Army ants algorithm for rare event sampling of delocalized nonadiabatic transitions by trajectory surface hopping and the estimation of sampling errors by the bootstrap method

Ultrafast photochemistry and electron diffraction for cyclobutanone in the S2 state: Surface hopping with time-dependent density functional theory

We simulate the photodynamics of gas-phase cyclobutanone excited to the S2 state using fewest switches surface hopping (FSSH) dynamics powered by time-dependent density functional theory (TDDFT). We predict a total photoproduct yield of 8%, with a C3:C2 product ratio of 0 trajectories to 8 trajectories. One primary S2 → S1 conical intersection is identified involving the compression of an α-carbon-carbon-hydrogen bond angle. Excited state lifetimes computed with respect to electronic state populations were found to be 3.96 ps (S2 → S1) and 498 fs (S1 → S0). We also generate time-resolved difference pair distribution functions (ΔPDFs) from our TDDFT-FSSH dynamics results in order to generate direct comparisons with ultrafast electron diffraction experiment observables. Global and target analysis of time-resolved ΔPDFs produced a distinct set of lifetimes: (i) a 0.548 ps decay and (ii) a 1.69 ps decay, both resembling the S2 minimum, as well as (iii) a long decay that resembles the S1 minimum geometry and the fully separated C2 products. Finally, we contextualize our results by considering the impact of the most likely sources of significant errors.

Unraveling the effect of aromaticity for the dynamics of excited states of single benzene fluorophores

The photophysical properties of a series of recently synthesized single benzene fluorophores were investigated using ensemble density functional theory calculations. The energetic stability of the ground and excited state species were counterposed against the aromaticity index derived from local vibrational modes. It was found that the large Stokes shift of the fluorophores (up to ca. 5800 cm  - 1 ) originates from the effect of electron donating and electron withdrawing substituents rather than π -delocalization and related (anti-)aromaticity. On the basis of nonadiabatic molecular dynamics simulations, the absence of fluorescence from one of the regioisomers was explained by the occurrence of easily accessible S  1 /S  0 conical intersections below the vertical excitation energy level. It is demonstrated in the manuscript that the analysis of local mode force constants and the related aromaticity index represent a useful tool for the characterization of π -delocalization effects in π -conjugated compounds.

Ultrafast photochemistry and electron-diffraction spectra in n → (3s) Rydberg excited cyclobutanone resolved at the multireference perturbative level

We study the ultrafast time evolution of cyclobutanone excited to the singlet n → Rydberg state through non-adiabatic surface-hopping simulationsperformed at extended multi-state complete active space second-order perturbation (XMS-CASPT2) level of theory. These dynamics predict relaxation to the ground-state with a timescale of 822 ± 45 fs with minimal involvement of the triplets. The major relaxation path to the ground-state involves a three-state degeneracy region and leads to a variety of fragmented photoproducts. We simulate the resulting time-resolved electron-diffraction spectra, which track the relaxation of the excited state and the formation of various photoproducts in the ground state.

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.

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.

Surface hopping modeling of charge and energy transfer in active environments

An active environment is any atomic or molecular system changing a chromophore's nonadiabatic dynamics compared to the isolated molecule. The action of the environment on the chromophore occurs by changing the potential energy landscape and triggering new energy and charge flows unavailable in the vacuum. Surface hopping is a mixed quantum-classical approach whose extreme flexibility has made it the primary platform for implementing novel methodologies to investigate the nonadiabatic dynamics of a chromophore in active environments. This Perspective paper surveys the latest developments in the field, focusing on charge and energy transfer processes.

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.

A Plausible Mechanism of Uracil Photohydration Involves an Unusual Intermediate

It is well-known that photolysis of pyrimidine nucleobases, such as uracil, in an aqueous environment results in the formation of hydrate as one of the main products. Although several hypotheses regarding photohydration have been proposed in the past, e.g., the zwitterionic and "hot" ground-state mechanisms, its detailed mechanism remains elusive. Here, theoretical nonadiabatic simulations of the uracil photodynamics reveal the formation of a highly energetic but kinetically stable intermediate that features a half-chair puckered pyrimidine ring and a strongly twisted intracyclic double bond. The existence and the kinetic stability of the intermediate are confirmed by a variety of computational chemistry methods. According to the simulations, the unusual intermediate is mainly formed almost immediately (∼50-200 fs) upon photoabsorption and survives long enough to engage in a hydration reaction with a neighboring water. A plausible mechanism of uracil photohydration is proposed on the basis of the modeling of nucleophilic insertion of water into the twisted double bond of the intermediate.

