Nonadiabatic dynamics: The SHARC approach

Nature of Hops, Coordinates, and Detailed Balance for Nonadiabatic Simulations in the Condensed Phase

Photoinduced processes play a crucial role in a multitude of important molecular phenomena. Accurately modeling these processes in an environment other than a vacuum requires a detailed description of the electronic states involved as well as how energy flows are coupled to the surroundings. Nonadiabatic effects must also be included in order to describe the exchange of energy between electronic and nuclear degrees of freedom correctly. In this work, we revisit the ring-opening reaction 1,3-cylohexadiene (CHD) in a solvent environment. Using our newly developed Interface for Non-Adiabatic Quantum mechanics/molecular mechanics in Solvent (INAQS) we trace the evolution of the reaction via hybrid quantum mechanics/molecular mechanics (QM/MM) surface hopping with a focus on the solvent's participation in the nonadiabatic relaxation process and the long-time approach to equilibrium. We explicitly include the MM solvent contribution to the nonadiabatic coupling vector─enabling an accurate approach to equilibrium at long times─and find that in highly multidimensional systems gradients can have little or nothing to do with the nonadiabatic couplings.

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.

HORTENSIA, a program package for the simulation of nonadiabatic autoionization dynamics in molecules

We present a program package for the simulation of ultrafast vibration-induced autoionization dynamics in molecular anions in the manifold of the adiabatic anionic states and the discretized ionization continuum. This program, called HORTENSIA (Hopping Real-time Trajectories for Electron-ejection by Nonadiabatic Self-Ionization in Anions), is based on the nonadiabatic surface-hopping methodology, wherein nuclei are propagated as an ensemble along classical trajectories in the quantum-mechanical potential created by the electronic density of the molecular system. The electronic Schrödinger equation is numerically integrated along the trajectory, providing the time evolution of electronic state coefficients, from which switching probabilities into discrete electronic states are determined. In the case of a discretized continuum state, this hopping event is interpreted as the ejection on an electron. The derived diabatic and nonadiabatic couplings in the time-dependent electronic Schrödinger equation are calculated from anionic and neutral wavefunctions obtained from quantum-chemical calculations with commercially available program packages interfaced with our program. Based on this methodology, we demonstrate the simulation of autoionization electron kinetic energy spectra that are both time- and angle-resolved. In addition, the program yields data that can be interpreted easily with respect to geometric characteristics, such as bonding distances and angles, which facilitate the detection of molecular configurations important for the autoionization process. Furthermore, several useful extensions are included, namely, tools for the generation of initial conditions and input files as well as for the evaluation of output files, all of this both through console commands and a graphical user interface.

Ultrafast Photocontrolled Rotation in a Molecular Motor Investigated by Machine Learning-Based Nonadiabatic Dynamics Simulations

The thermal helix inversion (THI) of the overcrowded alkene-based molecular motors determines the speed of the unidirectional rotation due to the high reaction barrier in the ground state, in comparison with the ultrafast photoreaction process. Recently, a phosphine-based motor has achieved all-photochemical rotation experimentally, promising to be controlled without a thermal step. However, the mechanism of this photochemical reaction has not yet been fully revealed. The comprehensive computational studies on photoisomerization still resort to nonadiabatic molecular dynamics (NAMD) simulations based on electronic structure calculations, which remains a high computational cost for large systems such as molecular motors. Machine learning (ML) has become an accelerating tool in NAMD simulations recently, where excited-state potential energy surfaces (PESs) are constructed analytically with high accuracy, providing an efficient approach for simulations in photochemistry. Herein the reaction pathway is explored by a spin-flip time-dependent density functional theory (SF-TDDFT) approach in combination with ML-based NAMD simulations. According to our computational simulations, we notice that one of the key factors of fulfilling all-photochemical rotation in the phosphine-based motor is that the excitation energies of four isomers are similar. Additionally, a shortcut photoinduced transformation between unstable isomers replaces the THI step, which shares the conical intersection (CI) with photoisomerization. In this study, we provide a practical approach to speed up the NAMD simulations in photochemical reactions for a large system that could be extended to other complex systems.

Efficient Modeling of Quantum Dynamics of Charge Carriers in Materials Using Short Nonequilibrium Molecular Dynamics

Nonadiabatic molecular dynamics provides essential insights into excited-state processes, but it is computationally intense and simplifications are needed. The classical path approximation provides critical savings. Still, long heating and equilibration steps are required. We demonstrate that practical results can be obtained with short, partially equilibrated ab initio trajectories. Once the system's structure is adequate and essential fluctuations are sampled, the nonadiabatic Hamiltonian can be constructed. Local structures require only 1-2 ps trajectories, as demonstrated with point defects in metal halide perovskites. Short trajectories represent anharmonic motions common in defective structures, an essential improvement over the harmonic approximation around the optimized geometry. Glassy systems, such as grain boundaries, require different simulation protocols, e.g., involving machine learning force fields. 10-fold shorter trajectories generate 10-20% time scale errors, which are acceptable, given experimental uncertainties and other approximations. The practical NAMD protocol enables fast screening of excited-state dynamics for rapid exploration of new materials.

Significance of Nonadiabatic Effects on Efficient Triplet Generation in Lumazines

The photophysics of lumazines leading to triplet formation and the effect of thionation are explored in the presence of near-degenerate electronic states. Wave packet simulations are performed on model potential energy surfaces to understand the nonadiabatic population transfer among close-lying excited states. Ultrafast population transfer among singlets opens up new intersystem crossing channels from the higher states. An increased spin-orbit coupling strength originating from thionation enhances intersystem crossing and populates the higher triplets first. The rapid internal conversion in the triplet manifold eventually brings the molecules to their respective low-lying long-lived triplet state.

