Trajectory Surface Hopping Simulations Research Articles

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

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

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

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

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 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.

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

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

A multiple time step algorithm for trajectory surface hopping simulations.

A multiple time step (MTS) algorithm for trajectory surface hopping molecular dynamics has been developed, implemented, and tested. The MTS scheme is an extension of the ab initio implementation for Born-Oppenheimer molecular dynamics presented in the work of Liberatore et al. [J. Chem. Theory Comput. 14, 2834 (2018)]. In particular, the MTS algorithm has been modified to enable the simulation of non-adiabatic processes with the trajectory surface hopping (TSH) method and Tully's fewest switches algorithm. The specificities of the implementation lie in the combination of Landau-Zener and Tully's transition probabilities during the inner MTS time steps. The new MTS-TSH method is applied successfully to the photorelaxation of protonated formaldimine, showing that the important characteristics of the process are recovered by the MTS algorithm. A computational speed-up between 1.5 and 3 has been obtained compared to standard TSH simulations, which is close to the ideal values that could be obtained with the computational settings considered.

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

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

Nonadiabatic dynamics with spin-flip vs linear-response time-dependent density functional theory: A case study for the protonated Schiffbase C5H6NH2.

Nonadiabatic trajectory surface hopping simulations are reported for trans-C5H6NH2 +, a model of the rhodopsinchromophore, using the augmented fewest-switches algorithm. Electronic structure calculations were performed using time-dependent density functional theory (TDDFT) in both its conventional linear-response (LR) and its spin-flip (SF) formulations. In the SF-TDDFT case, spin contamination in the low-lying singlet states is removed by projecting out the lowest triplet component during iterative solution of the TDDFT eigenvalue problem. The results show that SF-TDDFT qualitatively describes the photoisomerization of trans-C5H6NH2 +, with favorable comparison to previous studies using multireference electronic structure methods. In contrast, conventional LR-TDDFT affords qualitatively different photodynamics due to an incorrect excited-state potential surface near the Franck-Condon region. In addition, the photochemistry (involving pre-twisting of the central double bond) appears to be different for SF- and LR-TDDFT, which may be a consequence of different conical intersection topographies afforded by these two methods. The present results contrast with previous surface-hopping studies suggesting that the LR-TDDFT method's incorrect topology around S1/S0 conical intersections is immaterial to the photodynamics.

Time Resolved Photoelectron Spectroscopy as a Test of Electronic Structure and Nonadiabatic Dynamics.

We compare different levels of theory for simulating excited state molecular dynamics and use time-resolved photoelectron spectroscopy measurements to benchmark the theory. We perform trajectory surface hopping simulations for uracil excited to the first bright state (ππ*) using three different levels of theory (CASSCF, MRCIS, and XMS-CASPT2) in order to understand the role of dynamical correlation in determining the excited state dynamics, with a focus on the coupling between different electronic states and internal conversion back to the ground state. These dynamics calculations are used to simulate the time-resolved photoelectron spectra. The comparison of the calculated and measured spectra allows us to draw conclusions regarding the relative insights and quantitative accuracy of the calculations at the three different levels of theory, demonstrating that detailed quantitative comparisons of time-resolved photoelectron spectra can be used to benchmark methodology.

Surface hopping with cumulative probabilities: Even sampling and improved reproducibility.

Trajectory surface hopping simulations of photochemical reactions are a powerful and increasingly important tool to unravel complex photochemical reactivity. Within surface hopping, electronic transitions are mimicked by stochastic hops between electronic potential surfaces. Thus, statistical sampling is an inescapable component of trajectory-surface-hopping-based nonadiabatic molecular dynamics methods. However, the standard sampling strategy inhibits computational reproducibility, limits predictability, and results in trajectories that are overly sensitive to numerical parameters like the time step. We describe an equivalent approach to sampling electronic transitions within fewest switches surface hopping (FSSH) in which hops are decided in terms of the cumulative probability (FSSH-c) as opposed to the usual prescription, which is in terms of the instantaneous conditional probability (FSSH-i). FSSH-c is statistically equivalent to FSSH-i and can be implemented from trivial modifications to an existing surface hopping algorithm but has several key advantages: (i) a single trajectory is fully specified by just a handful of random numbers, (ii) all hopping decisions are independent of the time step such that the convergence behavior of individual trajectories can be explored, and (iii) alternative integral-based sampling schemes are enabled. In addition, we show that the conventional hopping probability overestimates the hopping rate and propose a simple scaling correction as a fix. Finally, we demonstrate these advantages numerically on model scattering problems.