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.

Extending the Time Scales of Nonadiabatic Molecular Dynamics via Machine Learning in the Time Domain

A novel methodology for direct modeling of long-time scale nonadiabatic dynamics in extended nanoscale and solid-state systems is developed. The presented approach enables forecasting the vibronic Hamiltonians as a direct function of time via machine-learning models trained directly in the time domain. The use of periodic and aperiodic functions that transform time into effective input modes of the artificial neural network is demonstrated to be essential for such an approach to work for both abstract and atomistic models. The best strategies and possible limitations pertaining to the new methodology are explored and discussed. An exemplary direct simulation of unprecedentedly long 20 picosecond trajectories is conducted for a divacancy-containing monolayer black phosphorus system, and the importance of conducting such extended simulations is demonstrated. New insights into the excited states photophysics in this system are presented, including the role of decoherence and model definition.

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

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

Surface hopping dynamics reveal ultrafast triplet generation promoted by S1-T2-T1 spin-vibronic coupling in 2-mercaptobenzothiazole

We investigate the T₁ formation upon populating the optically "bright" S₂ in 2-mercaptobenzothiazole to interpret the underlying relaxation pathways associated with the experimental decay constants reported by D. Koyama and A. J. Orr-Ewing, Phys. Chem. Chem. Phys., 2016, 18, 26224-26235. Energetics, electronic populations and geometries of various stationary points of low-lying electronic states are computed using the semi-classical ab initio surface hopping dynamics simulations. Estimated decay constants of S₂-S₁ internal conversion (IC) and S₁-T₂ intersystem crossing (ISC) are in excellent agreement with the experiment. The observed ultrafast ISC is analyzed based on the S₁-T₂-T₁ spin-vibronic coupling mechanism. In contrast to the previous assignment of 6 ps to the T₂-T₁ IC, our findings enable us to attribute this decay constant to the combined events of T₂-T₁ IC followed by relaxation of vibrationally hot T₁.

The Quest to Simulate Excited-State Dynamics of Transition Metal Complexes

This Perspective describes current computational efforts in the field of simulating photodynamics of transition metal complexes. We present the typical workflows and feature the strengths and limitations of the different contemporary approaches. From electronic structure methods suitable to describe transition metal complexes to approaches able to simulate their nuclear dynamics under the effect of light, we give particular attention to build a bridge between theory and experiment by critically discussing the different models commonly adopted in the interpretation of spectroscopic experiments and the simulation of particular observables. Thereby, we review all the studies of excited-state dynamics on transition metal complexes, both in gas phase and in solution from reduced to full dimensionality.

Ultrafast and long-time excited state kinetics of an NIR-emissive vanadium(iii) complex II. Elucidating triplet-to-singlet excited-state dynamics

We report the non-adiabatic dynamics of VIIICl3(ddpd), a complex based on the Earth-abundant first-row transition metal vanadium with a d2 electronic configuration which is able to emit phosphorescence in solution in the near-infrared spectral region. Trajectory surface-hopping dynamics based on linear vibronic coupling potentials obtained with CASSCF provide molecular-level insights into the intersystem crossing from triplet to singlet metal-centered states. While the majority of the singlet population undergoes back-intersystem crossing to the triplet manifold, 1-2% remains stable during the 10 ps simulation time, enabling the phosphorescence described in Dorn et al. Chem. Sci., 2021, DOI: 10.1039/D1SC02137K. Competing with intersystem crossing, two different relaxation channels via internal conversion through the triplet manifold occur. The nuclear motion that drives the dynamics through the different electronic states corresponds mainly to the increase of all metal-ligand bond distances as well as the decrease of the angles of trans-coordinated ligand atoms. Both motions lead to a decrease in the ligand-field splitting, which stabilizes the interconfigurational excited states populated during the dynamics. Analysis of the electronic character of the states reveals that increasing and stabilizing the singlet population, which in turn can result in enhanced phosphorescence, could be accomplished by further increasing the ligand-field strength.