Deciphering the Influence of Ground-State Distributions on the Calculation of Photolysis Observables

Nonadiabatic molecular dynamics offers a powerful tool for studying the photochemistry of molecular systems. Key to any nonadiabatic molecular dynamics simulation is the definition of its initial conditions (ICs), ideally representing the initial molecular quantum state of the system of interest. In this work, we provide a detailed analysis of how ICs may influence the calculation of experimental observables by focusing on the photochemistry of methylhydroperoxide (MHP), the simplest and most abundant organic peroxide in our atmosphere. We investigate the outcome of trajectory surface hopping simulations for distinct sets of ICs sampled from different approximate quantum distributions, namely harmonic Wigner functions and ab initio molecular dynamics using a quantum thermostat (QT). Calculating photoabsorption cross-sections, quantum yields, and translational kinetic energy maps from the results of these simulations reveals the significant effect of the ICs, in particular when low-frequency (∼ a few hundred cm-1) normal modes are connected to the photophysics of the molecule. Overall, our results indicate that sampling ICs from ab initio molecular dynamics using a QT is preferable for flexible molecules with photoactive low-frequency modes. From a photochemical perspective, our nonadiabatic dynamics simulations offer an explanation for a low-energy tail observed at high excitation energy in the translational kinetic energy map of MHP.

Ultrafast formation dynamics of D3+ from the light-driven bimolecular reaction of the D2-D2 dimer

The light-driven formation of trihydrogen cation has been attracting considerable attention because of its important role as an initiator of chemical reactions in interstellar clouds. To understand the formation dynamics, most previous studies focused on creating H3+ or D3+ from unimolecular reactions of various organic molecules. Here we observe and characterize the ultrafast formation dynamics of D3+ from a bimolecular reaction, using pump-probe experiments that employ ultrashort laser pulses to probe its formation from a D2-D2 dimer. Our molecular dynamics simulations provide an intuitive representation of the reaction dynamics, which agree well with the experimental observation. We also show that the emission direction of D3+ can be controlled using a tailored two-colour femtosecond laser field. The underlying control mechanism is in line with what is known from the light control of electron localization in the bond breaking of single molecules.

Rationalizing the environment-dependent photophysical behavior of a DNA luminescent probe by classical and non-adiabatic molecular dynamics simulations

Environment-sensitive fluorescent nucleoside analogs are of utmost importance to investigate the structure of nucleic acids, their intrinsic flexibility, and sequence-specific DNA- and RNA-binding proteins. The latter play indeed a key role in transcription, translation as well as in the regulation of RNA stability, localization and turnover, and many other cellular processes. The sensitivity of the embedded fluorophore to polarity, hydration, and base stacking is clearly dependent on the specific excited-state relaxation mechanism and can be rationalized combining experimental and computational techniques. In this work, we elucidate the mechanisms leading to the population of the triplet state manifold for a versatile nucleobase surrogate, namely the 2-thienyl-3-hydroxychromone in gas phase, owing to non-adiabatic molecular dynamics simulations. Furthermore, we analyze its behavior in the B-DNA environment via classical molecular dynamics simulations, which evidence a rapid extrusion of the adenine facing the 2-thienyl-3-hydroxychromone nucleobase surrogate. Our simulations provide new insights into the dynamics of this family of chromophores, which could give rise to an integrated view and a fine tuning of their photochemistry, and namely the role of excited-state intramolecular proton transfer for the rational design of the next generation of fluorescent nucleoside analogs.

NEXMD v2.0 Software Package for Nonadiabatic Excited State Molecular Dynamics Simulations

We present NEXMD version 2.0, the second release of the NEXMD (Nonadiabatic EXcited-state Molecular Dynamics) software package. Across a variety of new features, NEXMD v2.0 incorporates new implementations of two hybrid quantum-classical dynamics methods, namely, Ehrenfest dynamics (EHR) and the Ab-Initio Multiple Cloning sampling technique for Multiconfigurational Ehrenfest quantum dynamics (MCE-AIMC or simply AIMC), which are alternative options to the previously implemented trajectory surface hopping (TSH) method. To illustrate these methodologies, we outline a direct comparison of these three hybrid quantum-classical dynamics methods as implemented in the same NEXMD framework, discussing their weaknesses and strengths, using the modeled photodynamics of a polyphenylene ethylene dendrimer building block as a representative example. We also describe the expanded normal-mode analysis and constraints for both the ground and excited states, newly implemented in the NEXMD v2.0 framework, which allow for a deeper analysis of the main vibrational motions involved in vibronic dynamics. Overall, NEXMD v2.0 expands the range of applications of NEXMD to a larger variety of multichromophore organic molecules and photophysical processes involving quantum coherences and persistent couplings between electronic excited states and nuclear velocity.

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

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

Role of Ultrafast Internal Conversion and Intersystem Crossing in the Nonadiabatic Relaxation Dynamics of ortho-Nitrobenzaldehyde

ortho-Nitrobenzaldehyde (oNBA) is a well-known photoactivated acid and a prototypical photolabile nitro-aromatic compound. Despite extensive investigations, the ultrafast relaxation dynamics of oNBA is still not properly understood, especially concerning the role of the triplet states. In this work, we provide an in-depth picture of this dynamics by combining single- and multireference electronic structure methods with potential energy surface exploration and nonadiabatic dynamics simulations using the Surface Hopping including ARbitary Couplings (SHARC) approach. Our results reveal that the initial decay from the bright ππ* state to the S₁ minimum is barrierless. It involves three changes in electronic structure from ππ* (ring) to nπ* (nitro group), to nπ* (aldehyde group), and then to another nπ* (nitro group). The decay of the ππ* takes 60-80 fs and can be tracked with time-resolved luminescence spectroscopy, where we predict for the first time a short-lived coherence of the luminescence energy with a 25 fs period. Intersystem crossing can occur already during the S₄ → S₁ deactivation cascade but also from S₁, with a time constant of about 2.4 ps and such that first a triplet ππ* state localized on the nitro group is populated. The triplet population first evolves into an nπ* and then quickly undergoes hydrogen transfer to form a biradical intermediate, from where the ketene is eventually produced. The majority of the excited population decays from S₁ through two conical intersections of equal utilization, a previously unreported one involving a scissoring motion of the nitro group that leads back to the oNBA ground state and the one involving hydrogen transfer that leads to the ketene intermediate.

