond, displays optical properties that are significantly enhanced compared with L-glutamine itself. Ab initio molecular dynamics simulations highlight that these short hydrogen bonds prevent the appearance of a conical intersection between the excited and the ground states and thereby significantly decrease nonradiative transition probabilities. Our findings open the door to the design of new photoactive materials with biophotonic applications.

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.

On the molecular electronic flux: Role of nonadiabaticity and violation of conservation

Analysis of electron flux within and in between molecules is crucial in the study of real-time dynamics of molecular electron wavepacket evolution such as those in attosecond laser chemistry and ultrafast chemical reaction dynamics. We here address two mutually correlated issues on the conservation law of molecular electronic flux, which serves as a key consistency condition for electron dynamics. The first one is about a close relation between "weak" nonadiabaticity and the electron dynamics in low-energy chemical reactions. We show that the electronic flux in adiabatic reactions can be consistently reproduced by taking account of nonadiabaticity. Such nonadiabaticity is usually weak in the sense that it does not have a major effect on nuclear dynamics, whereas it plays an important role in electronic dynamics. Our discussion is based on a nonadiabatic extension of the electronic wavefunction similar in idea to the complete adiabatic formalism developed by Nafie [J. Chem. Phys. 79, 4950 (1983)], which has also recently been reformulated by Patchkovskii [J. Chem. Phys. 137, 084109 (2012)]. We give straightforward proof of the theoretical assertion presented by Nafie using a time-dependent mixed quantum-classical framework and a standard perturbation expansion. Explicitly taking account of the flux conservation, we show that the nonadiabatically induced flux realizes the adiabatic time evolution of the electronic density. In other words, the divergence of the nonadiabatic flux equals the time derivative of the electronic density along an adiabatic time evolution of the target molecule. The second issue is about the accurate computationability of the flux. The calculation of flux needs an accurate representation of the (relative) quantum phase, in addition to the amplitude factor, of a total wavefunction and demands special attention for practical calculations. This paper is the first one to approach this issue directly and show how the difficulties arise explicitly. In doing so, we reveal that a number of widely accepted truncation techniques for static property calculations are potential sources of numerical flux non-conservation. We also theoretically propose alternative strategies to realize better flux conservation.

Modeling Spin-Crossover Dynamics

In this article, we review nonadiabatic molecular dynamics (NAMD) methods for modeling spin-crossover transitions. First, we discuss different representations of electronic states employed in the grid-based and direct NAMD simulations. The nature of interstate couplings in different representations is highlighted, with the main focus on nonadiabatic and spin-orbit couplings. Second, we describe three NAMD methods that have been used to simulate spin-crossover dynamics, including trajectory surface hopping, ab initio multiple spawning, and multiconfiguration time-dependent Hartree. Some aspects of employing different electronic structure methods to obtain information about potential energy surfaces and interstate couplings for NAMD simulations are also discussed. Third, representative applications of NAMD to spin crossovers in molecular systems of different sizes and complexities are highlighted. Finally, we pose several fundamental questions related to spin-dependent processes. These questions should be possible to address with future methodological developments in NAMD.

Computational Comparison of Chemical and Isotopic Approaches to Control the Photoisomerization Dynamics of Light-Driven Molecular Motors

Synthetic molecular motors driven by E/Z photoisomerization reactions are able to produce unidirectional rotary motion because of a structural asymmetry that makes one direction of rotation more probable than the other. In most such motors, this asymmetry is realized through the incorporation of a chemically asymmetric carbon atom. Here, we present molecular dynamics simulations based on multiconfigurational quantum chemistry to investigate whether the merits of this approach can be equaled by an alternative approach that instead exploits isotopic chirality. By first considering an N-methylpyrrolidine–cyclopentadiene motor design, it is shown that isotopically chiral variants of this design undergo faster photoisomerizations than a chemically chiral counterpart, while maintaining rotary photoisomerization quantum yields of similarly high magnitude. However, by subsequently considering a pyrrolinium–cyclopentene design, it is also found that the introduction of isotopic chirality does not provide any control of the directionality of the photoinduced rotations within this framework. Taken together, the results highlight both the potential usefulness of isotopic rather than chemical chirality for the design of light-driven molecular motors, and the need for further studies to establish the exact structural circumstances under which this asymmetry is best exploited.