Energy Dependence of Ensemble-Averaged Energy Transfer Moments and Its Effect on Competing Decomposition Reactions

We carried out a direct dynamics study on the internal-energy dependence of the ensemble-averaged energy transfer moments of the isobutyl radical in collisions with N₂ bath gas. We find a linear dependence of the downward moment ⟨ΔE_d⟩ and the root-mean-square moment ⟨ΔE2⟩ on the initial internal energy, but the upward moment ⟨ΔE_u⟩ is found to be independent of the molecule's internal energy. We improved the exponential-down relaxation model by including a linear dependence of ⟨ΔE_d⟩ on the initial energy, and we used the improved treatment in the 1D master equation for isobutyl radical decomposition reactions and for a model of competitive reactions with a larger difference in barrier heights. We calculated phenomenological rate constants and branching ratios from chemically significant eigenmodes of the master equation and showed that the energy dependence of ⟨ΔE_d⟩ has a greater influence on channels with higher barriers in competitive reactions. Rate constants and branching ratios from master equation calculations indicate that for a given temperature and pressure, there is a constant ⟨ΔE_d⟩ that can reproduce results obtained with an E-dependent ⟨ΔE_d⟩. But a constant ⟨ΔE_d⟩ cannot do this for all temperatures and pressures, with larger differences when the barriers for the competing channels differ more. We conclude that when the branching ratio of competitive reactions is sensitive to pressure, including the energy dependence of ⟨ΔE_d⟩ in master equation simulations can make a significant difference in the results.

Impact of the Dynamic Electron Correlation on the Unusually Long Excited-State Lifetime of Thymine

Non-radiative relaxation of the photoexcited thymine in the gas phase shows an unusually long excited-state lifetime, and, over the years, a number of models, i.e., S₁-trapping, S₂-trapping, and S₁&S₂-trapping, have been put forward to explain its mechanism. Here, we investigate this mechanism using non-adiabatic molecular dynamics (NAMD) simulations in connection with the recently developed mixed-reference spin-flip time-dependent density functional theory (MRSF-TDDFT) method. We show that the previously predicted S₂-trapping model was due to an artifact caused by an insufficient account of the dynamic electron correlation. The current work supports the S₁-trapping mechanism with two lifetimes, τ₁ = 30 ± 1 fs and τ₂ = 6.1 ± 0.035 ps, quantitatively consistent with the recent time-resolved experiments. Upon excitation to the S₂ (ππ*) state, thymine undergoes an ultrafast (ca. 30 fs) S₂→S₁ internal conversion and resides around the minimum on the S₁ (n_Oπ*) surface, slowly decaying to the ground state (ca. 6.1 ps). While the S₂→S₁ internal conversion is mediated by fast bond length alternation distortion, the subsequent S₁→S₀ occurs through several conical intersections, involving a slow puckering motion.

Simulation of UV absorption spectra and relaxation dynamics of uracil and uracil-water clusters

Despite many studies, the mechanisms of nonradiative relaxation of uracil in the gas phase and in aqueous solution are still not fully resolved. Here we combine theoretical UV absorption spectroscopy with nonadiabatic dynamics simulations to identify the photophysical mechanisms that can give rise to experimentally observed decay time constants. We first compute and theoretically assign the electronic spectra of uracil using the second-order algebraic-diagrammatic-construction (ADC(2)) method. The obtained electronic states, their energy differences and state-specific solvation effects are the prerequisites for understanding the photodynamics. We then use nonadiabatic trajectory-surface-hopping dynamics simulations to investigate the photoinduced dynamics of uracil and uracil-water clusters. In contrast to previous studies, we found that a single mechanism - the ethylenic twist around the C[double bond, length as m-dash]C bond - is responsible for the ultrafast component of the nonradiative decay, both in the gas phase and in solution. Very good agreement with the experimentally determined ultrashort decay time constants is obtained.