Tetraphenyl-1,4-dioxin and Tetraphenyl-pyrane-4-one: Old Molecules, New Insights

Aggregation-induced emission (AIE) is a phenomenon where certain molecules or materials become highly luminescent when they aggregate or come together in a condensed state, such as a solid or a solution. Moreover, new molecules which show AIE properties are designed and synthesized for various applications like imaging, sensing, and optoelectronics. 2,3,5,6-Tetraphenylpyrazine (TPP) is one of the well-established examples of AIE. Herein, 2,3,5,6-tetraphenyl-1,4-dioxin (TPD) and 2,3,4,5-tetraphenyl-4H-pyran-4-one (TPPO), which are old molecules with TPP similarity, were studied, and new insights in terms of structure and aggregation-caused quenching (ACQ)/AIE properties were gained by means of theoretical calculations. Those calculations performed on TPD and TPPO aimed to provide a better understanding of their molecular structures and how they affect their luminescence properties. This information could be used to design new materials with improved AIE properties or to modify existing materials to overcome ACQ.

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.

Vibrational Funnels for Energy Transfer in Organic Chromophores

Photoinduced intramolecular energy transfers in multichromophoric molecules involve nonadiabatic vibronic channels that act as energy transfer funnels. They commonly take place through specific directions of motion dictated by the nonadiabatic coupling vectors. Vibrational funnels may support persistent coherences between electronic states and sometimes delineate the presence of minor alternative energy transfer pathways. The ultimate confirmation of their role on the interchromophoric energy transfer can be achieved by performing nonadiabatic excited-state molecular dynamics simulations by selectively freezing the nuclear motions in question. Our results point out this strategy as a useful tool to identify and evaluate the impact of these vibrational funnels on the energy transfer processes and guide the in silico design of materials with tunable properties and enhanced functionalities. Our work encourages applications of this methodology to different chemical and biochemical processes such as reactive scattering and protein conformational changes, to name a few.

Excited-State Dynamics during Primary C-I Homolysis in Acetyl Iodide Revealed by Ultrafast Core-Level Spectroscopy

In typical carbonyl-containing molecules, bond dissociation events follow initial excitation to nπC═O* states. However, in acetyl iodide, the iodine atom gives rise to electronic states with mixed nπC═O* and nσC-I* character, leading to complex excited-state dynamics, ultimately resulting in dissociation. Using ultrafast extreme ultraviolet (XUV) transient absorption spectroscopy and quantum chemical calculations, we present an investigation of the primary photodissociation dynamics of acetyl iodide via time-resolved spectroscopy of core-to-valence transitions of the I atom after 266 nm excitation. The probed I 4d-to-valence transitions show features that evolve on sub-100-fs time scales, reporting on excited-state wavepacket evolution during dissociation. These features subsequently evolve to yield spectral signatures corresponding to free iodine atoms in their spin-orbit ground and excited states with a branching ratio of 1.1:1 following dissociation of the C-I bond. Calculations of the valence excitation spectrum via equation-of-motion coupled cluster with single and double substitutions (EOM-CCSD) show that initial excited states are of spin-mixed character. From the initially pumped spin-mixed state, we use a combination of time-dependent density functional theory (TDDFT)-driven nonadiabatic ab initio molecular dynamics and EOM-CCSD calculations of the N4,5 edge to reveal a sharp inflection point in the transient XUV signal that corresponds to rapid C-I homolysis. By examining the molecular orbitals involved in the core-level excitations at and around this inflection point, we are able to piece together a detailed picture of C-I bond photolysis in which d → σ* transitions give way to d → p excitations as the bond dissociates. We also report theoretical predictions of short-lived, weak 4d → 5d transitions in acetyl iodide, validated by weak bleaching in the experimental transient XUV spectra. This joint experimental-theoretical effort has thus unraveled the detailed electronic structure and dynamics of a strongly spin-orbit coupled system.

Ultrafast Electronic Relaxation in Aqueous [Fe(bpy)3]2+: A Surface Hopping Study

Trajectory surface hopping simulations are performed to better understand the electronic relaxation dynamics of [Fe(bpy)₃]²⁺ in aqueous solution. Specifically, the ultrafast relaxation from the photoexcited singlet metal-to-ligand charge-transfer (MLCT) to the metastable quintet metal-centered (MC) states is simulated through the surface hopping method, where the MLCT and MC states of [Fe(bpy)₃]²⁺ in aqueous solution are computed by using a model electronic Hamiltonian developed previously. As a result, most of the trajectories are interpreted to show the sequential relaxation pathways via the triplet MC states, though some are the direct pathway from MLCT to the quintet MC states. Even though the triplet MC states are involved in the relaxation, the population transfer to the singlet MC ground state is very small, and the population of the quintet MC states reaches more than ∼96%, reasonably consistent with the unity quantum efficiency discussed experimentally.

Impact of the core on the inter-branch exciton exchange in dendrimers

Organic dendrimers with π conjugated systems are capable of capturing solar energy as a renewable source for human use. Nonetheless, further study regarding the relationship between the structure and the energy transfer mechanism in these types of molecules is still necessary. In this work, nonadiabatic excited state molecular dynamics (NEXMD) were carried out to study the intra- and inter-branch exciton migration in two tetra-branched dendrimers, C(dSSB)₄ and Ad(BuSSB)₄, which differ in their respective carbon and adamantane core. Both systems undergo a ladder decay mechanism between excited states, with back-and-forth transitions between S₁ and S₂. Despite presenting very similar absorption-emission spectra, differences in the photoinduced energy relaxation are observed. The size of the core impacts the inter-branch energy exchange and transient exciton localization/delocalization, which ultimately condition the relative energy relaxation rates, being faster in Ad(BuSSB)₄ with respect to C(dSSB)₄. Nevertheless, the photoinduced processes lead to a progressive final exciton-self-trapping in one of the branches of both dendrimers, which is a desirable feature in organic photovoltaic applications. Our results can inspire the design of more efficient dendrimers with the desired magnitude of inter-branch exciton exchange and localization/delocalization according to changes in their core.

Robust Inversion of Time-Resolved Data via Forward-Optimization in a Trajectory Basis

An inversion method for time-resolved data from ultrafast experiments is introduced, based on forward-optimization in a trajectory basis. The method is applied to experimental data from X-ray scattering of the photochemical ring-opening reaction of 1,3-cyclohexadiene and electron diffraction of the photodissociation of CS₂. In each case, inversion yields a model that reproduces the experimental data, identifies the main dynamic motifs, and agrees with independent experimental observations. Notably, the method explicitly accounts for continuity constraints and is robust even for noisy data.