Intersystem Crossing and Triplet Dynamics in an Iron(II) N-Heterocyclic Carbene Photosensitizer.

The electronic excited states of the iron(II) complex [FeII(tpy)(pyz-NHC)]2+ [tpy = 2,2′:6′,2″-terpyridine; pyz-NHC = 1,1′-bis(2,6-diisopropylphenyl)pyrazinyldiimidazolium-2,2′-diylidene] and their relaxation pathways have been theoretically investigated. To this purpose, trajectory surface-hopping simulations within a linear vibronic coupling model including a 244-dimensional potential energy surface (PES) with 20 singlet and 20 triplet coupled states have been used. The simulations show that, after excitation to the lowest-energy absorption band of predominant metal-to-ligand charge-transfer character involving the tpy ligand, almost 80% of the population undergoes intersystem crossing to the triplet manifold in about 50 fs, while the remaining 20% decays through internal conversion to the electronic ground state in about 300 fs. The population transferred to the triplet states is found to deactivate into two different regions of the PESs, one where the static dipole moment is small and shows increased metal-centered character and another with a large static dipole moment, where the electron density is transferred from the tpy to pyz-NHC ligand. Coherent oscillations of 400 fs are observed between these two sets of triplet populations, until the mixture equilibrates to a ratio of 60:40. Finally, the importance of selecting suitable normal modes is highlighted—a choice that can be far from straightforward in transition-metal complexes with hundreds of degrees of freedom.

Quantum mechanical/molecular mechanical trajectory surface hopping molecular dynamics simulation by spin-flip time-dependent density functional theory.

This paper presents the nonadiabatic molecular dynamics simulation in the solution phase using the spin-flip time-dependent density functional theory (SF-TDDFT). Despite the single-reference level of theory, the SF-TDDFT method can generate the correct topology of S0/S1 crossing points, thus providing a natural S1 → S0 nonadiabatic transition. We extend the gas-phase trajectory surface hopping simulation with the SF-TDDFT [N. Minezawa and T. Nakajima, J. Chem. Phys. 150, 204120 (2019)] to the hybrid quantum mechanical/molecular mechanics (QM/MM) scheme. To this end, we modify the code to evaluate the electrostatic interaction between the QM and MM atoms and to extract the classical MM energy and forces from the MM program package. We apply the proposed method to the photoisomerization reaction of aqueous E-azomethane and anionic green fluorescent protein chromophore in water and compare the results with those of the previous simulation studies based on the multireference methods.

The excited-state relaxation mechanism of potential UVA-activated phototherapeutic molecules: trajectory surface hopping simulations of both 4-thiothymine and 2,4-dithiothymine.

Recent experimental investigations of the photochemical properties of a series of sulfur-substituted pyrimidine derivatives provide insights into the phototherapeutic potential of these nucleobase variants. Herein we elucidate the triplet formation mechanism of two prospective UVA-activated phototherapeutic molecules, 4-thiothymine and 2,4-dithiothymine, upon photo-excitation by applying the trajectory surface hopping dynamics at the LR-TDDFT level. Our simulations reasonably reproduce the experimental time constants and demonstrate the preferred triplet formation pathway which starts from the S1(nSπ*) state for both molecules. It is found that deactivation of the first bright state to the S1(nSπ*) state proceeds through a mechanism involving elongation of the C5-C6 and C4-S8 bond-lengths and C2-pyramidalization in 4-thiothymine and involving elongation of the C5-C6 and C2-S7 bond-lengths in 2,4-dithiothymine. The intersystem crossing of 2,4-dithiothymine occurs either at geometries characterized by elongated C5-C6 and C2-S7 bond-lengths or at geometries showing elongated C5-C6 and C4-S8 bond-lengths as seen in 4-thiothymine. The solvents are found to affect the S2 state decay of 4-thiothymine, leading to a competing pathway between S2→ S1 and S2→ T3. This study provides a molecular-level understanding of the underlying excited-state relaxation of the two UVA-activated thiopyrimidines, which may be linked to their potential applications in pharmacological science and also prove helpful for designing more effective phototherapeutic agents.

Functional and Basis Set Dependence for Time-Dependent Density Functional Theory Trajectory Surface Hopping Molecular Dynamics: Cis-Azobenzene Photoisomerization.