Signatures of Conical Intersection Dynamics in the Time-Resolved Photoelectron Spectrum of Furan: Theoretical Modeling with an Ensemble Density Functional Theory Method

The non-adiabatic dynamics of furan excited in the ππ* state (S2 in the Franck-Condon geometry) was studied using non-adiabatic molecular dynamics simulations in connection with an ensemble density functional method. The time-resolved photoelectron spectra were theoretically simulated in a wide range of electron binding energies that covered the valence as well as the core electrons. The dynamics of the decay (rise) of the photoelectron signal were compared with the excited-state population dynamics. It was observed that the photoelectron signal decay parameters at certain electron binding energies displayed a good correlation with the events occurring during the excited-state dynamics. Thus, the time profile of the photoelectron intensity of the K-shell electrons of oxygen (decay constant of 34 ± 3 fs) showed a reasonable correlation with the time of passage through conical intersections with the ground state (47 ± 2 fs). The ground-state recovery constant of the photoelectron signal (121 ± 30 fs) was in good agreement with the theoretically obtained excited-state lifetime (93 ± 9 fs), as well as with the experimentally estimated recovery time constant (ca. 110 fs). Hence, it is proposed to complement the traditional TRPES observations with the trXPS (or trNEXAFS) measurements to obtain more reliable estimates of the most mechanistically important events during the excited-state dynamics.

Early Relaxation Dynamics in the Photoswitchable Complex trans-[RuCl(NO)(py)4 ]2

The design of photoswitchable transition metal complexes with tailored properties is one of the most important challenges in chemistry. Studies explaining the underlying mechanisms are, however, scarce. Herein, the early relaxation dynamics towards NO photoisomerization in trans-[RuCl(NO)(py)4 ]2+ is elucidated by means of non-adiabatic dynamics, which provided time-resolved information and branching ratios. Three deactivation mechanisms (I, II, III) in the ratio 3:2:4 were identified. Pathways I and III involve ultrafast intersystem crossing and internal conversion, whereas pathway II involves only internal conversion.

SSAIMS-Stochastic-Selection Ab Initio Multiple Spawning for Efficient Nonadiabatic Molecular Dynamics

Ab initio multiple spawning provides a powerful and accurate way of describing the excited-state dynamics of molecular systems, whose strength resides in the proper description of coherence effects during nonadiabatic processes thanks to the coupling of trajectory basis functions. However, the simultaneous propagation of a large number of trajectory basis functions can be numerically inconvenient. We propose here an elegant and simple solution to this issue, which consists of (i) detecting uncoupled groups of coupled trajectory basis functions and (ii) selecting stochastically one of these groups to continue the ab initio multiple spawning dynamics. We show that this procedure can reproduce the results of full ab initio multiple spawning dynamics in cases where the uncoupled groups of trajectory basis functions stay uncoupled throughout the dynamics (which is often the case in high-dimensional problems). We present and discuss the aforementioned idea in detail and provide simple numerical applications on indole, ethylene, and protonated formaldimine, highlighting the potential of stochastic-selection ab initio multiple spawning.

Modeling nonadiabatic dynamics in condensed matter materials: some recent advances and applications

This review focuses on recent developments in the field of nonadiabatic molecular dynamics (NA-MD), with particular attention given to condensed-matter systems. NA-MD simulations for small molecular systems can be performed using high-level electronic structure (ES) calculations, methods accounting for the quantization of nuclear motion, and using fewer approximations in the dynamical methodology itself. Modeling condensed-matter systems imposes many limitations on various aspects of NA-MD computations, requiring approximations at various levels of theory-from the ES, to the ways in which the coupling of electrons and nuclei are accounted for. Nonetheless, the approximate treatment of NA-MD in condensed-phase materials has gained a spin lately in many applied studies. A number of advancements of the methodology and computational tools have been undertaken, including general-purpose methods, as well as those tailored to nanoscale and condensed matter systems. This review summarizes such methodological and software developments, puts them into the broader context of existing approaches, and highlights some of the challenges that remain to be solved.

Nonadiabatic Dynamics Simulation Predict Intersystem Crossing in Nitroaromatic Molecules on a Picosecond Time Scale

Previous time-resolved spectroscopic experiments and static quantum-chemical calculations attributed nitronaphthalene derivatives one of the fastest time scales for intersystem crossing within organic molecules, reaching the 100 fs mark. Nonadiabatic dynamics simulations on three nitronaphthalene derivatives challenge this view, showing that the experimentally observed ∼100 fs process corresponds to internal conversion in the singlet manifolds. Intersystem crossing, instead, takes place on a longer time scale of ∼1 ps. The dynamics simulations further reveal that the spin transitions occur via two distinct pathways with different contribution for the three systems, which are determined by electronic factors and the torsion of the nitro group. This study, therefore, indicates that the existence of sub-picosecond intersystem crossing in other nitroaromatic molecules should be questioned.