A theoretical study of the time-resolved x-ray absorption spectrum of the photoionized BT-1T cation

The time-resolved x-ray absorption spectrum of the BT-1T cation (BT-1T+) is theoretically simulated in order to investigate the charge transfer reaction of the system. We employ both trajectory surface hopping and quantum dynamics to simulate the structural evolution over time and the changes in the state populations. To compute the static x-ray absorption spectra (XAS) of the ground and excited states, we apply both the time-dependent density functional theory and the coupled cluster singles and doubles method. The results obtained are in good agreement between the methods. It is, furthermore, found that the small structural changes that occur during the reaction have little effect on the static XAS. Hence, the tr-XAS can be computed based on the state populations determined from a nuclear dynamics simulation and one set of static XAS calculations, utilizing the ground state optimized geometry. This approach can save considerable computational resources, as the static spectra need not to be calculated for all geometries. As BT-1T is a relatively rigid molecule, the outlined approach should only be considered when investigating non-radiative decay processes in the vicinity of the Franck-Condon point.

New Gradient Correction Scheme for Electronically Nonadiabatic Dynamics Involving Multiple Spin States

It has been recommended that the best representation to use for trajectory surface hopping (TSH) calculations is the fully adiabatic basis in which the Hamiltonian is diagonal. Simulations of intersystem crossing processes with conventional TSH methods require an explicit computation of nonadiabatic coupling vectors (NACs) in the molecular-Coulomb-Hamiltonian (MCH) basis, also called the spin-orbit-free basis, in order to compute the gradient in the fully adiabatic basis (also called the diagonal representation). This explicit requirement destroys some of the advantages of the overlap-based algorithms and curvature-driven algorithms that can be used for the most efficient TSH calculations. Therefore, although these algorithms allow one to perform NAC-free simulations for internal conversion processes, one still requires NACs for intersystem crossing. Here, we show that how the NAC requirement is circumvented by a new computation scheme called the time-derivative-matrix scheme.

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.

Structural Sampling and Solvation Models for the Simulation of Electronic Spectra: Pyrazine as a Case Study

The impact of sampling methods on spectral broadening in the gas phase and on the convergence of spectra in aqueous solution when using microsolvation, continuum solvation, and hybrid models is studied using pyrazine as a test case. For the sake of comparing classical Maxwell-Boltzmann and Wigner samplings in the gas phase, static and time-resolved X-ray absorption spectra after photoexcitation to the lowest ¹B_2u(ππ*) state, as well as the static UV-vis absorption spectrum, are considered. In addition, the UV-vis absorption spectrum of pyrazine in aqueous solution is also computed in order to systematically investigate its convergence with the number of explicitly included solvent shells with and without taking bulk solvation effects into account with the conductor-like screening model to represent implicit water beyond such explicit solute complexes. Concerning the static and time-resolved X-ray absorption spectra of pyrazine at the carbon K-edge as well as its UV-vis absorption spectrum in the gas phase, we find that these spectra obtained with Wigner and Maxwell-Boltzmann samplings substantially agree. For the UV-vis absorption spectrum in the aqueous solution, only the first two energetically low-lying bands converge quickly with the size of the explicitly included solvation shells, either with or without an additional continuum solvation taken into account. In stark contrast, calculations of the higher-lying excitations relying on finite microsolvated clusters without additional continuum solvation severely suffer from unphysical charge-transfer excitations into Rydberg-like orbitals at the cluster/vacuum interface. This finding indicates that computational UV-vis absorption spectra covering sufficiently high-lying states converge only if continuum solvation of the explicitly microsolvated solutes is included in the models.

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.

A mapping approach to surface hopping

We present a nonadiabatic classical-trajectory approach that offers the best of both worlds between fewest-switches surface hopping (FSSH) and quasiclassical mapping dynamics. This mapping approach to surface hopping (MASH) propagates the nuclei on the active adiabatic potential-energy surface, such as in FSSH. However, unlike in FSSH, transitions between active surfaces are deterministic and occur when the electronic mapping variables evolve between specified regions of the electronic phase space. This guarantees internal consistency between the active surface and the electronic degrees of freedom throughout the dynamics. MASH is rigorously derivable from exact quantum mechanics as a limit of the quantum-classical Liouville equation (QCLE), leading to a unique prescription for momentum rescaling and frustrated hops. Hence, a quantum-jump procedure can, in principle, be used to systematically converge the accuracy of the results to that of the QCLE. This jump procedure also provides a rigorous framework for deriving approximate decoherence corrections similar to those proposed for FSSH. We apply MASH to simulate the nonadiabatic dynamics in various model systems and show that it consistently produces more accurate results than FSSH at a comparable computational cost.

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.

Direct Nonadiabatic Dynamics of Ammonia with Curvature-Driven Coherent Switching with Decay of Mixing and with Fewest Switches with Time Uncertainty: An Illustration of Population Leaking in Trajectory Surface Hopping Due to Frustrated Hops

Mixed quantum-classical nonadiabatic dynamics is a widely used approach to simulate molecular dynamics involving multiple electronic states. There are two main categories of mixed quantum-classical nonadiabatic dynamics algorithms, namely, trajectory surface hopping (TSH) in which the trajectory propagates on a single potential energy surface, interrupted by hops, and self-consistent-potential (SCP) methods, such as semiclassical Ehrenfest, in which propagation occurs on a mean-field surface without hops. In this work, we will illustrate an example of severe population leaking in TSH. We emphasize that such leaking is a combined effect of frustrated hops and long-time simulations that drive the final excited-state population toward zero as a function of time. We further show that such leaking can be alleviated-but not eliminated-by the fewest switches with time uncertainty TSH algorithm (here implemented in the SHARC program); the time uncertainty algorithm slows down the leaking process by a factor of 4.1. The population leaking is not present in coherent switching with decay of mixing (CSDM), which is an SCP method with non-Markovian decoherence included. Another result in this paper is that we find very similar results with the original CSDM algorithm, with time-derivative CSDM (tCSDM), and with curvature-driven CSDM (κCSDM). Not only do we find good agreement for electronically nonadiabatic transition probabilities but also we find good agreement of the norms of the effective nonadiabatic couplings (NACs) that are derived from the curvature-driven time-derivative couplings as implemented in κCSDM with the time-dependent norms of the nonadiabatic coupling vectors computed by state-averaged complete-active-space self-consistent field theory.