Within three functionals (TD-B3LYP, TD-BHandHLYP, and TD-CAM-B3LYP) in combination with four basis sets (3-21g, 6-31g, 6-31g(d), and cc-pvdz), global switching (GS) trajectory surface hopping molecular dynamics has been performed for cis-to-trans azobenzene photoisomerization up to the S1 (nπ*) excitation. Although all the combinations show artificial double-cone structure of conical intersection between ground and first excited states, simulated quantum yields and lifetimes are in good agreement with one another; 0.6 (±5%) and 40.5 fs (±10%) by TD-B3LYP, 0.5 (±10%) and 35.5 fs (±4%) by TD-BHandHLYP, and 0.44 (±9%) and 35.2 fs (±10%) by TD-CAM-B3LYP. By analyzing distributions of excited-state population decays, hopping spots, and typical trajectories with performance of 12 functional/basis set combinations, it has been concluded that functional dependence for given basis set is slightly more sensitive than basis set dependence for given functional. The present GS on-the-fly time-dependent density functional theory (TDDFT) trajectory surface hopping simulation can provide practical benchmark guidelines for conical intersection driven excited-state molecular dynamics simulation involving in large complex system within ordinary TDDFT framework. © 2019 Wiley Periodicals, Inc.

Analysis of trajectory similarity and configuration similarity in on-the-fly surface-hopping simulation on multi-channel nonadiabatic photoisomerization dynamics.

We propose an "automatic" approach to analyze the results of the on-the-fly trajectory surface hopping simulation on the multi-channel nonadiabatic photoisomerization dynamics by considering the trajectory similarity and the configuration similarity. We choose a representative system phytochromobilin (P B) chromophore model to illustrate the analysis protocol. After a large number of trajectories are obtained, it is possible to define the similarity of different trajectories by the Fréchet distance and to employ the trajectory clustering analysis to divide all trajectories into several clusters. Each cluster in principle represents a photoinduced isomerization reaction channel. This idea provides an effective approach to understand the branching ratio of the multi-channel photoisomerization dynamics. For each cluster, the dimensionality reduction is employed to understand the configuration similarity in the trajectory propagation, which provides the understanding of the major geometry evolution features in each reaction channel. The results show that this analysis protocol not only assigns all trajectories into different photoisomerization reaction channels but also extracts the major molecular motion without the requirement of the pre-known knowledge of the active photoisomerization site. As a side product of this analysis tool, it is also easy to find the so-called "typical" or "representative" trajectory for each reaction channel.

Probing the π → π* photoisomerization mechanism of trans-azobenzene by multi-state ab initio on-the-fly trajectory dynamics simulations

Global nonadiabatic switching on-the-fly trajectory surface hopping simulations at the 5SA-CASSCF(6,6)/6-31G quantum level have been employed to probe the photoisomerization mechanism of trans-azobenzene upon ππ* excitation within four coupled singlet low-lying electronic states (S0, S1, S2, and S3). We have performed 586 sampling trajectories (331 starting from S2 and 255 from S3), and we found about half of the sampling trajectories staying on S1 or S2 states as resonances and the other half of them ending on the ground S0 state as active trajectories. The present simulation has demonstrated that there are six distinct photoisomerization pathways which can be summarized as three categories; one is the newly opened inversion-inversion nonreactive isomerization pathway accounting for 40% (34%) of active trajectories at a time constant of 80 fs (320 fs), the other is the inversion-torsion reactive and nonreactive isomerization pathways accounting for 40% (20%) of active trajectories at a time constant of 880 fs (1700 fs), and the third is the torsion-torsion reactive and nonreactive isomerization pathways accounting for 20% (46%) of active trajectories at a time constant of 780 fs (1000 fs) upon S2 (S3) ππ* excitation. The simulated total reactive quantum yield for trans-azobenzene photoisomerization upon S2 (S3) ππ* excitation is about 0.11 (0.13) which is in good agreement with recent experimental results of 0.09-0.20. Furthermore, the newly opened inversion-inversion nonreactive isomerization pathway from the present simulation agrees well with cascade experimental measurements of the Sn → S1 → S0 relaxation mechanism in both branching ratio and time constant.

Ultrafast intersystem crossing for nitrophenols: ab initio nonadiabatic molecular dynamics simulation.