Energy transfer in intermolecular collisions of polycyclic aromatic hydrocarbons with bath gases He and Ar

Classical trajectory simulations of intermolecular collisions were performed for a series of polycyclic aromatic hydrocarbons interacting with the bath gases helium and argon for bath gas temperature from 300 to 2500 K. The phase-space average energy transferred per deactivating collision, ⟨∆E_down⟩, was obtained. The Buckingham pairwise intermolecular potentials were validated against high-level quantum chemistry calculations and used in the simulations. The reactive force-field was used to describe intramolecular potentials. The dependence of ⟨∆E_down⟩ on initial vibrational energy is discussed. A canonical sampling method was compared with a microcanonical sampling method for selecting initial vibrational energy at high bath gas temperatures. Uncertainties introduced by the initial angular momentum distribution were identified. The dependence of the collisional energy transfer parameters on the type of bath gas and the molecular structure of polycyclic aromatic hydrocarbons was examined.

Multistate hybrid time-dependent density functional theory with surface hopping accurately captures ultrafast thymine photodeactivation

We report an efficient analytical implementation of first-order nonadiabatic derivative couplings between arbitrary Born–Oppenheimer states in the hybrid time-dependent density functional theory (TDDFT) framework using atom-centered basis functions.

Design and photoisomerization dynamics of a new family of synthetic 2-stroke light driven molecular rotary motors

Synthetic 2-stroke light driven molecular rotary motors with ultrafast function and high quantum efficiency.

Finite-temperature Wigner phase-space sampling and temperature effects on the excited-state dynamics of 2-nitronaphthalene

The concept of finite temperature Wigner phase-space sampling allowing the population of vibrationally excited states is introduced and employed to study temperature effects on the absorption spectrum of 2-nitronaphtalene (2NN) and its relaxation dynamics.

Highly efficient surface hopping dynamics using a linear vibronic coupling model

We report an implementation of the linear vibronic coupling (LVC) model within the surface hopping dynamics approach and present utilities for parameterizing this model in a blackbox fashion. This results in an extremely efficient method to obtain qualitative and even semi-quantitative information about the photodynamical behavior of a molecule, and provides a new route toward benchmarking the results of surface hopping computations. The merits and applicability of the method are demonstrated in a number of applications. First, the method is applied to the SO2 molecule showing that it is possible to compute its absorption spectrum beyond the Condon approximation, and that all the main features and timescales of previous on-the-fly dynamics simulations of intersystem crossing are reproduced while reducing the computational effort by three orders of magnitude. The dynamics results are benchmarked against exact wavepacket propagations on the same LVC potentials and against a variation of the electronic structure level. Four additional test cases are presented to exemplify the broader applicability of the model. The photodynamics of the isomeric adenine and 2-aminopurine molecules are studied and it is shown that the LVC model correctly predicts ultrafast decay in the former and an extended excited-state lifetime in the latter. Futhermore, the method correctly predicts ultrafast intersystem crossing in the modified nucleobase 2-thiocytosine and its absence in 5-azacytosine while it fails to describe the ultrafast internal conversion to the ground state in the latter.

Nonadiabatic dynamics: The SHARC approach

We review the Surface Hopping including ARbitrary Couplings (SHARC) approach for excited-state nonadiabatic dynamics simulations. As a generalization of the popular surface hopping method, SHARC allows simulating the full-dimensional dynamics of molecules including any type of coupling terms beyond nonadiabatic couplings. Examples of these arbitrary couplings include spin-orbit couplings or dipole moment-laser field couplings, such that SHARC can describe ultrafast internal conversion, intersystem crossing, and radiative processes. The key step of the SHARC approach consists of a diagonalization of the Hamiltonian including these couplings, such that the nuclear dynamics is carried out on potential energy surfaces including the effects of the couplings-this is critical in any applications considering, for example, transition metal complexes or strong laser fields. We also give an overview over the new SHARC2.0 dynamics software package, released under the GNU General Public License, which implements the SHARC approach and several analysis tools. The review closes with a brief survey of applications where SHARC was employed to study the nonadiabatic dynamics of a wide range of molecular systems. This article is categorized under: Theoretical and Physical Chemistry > Reaction Dynamics and KineticsSoftware > Simulation MethodsSoftware > Quantum Chemistry.