Efficient implementation and performance analysis of the independent electron surface hopping method for dynamics at metal surfaces

Independent electron surface hopping (IESH) is a computational algorithm for simulating the mixed quantum-classical molecular dynamics of adsorbate atoms and molecules interacting with metal surfaces. It is capable of modeling the nonadiabatic effects of electron-hole pair excitations on molecular dynamics. Here, we present a transparent, reliable, and efficient implementation of IESH, demonstrating its ability to predict scattering and desorption probabilities across a variety of systems, ranging from model Hamiltonians to full dimensional atomistic systems. We further show how the algorithm can be modified to account for the application of an external bias potential, comparing its accuracy to results obtained using the hierarchical quantum master equation. Our results show that IESH is a practical method for modeling coupled electron-nuclear dynamics at metal surfaces, especially for highly energetic scattering events.

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.

Neural network potentials for chemistry: concepts, applications and prospects

Artificial Neural Networks (NN) are already heavily involved in methods and applications for frequent tasks in the field of computational chemistry such as representation of potential energy surfaces (PES) and spectroscopic predictions. This perspective provides an overview of the foundations of neural network-based full-dimensional potential energy surfaces, their architectures, underlying concepts, their representation and applications to chemical systems. Methods for data generation and training procedures for PES construction are discussed and means for error assessment and refinement through transfer learning are presented. A selection of recent results illustrates the latest improvements regarding accuracy of PES representations and system size limitations in dynamics simulations, but also NN application enabling direct prediction of physical results without dynamics simulations. The aim is to provide an overview for the current state-of-the-art NN approaches in computational chemistry and also to point out the current challenges in enhancing reliability and applicability of NN methods on a larger scale.

Photodynamics of the Molecular Ruby [Cr(ddpd)2]3

The introduction of strong-field ligands can enable luminescence in first-row transition-metal complexes. In this way, earth-abundant near-infrared emitters can be obtained using early 3d metals. A prime example is the molecular ruby [Cr(ddpd)₂]³⁺ (ddpd = N,N'-dimethyl-N,N'-dipyridin-2-ylpyridine-2,6-diamine) that can achieve high phosphorescence quantum yields at room temperature in aqueous solution. To understand these remarkable properties, here, we simulate its photodynamics in water using trajectory surface hopping on linear vibronic coupling potentials parametrized from multiconfigurational CASSCF/CASPT2 calculations. We find that after excitation to the second absorption band, a relaxation cascade through metal-centered states occurs. After an initial back-and-forth intersystem crossing with higher-lying doublet states, the complex relaxes through a manifold of quartet metal-centered states to the low-lying doublet metal-centered states which are responsible for the experimentally observed emission. These electronic processes are driven by an elongation of the Cr-ligand bond lengths as well as the twisting motion of the trans-coordinated pyridine units in the ddpd ligands. The low-lying doublet states are reached within 1-2 ps and are close in geometry to the doublet minima, thus explaining the high phosphorescence quantum yield of the molecular ruby [Cr(ddpd)₂]³⁺.

MoBioTools: A toolkit to setup quantum mechanics/molecular mechanics calculations

We present a toolkit that allows for the preparation of QM/MM input files from a conformational ensemble of molecular geometries. The package is currently compatible with trajectory and topology files in Amber, CHARMM, GROMACS and NAMD formats, and has the possibility to generate QM/MM input files for Gaussian (09 and 16), Orca (≥4.0), NWChem and (Open)Molcas. The toolkit can be used in command line, so that no programming experience is required, although it presents some features that can also be employed as a python application programming interface. We apply the toolkit in four situations in which different electronic-structure properties of organic molecules in the presence of a solvent or a complex biological environment are computed: the reduction potential of the nucleobases in acetonitrile, an energy decomposition analysis of tyrosine interacting with water, the absorption spectrum of an azobenzene derivative integrated into a voltage-gated ion channel, and the absorption and emission spectra of the luciferine/luciferase complex. These examples show that the toolkit can be employed in a manifold of situations for both the electronic ground state and electronically excited states. It also allows for the automatic correction of the active space in the case of CASSCF calculations on an ensemble of geometries, as it is shown for the azobenzene derivative photoswitch case.

Electronic Spectroscopy and Dissociation Dynamics of Vinyl-Substituted Criegee Intermediates: 2-Butenal Oxide and Comparison with Methyl Vinyl Ketone Oxide and Methacrolein Oxide Isomers

The 2-butenal oxide Criegee intermediate [(CH₃CH═CH)CHOO], an isomer of the four-carbon unsaturated Criegee intermediates derived from isoprene ozonolysis, is characterized on its first π* ← π electronic transition and by the resultant dissociation dynamics to O (¹D) + 2-butenal [(CH₃CH═CH)CHO] products. The electronic spectrum of 2-butenal oxide under jet-cooled conditions is observed to be broad and unstructured with peak absorption at 373 nm, spanning to half maxima at 320 and 420 nm, and in good accord with the computed vertical excitation energies and absorption spectra obtained for its lowest energy conformers. The distribution of total kinetic energy released to products is ascertained through velocity map imaging of the O (¹D) products. About half of the available energy, deduced from the theoretically computed asymptotic energy, is accommodated as internal excitation of the 2-butenal fragment. A reduced impulsive model is introduced to interpret the photodissociation dynamics, which accounts for the geometric changes between 2-butenal oxide and the 2-butenal fragment, and vibrational activation of associated modes in the 2-butenal product. Application of the reduced impulsive model to the photodissociation of isomeric methyl vinyl ketone oxide reveals greater internal activation of the methyl vinyl ketone product arising from methyl internal rotation and rock, which is distinctly different from the dissociation dynamics of 2-butenal oxide or methacrolein oxide.