Ultrafast intersystem crossing mechanisms for two p- and m-nitrophenol groups (PNP and MNP) have been investigated using ab initio nonadiabatic molecular dynamics simulations at the 6SA-CASSCF level of theory. Trajectory surface hopping simulation has been performed within an intersystem crossing network constructed from two low-lying singlets (S0 and S1) and two low-lying triplets (T1 and T2). It is found that the dominant relaxation S1 → T2 pathway accounts for 65.4% (85.0%) of the quantum yield with a time constant of 13.4 fs (22 fs) and the S1 → T2 → S0 pathway accounts for 33.1% (13.5%) with a time constant of 275 fs (375 fs) for PNP (MNP). In comparison with the previously studied excited-state proton transfer process for ONP, the dominant relaxation S1 → T2 → T1 pathway accounts for 49.3% with a time constant of 40 fs and the S1 → T2 → T1 → S0 pathway accounts for 47.5% with a time constant of 300 fs. The relaxation mechanisms and electronic structures of the intersystem crossings are in close relation with the relative motion between the torsion motions of the nitro-group and the hydroxyl group. The present simulation provides new physical insight for understanding ultrafast photochemical intersystem crossing dynamics.

Spin crossover dynamics studies on the thermally activated molecular oxygen binding mechanism on a model copper complex.

The theoretical description of the primary dioxygen (O2) binding and activation step in many copper or iron enzymes, suffers from the intrinsically electronic non-adiabaticity of the spin flip events of the triplet dioxygen molecule (3O2), mediated by spin-orbit couplings. In this work, we presented the early-stage ultrafast spin flip dynamics of O2 binding for a simplified monocopper complex, involving the coupled singlet and triplet electronic states. The on-the-fly trajectory surface hopping (TSH) simulations have identified the dynamical effects that may influence the mode of O2 coordination (end-on vs. side-on), and the electronic structures can be viewed as complexes of molecular O2 with Cu(i) or as Cu(ii)-superoxide compounds. In addition, significant spin flip events are obversed within the sub-picosecond regime. We hope this work may provide complimentary insights on the traditional interpretation of O2 binding on copper complexes and subsequent catalytic reaction mechanisms.

Intersystem crossing-branched excited-state intramolecular proton transfer for o-nitrophenol: An ab initio on-the-fly nonadiabatic molecular dynamic simulation.

The 6SA-CASSCF(10, 10)/6-31G (d, p) quantum chemistry method has been applied to perform on-the-fly trajectory surface hopping simulation with global switching algorithm and to explore excited-state intramolecular proton transfer reactions for the o-nitrophenol molecule within low-lying electronic singlet states (S0 and S1) and triplet states (T1 and T2). The decisive photoisomerization mechanisms of o-nitrophenol upon S1 excitation are found by three intersystem crossings and one conical intersection between two triplet states, in which T1 state plays an essential role. The present simulation shows branch ratios and timescales of three key processes via T1 state, non-hydrogen transfer with ratio 48% and timescale 300 fs, the tunneling hydrogen transfer with ratios 36% and timescale 10 ps, and the direct hydrogen transfer with ratios 13% and timescale 40 fs. The present simulated timescales might be close to low limit of the recent experiment results.

Adaptive time steps in trajectory surface hopping simulations

Trajectory surface hopping (TSH) simulations are often performed in combination with active-space multi-reference configuration interaction (MRCI) treatments. Technical problems may arise in such simulations if active and inactive orbitals strongly mix and switch in some particular regions. We propose to use adaptive time steps when such regions are encountered in TSH simulations. For this purpose, we present a computational protocol that is easy to implement and increases the computational effort only in the critical regions. We test this procedure through TSH simulations of a GFP chromophore model (OHBI) and a light-driven rotary molecular motor (F-NAIBP) on semiempirical MRCI potential energy surfaces, by comparing the results from simulations with adaptive time steps to analogous ones with constant time steps. For both test molecules, the number of successful trajectories without technical failures rises significantly, from 53% to 95% for OHBI and from 25% to 96% for F-NAIBP. The computed excited-state lifetime remains essentially the same for OHBI and increases somewhat for F-NAIBP, and there is almost no change in the computed quantum efficiency for internal rotation in F-NAIBP. We recommend the general use of adaptive time steps in TSH simulations with active-space CI methods because this will help to avoid technical problems, increase the overall efficiency and robustness of the simulations, and allow for a more complete sampling.