Novel Molecular-Dynamics-Based Protocols for Phase Space Sampling in Complex Systems

The adequate exploration of the phase space of a chromophore is a fundamental necessity for the simulation of their optical and photophysical properties, taking into account the effects of vibrational motion and, most importantly, the coupling with a (non-homogeneous) molecular environment. A representative set of conformational snapshots around the Franck-Condon region is also required to perform non-adiabatic molecular dynamics, for instance in the framework of surface hopping. Indeed, in the latter case one needs to prepare a set of initial conditions providing a meaningful and complete statistical base for the subsequent trajectory propagation. In this contribution, we propose two new protocols for molecular dynamics-based phase space sampling, called "local temperature adjustment" and "individual QM/MM-based relaxation." These protocols are intended for situations in which the popular Wigner distribution sampling procedure is not applicable-as it is the case when anharmonic or nonlinear vibrations are present-and where regular molecular dynamics sampling might suffer from an inaccurate distribution of internal energy or from inaccurate force fields. The new protocols are applied to the case of phase space sampling of [Re(CO)3(Im)(Phen)]+ (im, imidazole; phen, phenanthroline) in aqueous solution, showing the advantages and limitations of regular Wigner and molecular dynamics sampling as well as the strengths of the new protocols.

Mechanism of Ultrafast Intersystem Crossing in 2-Nitronaphthalene

Nitronaphthalene derivatives efficiently populate their electronically excited triplet states upon photoexcitation through ultrafast intersystem crossing (ISC). Despite having been studied extensively by time-resolved spectroscopy, the reasons behind their ultrafast ISC remain unknown. Herein, we present the first ab initio nonadiabatic molecular dynamics study of a nitronaphthalene derivative, 2-nitronaphthalene, including singlet and triplet states. We find that there are two distinct ISC reaction pathways involving different electronic states at distinct nuclear configurations. The high ISC efficiency is explained by the very small electronic and nuclear alterations that the chromophore needs to undergo during the singlet-triplet transition in the dominating ISC pathway after initial dynamics in the singlet manifold. The insights gained in this work are expected to shed new light on the photochemistry of other nitro polycyclic aromatic hydrocarbons that exhibit ultrafast intersystem crossing.

Trajectory Surface-Hopping Dynamics Including Intersystem Crossing in [Ru(bpy)3]2

Surface-hopping dynamics coupled to linear response TDDFT and explicit nonadiabatic and spin-orbit couplings have been used to model the ultrafast intersystem crossing (ISC) dynamics in [Ru(bpy)₃]²⁺. Simulations using an ensemble of trajectories starting from the singlet metal-to-ligand charge transfer (¹MLCT) band show that the manifold of ³MLCT triplet states is first populated from high-lying singlet states within 26 ± 3 fs. ISC competes with an intricate internal conversion relaxation process within the singlet manifold to the lowest singlet state. Normal-mode analysis and principal component analysis, combined with further dynamical simulations where the nuclei are frozen, unequivocally demonstrate that it is not only the high density of states and the large spin-orbit couplings of the system that promote ISC. Instead, geometrical relaxation involving the nitrogen atoms is required to allow for state mixing and efficient triplet population transfer.

Insights into the deactivation of 5-bromouracil after ultraviolet excitation

5-Bromouracil is a nucleobase analogue that can replace thymine in DNA strands and acts as a strong radiosensitizer, with potential applications in molecular biology and cancer therapy. Here, the deactivation of 5-bromouracil after ultraviolet irradiation is investigated in the singlet and triplet manifold by accurate quantum chemistry calculations and non-adiabatic dynamics simulations. It is found that, after irradiation to the bright ππ* state, three main relaxation pathways are, in principle, possible: relaxation back to the ground state, intersystem crossing (ISC) and C-Br photodissociation. Based on accurate MS-CASPT2 optimizations, we propose that ground-state relaxation should be the predominant deactivation pathway in the gas phase. We then employ different electronic structure methods to assess their suitability to carry out excited-state dynamics simulations. MRCIS (multi-reference configuration interaction including single excitations) was used in surface hopping simulations to compute the ultrafast ISC dynamics, which mostly involves the 1nOπ* and 3ππ* states.This article is part of the themed issue 'Theoretical and computational studies of non-equilibrium and non-statistical dynamics in the gas phase, in the condensed phase and at interfaces'.