Interexcited State Photophysics I: Benchmarking Density Functionals for Computing Nonadiabatic Couplings and Internal Conversion Rate Constants

We present the first benchmarking study of nonadiabatic matrix coupling elements (NACMEs) calculated using different density functionals. Using the S₁ → S₀ transition in perylene solvated in toluene as a case study, we calculate the photophysical properties and corresponding rate constants for a variety of density functionals from each rung of Jacob's ladder. The singlet photoluminescence quantum yield (sPLQY) is taken as a measure of accuracy, measured experimentally here as 0.955. Important quantum chemical parameters such as geometries, absorption, emission, and adiabatic energies, NACMEs, Hessians, and transition dipole moments were calculated for each density functional basis set combination (data set) using density functional theory based multireference configuration interaction (DFT/MRCI) and compared to experiment where possible. We were able to derive simple relations between the TDDFT and DFT/MRCI photophysical properties; with semiempirical damping factors of ∼0.843 ± 0.017 and ∼0.954 ± 0.064 for TDDFT transition dipole moments and energies to DFT/MRCI level approximations, respectively. NACMEs were dominated by out-of-plane derivative components belonging to the center-most ring atoms with weaker contributions from perturbations along the transverse and longitudinal axes. Calculated theoretical spectra compared well to both experiment and literature, with fluorescence lifetimes between 7.1 and 12.5 ns, agreeing within a factor of 2 with experiment. Internal conversion (IC) rates were then calculated and were found to vary wildly between 10⁶-10¹⁶ s^-1 compared with an experimental rate of the order 10⁷ s^-1. Following further testing by mixing data sets, we found a strong dependence on the method used to obtain the Hessian. The 5 characterized data sets ranked in order of most promising are PBE0/def2-TZVP, ωB97XD/def2-TZVP, HCTH407/TZVP, PBE/TZVP, and PBE/def2-TZVP.

Decoherence and Its Role in Electronically Nonadiabatic Dynamics

Decoherence is the tendency of a time-evolved reduced density matrix for a subsystem to assume a form corresponding to a statistical ensemble of states rather than a coherent combination of pure-state wave functions. When a molecular process involves changes in the electronic state and the coordinates of the nuclei, as in ultraviolet or visible light photochemistry or electronically inelastic collisions, the reduced density matrix of the electronic subsystem suffers decoherence, due to its interaction with the nuclear subsystem. We present the background necessary to conceptualize this decoherence; in particular, we discuss the density matrix description of pure states and mixed states, and we discuss pointer states and decoherence time. We then discuss how decoherence is treated in the coherent switching with decay of mixing algorithm and the trajectory surface hopping method for semiclassical calculations of electronically nonadiabatic processes.

Branching mechanism of photoswitching in an Fe(II) polypyridyl complex explained by full singlet-triplet-quintet dynamics

It has long been known that irradiation with visible light converts Fe(II) polypyridines from their low-spin (singlet) to high-spin (quintet) state, yet mechanistic interpretation of the photorelaxation remains controversial. Herein, we simulate the full singlet-triplet-quintet dynamics of the [Fe(terpy)₂]²⁺ (terpy = 2,2':6',2"-terpyridine) complex in full dimension, in order to clarify the complex photodynamics. Importantly, we report a branching mechanism involving two sequential processes: a dominant ³MLCT→³MC(³T_2g)→³MC(³T_1g)→⁵MC, and a minor ³MLCT→³MC(³T_2g)→⁵MC component. (MLCT = metal-to-ligand charge transfer, MC = metal-centered). While the direct ³MLCT→⁵MC mechanism is considered as a relevant alternative, we show that it could only be operative, and thus lead to competing pathways, in the absence of ³MC states. The quintet state is populated on the sub-picosecond timescale involving non-exponential dynamics and coherent Fe-N breathing oscillations. The results are in agreement with the available time-resolved experimental data on Fe(II) polypyridines, and fully describe the photorelaxation dynamics.

Equation-of-Motion Methods for the Calculation of Femtosecond Time-Resolved 4-Wave-Mixing and N-Wave-Mixing Signals

Femtosecond nonlinear spectroscopy is the main tool for the time-resolved detection of photophysical and photochemical processes. Since most systems of chemical interest are rather complex, theoretical support is indispensable for the extraction of the intrinsic system dynamics from the detected spectroscopic responses. There exist two alternative theoretical formalisms for the calculation of spectroscopic signals, the nonlinear response-function (NRF) approach and the spectroscopic equation-of-motion (EOM) approach. In the NRF formalism, the system-field interaction is assumed to be sufficiently weak and is treated in lowest-order perturbation theory for each laser pulse interacting with the sample. The conceptual alternative to the NRF method is the extraction of the spectroscopic signals from the solutions of quantum mechanical, semiclassical, or quasiclassical EOMs which govern the time evolution of the material system interacting with the radiation field of the laser pulses. The NRF formalism and its applications to a broad range of material systems and spectroscopic signals have been comprehensively reviewed in the literature. This article provides a detailed review of the suite of EOM methods, including applications to 4-wave-mixing and N-wave-mixing signals detected with weak or strong fields. Under certain circumstances, the spectroscopic EOM methods may be more efficient than the NRF method for the computation of various nonlinear spectroscopic signals.

Transient vibration and product formation of photoexcited CS2 measured by time-resolved x-ray scattering

We have observed details of the internal motion and dissociation channels in photoexcited carbon disulfide (CS2) using time-resolved x-ray scattering (TRXS). Photoexcitation of gas-phase CS2 with a 200 nm laser pulse launches oscillatory bending and stretching motion, leading to dissociation of atomic sulfur in under a picosecond. During the first 300 fs following excitation, we observe significant changes in the vibrational frequency as well as some dissociation of the C-S bond, leading to atomic sulfur in the both 1D and 3P states. Beyond 1400 fs, the dissociation is consistent with primarily 3P atomic sulfur dissociation. This channel-resolved measurement of the dissociation time is based on our analysis of the time-windowed dissociation radial velocity distribution, which is measured using the temporal Fourier transform of the TRXS data aided by a Hough transform that extracts the slopes of linear features in an image. The relative strength of the two dissociation channels reflects both their branching ratio and differences in the spread of their dissociation times. Measuring the time-resolved dissociation radial velocity distribution aids the resolution of discrepancies between models for dissociation proposed by prior photoelectron spectroscopy work.