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

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

Unraveling the internal conversion process within the Q-bands of a chlorophyll-like-system through surface-hopping molecular dynamics simulations

The non-radiative relaxation process within the Q-bands of chlorophylls represents a crucial preliminary step during the photosynthetic mechanism. Despite several experimental and theoretical efforts performed in order to clarify the complex dynamics characterizing this stage, a complete understanding of this mechanism is still far to be reached. In this study, non-adiabatic excited-state molecular dynamic simulations have been performed to model the non-radiative process within the Q-bands for a model system of chlorophylls. This system has been considered in the gas phase and then, to have a more representative picture of the environment, with implicit and mixed implicit-explicit solvation models. In the first part of this analysis, absorption spectra have been simulated for each model in order to guide the setup for the non-adiabatic excited-state molecular dynamic simulations. Then, non-adiabatic excited-state molecular dynamic simulations have been performed on a large set of independent trajectories and the population of the Q_x and Q_y states has been computed as the average of all the trajectories, estimating the rate constant for the process. Finally, with the aim of investigating the possible role played by the solvent in the Q_x-Q_y crossing mechanism, an essential dynamic analysis has been performed on the generated data, allowing one to find the most important motions during the simulated dynamics.

Benchmarking the Surface Hopping Method to Include Nuclear Quantum Effects

We have benchmarked the surface hopping method to capture nuclear quantum effects in the spin-Boson model in the deep tunneling regime. The thermal populations and the rate constants calculated using the surface hopping method are compared with those calculated using Boltzmann theory and Fermi's golden rule, respectively. Additionally, we have proposed a simple kinetic model that partially includes nuclear quantum effects within Marcus theory, and the results of the surface hopping method are analyzed under the framework of this simple kinetic model. A broad range of parameters are investigated to identify the regimes for the successes and failures of the surface hopping method. This work shows that with the accurate treatment of decoherence and velocity reversal, surface hopping can generally capture the nuclear quantum effects in the deep tunneling and weak diabatic coupling regime.

Artificial Photosynthesis: Is Computation Ready for the Challenge Ahead?

A tremendous effort is currently devoted to the generation of novel hybrid materials with enhanced electronic properties for the creation of artificial photosynthetic systems. This compelling and challenging problem is well-defined from an experimental point of view, as the design of such materials relies on combining organic materials or metals with biological systems like light harvesting and redox-active proteins. Such hybrid systems can be used, e.g., as bio-sensors, bio-fuel cells, biohybrid photoelectrochemical cells, and nanostructured photoelectronic devices. Despite these efforts, the main bottleneck is the formation of efficient interfaces between the biological and the organic/metal counterparts for efficient electron transfer (ET). It is within this aspect that computation can make the difference and improve the current understanding of the mechanisms underneath the interface formation and the charge transfer efficiency. Yet, the systems considered (i.e., light harvesting protein, self-assembly monolayer and surface assembly) are more and more complex, reaching (and often passing) the limit of current computation power. In this review, recent developments in computational methods for studying complex interfaces for artificial photosynthesis will be provided and selected cases discussed, to assess the inherent ability of computation to leave a mark in this field of research.

Intermolecular conical intersections in molecular aggregates

Conical intersections (CoIns) of multidimensional potential energy surfaces are ubiquitous in nature and control pathways and yields of many photo-initiated intramolecular processes. Such topologies can be potentially involved in the energy transport in aggregated molecules or polymers but are yet to be uncovered. Here, using ultrafast two-dimensional electronic spectroscopy (2DES), we reveal the existence of intermolecular CoIns in molecular aggregates relevant for photovoltaics. Ultrafast, sub-10-fs 2DES tracks the coherent motion of a vibrational wave packet on an optically bright state and its abrupt transition into a dark state via a CoIn after only 40 fs. Non-adiabatic dynamics simulations identify an intermolecular CoIn as the source of these unusual dynamics. Our results indicate that intermolecular CoIns may effectively steer energy pathways in functional nanostructures for optoelectronics.

Signatures of electronic and nuclear coherences in ultrafast molecular x-ray and electron diffraction

Femtosecond x-ray and electron diffraction hold promise to image the evolving structures of single molecules. We present a unified quantum-electrodynamical formulation of diffraction signals, based on the exact many-body nuclear + electronic wavefunction that can be extracted from quantum chemistry simulations. This gives a framework for analyzing various approximate molecular dynamics simulations. We show that the complete description of ultrafast diffraction signals contains interesting contributions involving mixed elastic and inelastic scattered photons that are usually masked by other larger contributions and are neglected. These terms include overlaps of nuclear wavepackets between different electronic states that provide an electronic decoherence mechanism and are important for the time-resolved imaging of conical intersections.

Experimental and theoretical study of energy transfer in a chromophore triad: What makes modeling dynamics successful?