Ab initio molecular dynamics relaxation and intersystem crossing mechanisms of 5-azacytosine

Nonadiabatic SHARC dynamics simulations reveal the molecular deformations involved in the photodeactivation pathways of 5-azacytosine.

Intersystem Crossing Pathways in the Noncanonical Nucleobase 2-Thiouracil: A Time-Dependent Picture

The deactivation mechanism after ultraviolet irradiation of 2-thiouracil has been investigated using nonadiabatic dynamics simulations at the MS-CASPT2 level of theory. It is found that after excitation the S2 quickly relaxes to S1, and from there intersystem crossing takes place to both T2 and T1 with a time constant of 400 fs and a triplet yield above 80%, in very good agreement with recent femtosecond experiments in solution. Both indirect S1 → T2 → T1 and direct S1 → T1 pathways contribute to intersystem crossing, with the former being predominant. The results contribute to the understanding of how some noncanonical nucleobases respond to harmful ultraviolet light, which could be relevant for prospective photochemotherapeutic applications.

CO-dynamics in the active site of cytochrome c oxidase

The transfer of CO from heme a3 to the Cu(B) site in Cytochrome c oxidase (CcO) after photolysis is studied using molecular dynamics simulations using an explicitly reactive, parametrized potential energy surface based on density functional theory calculations. After photodissociation from the heme-Fe, the CO ligand rebinds to the Cu(B) site on the sub-picosecond time scale. Depending on the simulation protocol the characteristic time ranges from 260 fs to 380 fs which compares with an estimated 450 fs from experiment based on the analysis of the spectral changes as a function of time delay after the photodissociating pulse. Following photoexcitation ≈90% of the ligands are found to rebind to either the Cu(B) (major component, 85%) or the heme-Fe (minor component, 2%) whereas about 10% remain in an unbound state. The infrared spectra of unbound CO in the active site is broad and featureless and no appreciable shift relative to gas-phase CO is found, which is in contrast to the situation in myoglobin. These observations explain why experimentally, unbound CO in the binuclear site of CcO has not been found as yet.

Signaling factor interactions with polysaccharide aggregates of bacterial biofilms

Biofilms are surface-attached colonies of bacteria embedded in an extracellular polymeric substance (EPS). Inside the eukaryotic hosts, bacterial biofilms interact with the host cells through signaling factors (SFs). These signaling processes play important roles in the interaction between bacteria and host cells and the outcome of infections and symbiosis. However, how host immune factors diffuse through biofilms is not well understood. Here, we describe synergistic molecular dynamics and experimental approaches for studying the translocation of signaling factors through polysaccharide chain aggregates present in the extracellular matrix of bacterial biofilms. The effect of polysaccharide chain degradation on the energetics of SF-EPS interactions was examined by simulating an EPS consisting of various polysaccharide chain lengths. It is shown that the SF stabilization energy, defined as the average potential of mean force difference between the environments outside and within the matrix, increases linearly with decreasing chain length. This effect has been explained based on the changes in the polysaccharide configurations around the SF. Specifically, shorter chains are packed tightly around the SF, promoting favorable SF-EPS interactions, while longer chains are packed loosely resulting in screening of interactions with neighboring chains. We further investigated the translocation of SFs through the host cell membrane using molecular dynamics simulations. Further, simulations predict the existence of energy barriers greater than 1000 kJ mol(-1) associated with the translocation of the signaling factors necrosis factor-alpha (TNF-α) and granulocyte macrophage colony stimulating factor (GM-CSF) across the lipid bilayer. The agreement of computational and experimental findings motivates future computational studies using a more detailed description of the EPS aimed at understanding the role of the extracellular matrix on biofilm drug resistance.

Non-adiabatic dynamics close to conical intersections and the surface hopping perspective

Conical intersections play a major role in the current understanding of electronic de-excitation in polyatomic molecules, and thus in the description of photochemistry and photophysics of molecular systems. This article reviews aspects of the basic theory underlying the description of non-adiabatic transitions at conical intersections, with particular emphasis on the important case when the dynamics of the nuclei are treated classically. Within this classical nuclear motion framework, the main aspects of the surface hopping methodology in the conical intersection context are presented. The emerging picture from this treatment is that of electronic transitions around conical intersections dominated by the interplay of the nuclear velocity and the derivative non-adiabatic coupling vector field.