Spectroscopic Signature of Dynamical Instability of the Aqueous Complex in the Brown-Ring Nitrate Test

The chemistry of the brown-ring test has been investigated for nearly a century. Though recent studies have focused on solid state structure determination and measurement of spectra, mechanistic details and kinetics, the aspects of solution structure and dynamics remain unknown. We have studied structural fluctuations of the brown-ring complex in aqueous solution with ab-initio molecular dynamics simulations, from which we identified that the classically established pseudo-octahedral [Fe(H2 O)5 (NO)]2+ complex is present along with a square-pyramidal [Fe(H2 O)4 (NO)]2+ complex. Based on the inability in multi-reference calculations to reproduce the experimental UV-vis spectra in aqueous solution by inclusion of thermal fluctuations of the [Fe(H2 O)5 (NO)]2+ complex alone, we propose the existence of an equilibrium between pseudo-octahedral and square-pyramidal complexes. Despite challenges in constructing models reproducing the solid-state UV-vis spectrum, the advanced spectrum simulation tool motivates us to challenge the established picture of a sole pseudo-octahedral complex in solution.

Nonadiabatic Excited State Dynamics of Organic Chromophores: Take-Home Messages

Nonadiabatic excited state dynamics are important in a variety of processes. Theoretical and experimental developments have allowed for a great progress in this area, while combining the two is often necessary and the best approach to obtain insight into the photophysical behavior of molecules. In this Feature Article we use examples of our recent work combining time-resolved photoelectron spectroscopy with theoretical nonadiabatic dynamics to highlight important lessons we learned. We compare the nonadiabatic excited state dynamics of three different organic molecules with the aim of elucidating connections between structure and dynamics. Calculations and measurements are compared for uracil, 1,3-cyclooctadiene, and 1,3-cyclohexadiene. The comparison highlights the role of rigidity in influencing the dynamics and the difficulty of capturing the dynamics accurately with calculations.

Rapid Intersystem Crossing Induced by Ultrafast Excited-State Intramolecular Proton Transfer in 3-Mercaptopyran-4-one

Investigation into the photoinduced processes of 3-mercaptopyran-4-one is carried out using trajectory-based surface hopping simulations. Excitation into the near-degenerate higher singlet excited states reveals rapid internal conversion (IC) into S₁ on a sub-50 fs timescale. Excited-state intramolecular proton transfer (ESIPT) also takes place simultaneously with IC. We observe that following tautomerization, the molecule has multiple relaxation pathways. A channel exists for it to nonradiatively decay into the tautomer ground-state or undergo rapid intersystem crossing (ISC) into the close-lying higher triplet state, which ultimately decays into T₁. The simulations show that ISC is significantly enhanced after ESIPT, which is studied by tracking the changes in energy gaps and associated spin-orbit coupling elements.

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.

INAQS, a Generic Interface for Nonadiabatic QM/MM Dynamics: Design, Implementation, and Validation for GROMACS/Q-CHEM simulations

The accurate description of large molecular systems in complex environments remains an ongoing challenge for the field of computational chemistry. This problem is even more pronounced for photoinduced processes, as multiple excited electronic states and their corresponding nonadiabatic couplings must be taken into account. Multiscale approaches such as hybrid quantum mechanics/molecular mechanics (QM/MM) offer a balanced compromise between accuracy and computational burden. Here, we introduce an open-source software package (INAQS) for nonadiabatic QM/MM simulations that bridges the sampling capabilities of the GROMACS MD package and the excited-state infrastructure of the Q-CHEM electronic structure software. The interface is simple and can be adapted easily to other MD codes. The code supports a variety of different trajectory-based molecular dynamics, ranging from Born-Oppenheimer to surface hopping dynamics. To illustrate the power of this combination, we simulate electronic absorption spectra, free-energy surfaces along a reaction coordinate, and the excited-state dynamics of 1,3-cyclohexadiene in solution.

A Theoretical Perspective on the Actinic Photochemistry of 2-Hydroperoxypropanal

The photochemical reactions triggered by the sunlight absorption of transient volatile organic compounds in the troposphere are notoriously difficult to characterize experimentally due to the unstable and short-lived nature of these organic molecules. Some members of this family of compounds are likely to exhibit a rich photochemistry given the diversity of functional groups they can bear. Even more interesting is the photochemical fate of volatile organic compounds bearing more than one functional group that can absorb light—this is the case, for example, of α-hydroperoxycarbonyls, which are formed during the oxidation of isoprene. Experimental observables characterizing the photochemistry of these molecules like photoabsorption cross-sections or photolysis quantum yields are currently missing, and we propose here to leverage a recently developed computational protocol to predict in silico the photochemical fate of 2-hydroperoxypropanal (2-HPP) in the actinic region. We combine different levels of electronic structure methods—SCS-ADC(2) and XMS-CASPT2—with the nuclear ensemble approach and trajectory surface hopping to understand the mechanistic details of the possible nonradiative processes of 2-HPP. In particular, we predict the photoabsorption cross-section and the wavelength-dependent quantum yields for the observed photolytic pathways and combine them to determine in silico photolysis rate constants. The limitations of our protocol and possible future improvements are discussed.

Ultrafast Intersystem Crossing Dynamics of 6-Selenoguanine in Water

Rationalizing the photochemistry of nucleobases where an oxygen is replaced by a heavier atom is essential for applications that exploit near-unity triplet quantum yields. Herein, we report on the ultrafast excited-state deactivation mechanism of 6-selenoguanine (6SeGua) in water by combining nonadiabatic trajectory surface-hopping dynamics with an electrostatic embedding quantum mechanics/molecular mechanics (QM/MM) scheme. We find that the predominant relaxation mechanism after irradiation starts on the bright singlet S₂ state that converts internally to the dark S₁ state, from which the population is transferred to the triplet T₂ state via intersystem crossing and finally to the lowest T₁ state. This S₂ → S₁ → T₂ → T₁ deactivation pathway is similar to that observed for the lighter 6-thioguanine (6tGua) analogue, but counterintuitively, the T₁ lifetime of the heavier 6SeGua is shorter than that of 6tGua. This fact is explained by the smaller activation barrier to reach the T₁/S₀ crossing point and the larger spin-orbit couplings of 6SeGua compared to 6tGua. From the dynamical simulations, we also calculate transient absorption spectra (TAS), which provide two time constants (τ₁ = 131 fs and τ₂ = 191 fs) that are in excellent agreement with the experimentally reported value (τ_exp = 130 ± 50 fs) (Farrel et al. J. Am. Chem. Soc. 2018, 140, 11214). Intersystem crossing itself is calculated to occur with a time scale of 452 ± 38 fs, highlighting that the TAS is the result of a complex average of signals coming from different nonradiative processes and not intersystem crossing alone.