Simulation of electronic dynamics in realistically large molecular systems is a demanding task that has not yet achieved the same level of quantitative prediction already realized for its static counterpart. This is particularly true for processes occurring beyond the Born-Oppenheimer regime. Non-adiabatic molecular dynamics (NAMD) simulations suffer from two convoluted sources of error: numerical algorithms for dynamics and electronic structure calculations. While the former has gained increasing attention, particularly addressing the validity of ad hoc methodologies, the effect of the latter remains relatively unexplored. Indeed, the required accuracy for electronic structure calculations to reach quantitative agreement with experiment in dynamics may be even more strict than that required for static simulations. Here, we address this issue by modeling the electronic energy transfer in a donor-acceptor-donor (D-A-D) molecular light harvesting system using fewest switches surface hopping NAMD simulations. In the studied system, time-resolved experimental measurements deliver complete information on spectra and energy transfer rates. Subsequent modeling shows that the calculated electronic transition energies are "sufficiently good" to reproduce experimental spectra but produce over an order of magnitude error in simulated dynamical rates. We further perform simulations using artificially shifted energy gaps to investigate the complex relationship between transition energies and modeled dynamics to understand factors affecting non-radiative relaxation and energy transfer rates.

PySurf: A Framework for Database Accelerated Direct Dynamics

The greatest restriction to the theoretical study of the dynamics of photoinduced processes is computationally expensive electronic structure calculations. Machine learning algorithms have the potential to reduce the number of these computations significantly. Here, PySurf is introduced as an innovative code framework, which is specifically designed for rapid prototyping and development tasks for data science applications in computational chemistry. It comes with powerful Plugin and Workflow engines, which allows intuitive customization for individual tasks. Data is automatically stored through the database framework, which enables additional interpolation of properties in previously evaluated regions of the conformational space. To illustrate the potential of the framework, a code for nonadiabatic surface hopping simulations based on the Landau-Zener algorithm is presented here. Deriving gradients from the interpolated potential energy surfaces allows for full-dimensional nonadiabatic surface hopping simulations using only adiabatic energies (energy only). Simulations of a pyrazine model and ab initio-based calculations of the SO2 molecule show that energy-only calculations with PySurf are able to correctly predict the nonadiabatic dynamics of these prototype systems. The results reveal the degree of sophistication, which can be achieved by the database accelerated energy-only surface hopping simulations being competitive to commonly used semiclassical approaches.

The Photoisomerization Pathway(s) of Push-Pull Phenylazoheteroarenes*

Azoheteroarenes are the most recent derivatives targeted to further improve the properties of azo-based photoswitches. Their light-induced mechanism for trans-cis isomerization is assumed to be very similar to that of the parent azobenzene. As such, they inherited the controversy about the dominant isomerization pathway (rotation vs. inversion) depending on the excited state (nπ* vs. ππ*). Although the controversy seems settled in azobenzene, the extent to which the same conclusions apply to the more structurally diverse family of azoheteroarenes is unclear. Here, by means of non-adiabatic molecular dynamics, the photoisomerization mechanism of three prototypical phenyl-azoheteroarenes with increasing push-pull character is unraveled. The evolution of the rotational and inversion conical intersection energies, the preferred pathway, and the associated kinetics upon both nπ* and ππ* excitations can be linked directly with the push-pull substitution effects. Overall, the working conditions of this family of azo-dyes is clarified and a possibility to exploit push-pull substituents to tune their photoisomerization mechanism is identified, with potential impact on their quantum yield.

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

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

Excited-state dynamics of CH2I2 and CH2IBr studied with UV-pump VUV-probe momentum-resolved photoion spectroscopy

We perform time-resolved ionization spectroscopy measurements of the excited state dynamics of CH₂I₂ and CH₂IBr following photoexcitation in the deep UV. The fragment ions produced by ionization with a vacuum-ultraviolet probe pulse are measured with velocity map imaging, and the momentum resolved yields are compared with trajectory surface hopping calculations of the measurement observable. Together with recent time-resolved photoelectron spectroscopy measurements of the same dynamics, these results provide a detailed picture of the coupled electronic and nuclear dynamics involved. Our measurements highlight the non-adiabatic coupling between electronic states, which leads to notable differences in the dissociation dynamics for the two molecules.

Fluorescence Quantum Yields in Complex Environments from QM-MM TDDFT Simulations: The Case of Indole in Different Solvents

Fluorescence is commonly exploited to probe microscopic properties. An important example is tryptophan in protein environments, where variations in fluorescence quantum yield, and in absorption and emission maxima, are used as indicators of changes in the environment. Modeling the fluorescence quantum yield requires the determination of both radiative and nonradiative decay constants, both on the potential energy surface of the excited fluorophore. Furthermore, the inclusion of complex environments implies their accurate representation as well as extensive configurational sampling. In this work, we present and test various methodologies based on time-dependent density functional theory (TDDFT) and quantum mechanics/molecular mechanics (QM/MM) dynamics that take all of these requirements into account to provide a quantitative prediction of the effect of the environment on the fluorescence quantum yield of indole, a tryptophan fluorophore. This investigation paves the way for applications to the realistic spectroscopic characterization of the local protein environment of tryptophan from computer simulations.