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.

A Look Inside the Black Box of Machine Learning Photodynamics Simulations

ConspectusPhotochemical reactions are of great importance in chemistry, biology, and materials science because they take advantage of a renewable energy source, mild reaction conditions, and high atom economy. Light absorption can excite molecules to a higher energy electronic state of the same spin multiplicity. The following nonadiabatic processes induce molecular transformations that afford exotic molecular architectures and high-energy-isomers that are inaccessible by thermal means. Computational simulations now complement time-resolved instrumentation to reveal ultrafast excited-state mechanistic information for photochemical reactions that is essential in disentangling elusive spectroscopic features, excited-state lifetimes, and excited-state mechanistic critical points. Nonadiabatic molecular dynamics (NAMD), powered by surface hopping techniques, is among the most widely applied techniques to model the photochemical reactions of medium-sized molecules. However, the computational efficiency is limited because of the requisite thousands of multiconfigurational quantum-chemical calculations multiplied by hundreds of trajectories. Machine learning (ML) has emerged as a revolutionary force in computational chemistry to predict the outcome of the resource-intensive multiconfigurational calculations on the fly. An ML potential trained with a substantial set of quantum-chemical calculations can predict the energies and forces with errors under chemical accuracy at a negligible cost. The integration of ML potentials in NAMD dramatically extends the maximum simulation time scale by ∼10 000-fold to the nanosecond regime.In this Account, we present a comprehensive demonstration of ML photodynamics simulations and summarize our most recent applications in resolving complex photochemical reactions. First, we address three fundamental components of ML techniques for photodynamics simulations: the quantum-chemical data set, the ML potential, and NAMD. Second, we describe best practices in building training data and our procedure toward training the ML photodynamics model with our recent literature contributions. We introduce a convenient training data generation scheme combining Wigner sampling and geometrical interpolation. It trains reliable and effective ML potentials suitable for subsequent active learning to detect undersampled data. We demonstrate how active learning automatically discovers new mechanistic pathways and reproduces experimental results. We point out that atomic permutation is an essential data augmentation approach to improve the learnability of distance-based molecular descriptors for highly symmetric molecules. Third, we demonstrate the utility of ML-photodynamics by showing the results of ML photodynamics simulations of (1) photo-torquoselective 4π disrotatory electrocyclic ring closing of norbornyl cyclohexadiene, which reveals a thermal conversion from experimentally unobserved intermediates to the reactant in 1 ns; (2) [2 + 2] photocycloaddition of substituted [3]-syn-ladderdienes in competition with 4π and 6π electrocyclic ring-opening reactions, uncovering substituent effects to explain the reported increased quantum yield of substituted cubane precursors; and (3) photochemical 4π disrotatory electrocyclic reactions of fluorobenzenes in nanoseconds with XMS-CASPT2-level training data. We expect this Account to broaden understanding of ML photodynamics and inspire future developments and applications to increasingly large molecules within complex environments on long time scales.

Resolving Femtosecond Solvent Reorganization Dynamics in an Iron Complex by Nonadiabatic Dynamics Simulations

The ultrafast dynamical response of solute–solvent interactions plays a key role in transition metal complexes, where charge transfer states are ubiquitous. Nonetheless, there exist very few excited-state simulations of transition metal complexes in solution. Here, we carry out a nonadiabatic dynamics study of the iron complex [Fe(CN)₄(bpy)]^2– (bpy = 2,2′-bipyridine) in explicit aqueous solution. Implicit solvation models were found inadequate for reproducing the strong solvatochromism in the absorption spectra. Instead, direct solute–solvent interactions, in the form of hydrogen bonds, are responsible for the large observed solvatochromic shift and the general dynamical behavior of the complex in water. The simulations reveal an overall intersystem crossing time scale of 0.21 ± 0.01 ps and a strong reliance of this process on nuclear motion. A charge transfer character analysis shows a branched decay mechanism from the initially excited singlet metal-to-ligand charge transfer (¹MLCT) states to triplet states of ³MLCT and metal-centered (³MC) character. We also find that solvent reorganization after excitation is ultrafast, on the order of 50 fs around the cyanides and slower around the bpy ligand. In contrast, the nuclear vibrational dynamics, in the form of Fe–ligand bond changes, takes place on slightly longer time scales. We demonstrate that the surprisingly fast solvent reorganizing should be observable in time-resolved X-ray solution scattering experiments, as simulated signals show strong contributions from the solute–solvent scattering cross term. Altogether, the simulations paint a comprehensive picture of the coupled and concurrent electronic, nuclear, and solvent dynamics and interactions in the first hundreds of femtoseconds after excitation.

The Chemistry of Mercury in the Stratosphere

Mercury, a global contaminant, enters the stratosphere through convective uplift, but its chemical cycling in the stratosphere is unknown. We report the first model of stratospheric mercury chemistry based on a novel photosensitized oxidation mechanism. We find two very distinct Hg chemical regimes in the stratosphere: in the upper stratosphere, above the ozone maximum concentration, Hg⁰ oxidation is initiated by photosensitized reactions, followed by second-step chlorine chemistry. In the lower stratosphere, ground-state Hg⁰ is oxidized by thermal reactions at much slower rates. This dichotomy arises due to the coincidence of the mercury absorption at 253.7 nm with the ozone Hartley band maximum at 254 nm. We also find that stratospheric Hg oxidation, controlled by chlorine and hydroxyl radicals, is much faster than previously assumed, but moderated by efficient photo-reduction of mercury compounds. Mercury lifetime shows a steep increase from hours in the upper-middle stratosphere to years in the lower stratosphere.