Surface Hopping Research Articles

Photofragmentation of cyclobutanone at 200nm: TDDFT vs CASSCF electron diffraction.

To simulate a 200nm photoexcitation in cyclobutanone to the n-3s Rydberg state, classical trajectories were excited from a Wigner distribution to the singlet state manifold based on excitation energies and oscillator strengths. Twelve singlet and 12 triplet states are treated using TD-B3LYP-D3/6-31+G** for the electronic structure, and the nuclei are propagated with the Tully surface hopping method. Using time-dependent density functional theory, we are able to predict the bond cleavage that takes place on the S1 surface as well as the ultrafast deactivation from the Rydberg n-3s state to the nπ*. After showing that triplet states and higher-lying singlet states do not play any crucial role during the early dynamics (i.e., the first 300fs), the SA(6)-CASSCF(8,11)/aug-cc-pVDZ method is used as an electronic structure and the outcome of the non-adiabatic dynamic simulations is recomputed. Gas-phase ultrafast electron diffraction spectra are computed for both electronic structure methods, showing significantly different results.

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.

Nonadiabatic Molecular Dynamics of Water Cluster Dissociation by Vacuum Ultraviolet Absorption or Electron Impact Excitation.

After five decades of investigation since the 1970s, the nature of photon-induced or electron-induced water dissociation is still largely studied only in the gas phase, with a notable absence of dynamics studies of water clusters and bulk water. We study the problem with density functional theory and the nonadiabatic fewest switches surface hopping technique considering both singlet and triplet excited states to study the dissociation of water clusters leading mainly to OH + H. For clusters of 40 water molecules, the mean dissociation time was found to be <10 fs, and the threshold energy was ∼6 eV. Dissociation is almost exclusively associated with the cluster surface due to the lower energy of surface water excited states relative to the bulk. Recombination plays a major role in vacuum ultraviolet dissociation. O + H2 is found as a minor product in the dissociation and is mostly produced in "roaming" trajectories.

Non-Hermitian molecular dynamics simulations of exciton-polaritons in lossy cavities.

The observation that materials can change their properties when placed inside or near an optical resonator has sparked a fervid interest in understanding the effects of strong light-matter coupling on molecular dynamics, and several approaches have been proposed to extend the methods of computational chemistry into this regime. Whereas the majority of these approaches have focused on modeling a single molecule coupled to a single cavity mode, changes to chemistry have so far only been observed experimentally when very many molecules are coupled collectively to multiple modes with short lifetimes. While atomistic simulations of many molecules coupled to multiple cavity modes have been performed with semi-classical molecular dynamics, an explicit description of cavity losses has so far been restricted to simulations in which only a very few molecular degrees of freedom were considered. Here, we have implemented an effective non-Hermitian Hamiltonian to explicitly treat cavity losses in large-scale semi-classical molecular dynamics simulations of organic polaritons and used it to perform both mean-field and surface hopping simulations of polariton relaxation, propagation, and energy transfer.

Exact-Factorization-Based Surface Hopping without Velocity Adjustment.

While surface hopping has emerged as a powerful method for simulating non-adiabatic dynamics in large molecules, the ad hoc nature of the necessary velocity adjustments and decoherence corrections in the algorithm somewhat reduces its reliability. Here we propose a new scheme that eliminates these aspects by combining the nuclear equation from the quantum-trajectory surface-hopping approach with the electronic equation derived from the exact-factorization approach. The resulting method, denoted QTSH-XF, yields a surface-hopping method on firmer ground than previous and is shown to successfully capture dynamics in Tully models and in a linear vibronic coupling model of the photoexcited uracil cation.

Dissociation Time, Quantum Yield, and Dynamic Reaction Pathways in the Thermolysis of trans-3,4-Dimethyl-1,2-dioxetane.

The thermolysis of trans-3,4-dimethyl-1,2-dioxetane is studied by trajectory surface hopping. The significant difference between long and short dissociation times is rationalized by frustrated dissociations and the time spent in triplet states. If the C-C bond breaks through an excited state channel, then the trajectory passes over a ridge of the potential energy surface of that state. The calculated triplet quantum yields match the experimental results. The dissociation half-times and quantum yields follow the same ascending order as per the product states, justifying the conjecture that the longer dissociation time leads to a higher quantum yield, proposed in the context of the methylation effect. The populations of the molecular Coulomb Hamiltonian and diagonal states reach equilibrium, but the triplet populations with different Sz components fluctuate indefinitely. Certain initial velocities, leading the trajectories to given product states, can be identified as the most characteristic features for sorting trajectories according to their product states.

Visible Light Induced Exciton Dynamics and trans-to-cis Isomerization in Azobenzene Aggregates: Insights from Surface Hopping/Semiempirical Configuration Interaction Molecular Dynamics Simulations.

Assemblies of photochromic molecules feature exciton states, which govern photochemical and photophysical processes in multichromophoric systems. Understanding the photoinduced dynamics of the assemblies requires nonadiabatic treatment involving multiple exciton states and numerous nuclear degrees of freedom, thus posing a challenge for simulations. In this work, we address this challenge for aggregates of azobenzene, a prototypical molecular switch, performing on-the-fly surface hopping calculations combined with semiempirical configuration interaction electronic structure and augmented with transition density matrix analysis to characterize exciton evolution. Specifically, we consider excitation of azobenzene tetramers in the nπ* absorption band located in the visible (blue) part of the electromagnetic spectrum, thus extending our recent work on dynamics after ππ* excitation corresponding to the ultraviolet region [Titov, J. Phys. Chem. C2023, 127, 13678-13688]. We find that the nπ* excitons, which are initially strongly localized by ground-state conformational disorder, undergo further (very strong) localization during short-time photodynamics. This excited-state localization process is extremely ultrafast, occurring within the first 10 fs of photodynamics. We observe virtually no exciton transfer of the localized excitons in the nπ* manifold. However, the transfer may occur via secondary pathways involving ππ* states or the ground state. Moreover, we find that the nπ* quantum yields of the trans-to-cis isomerization are reduced in the aggregated state.

Nonadiabatic dynamics with classical trajectories: The problem of an initial coherent superposition of electronic states.

Advances in coherent light sources and development of pump-probe techniques in recent decades have opened the way to study electronic motion in its natural time scale. When an ultrashort laser pulse interacts with a molecular target, a coherent superposition of electronic states is created and the triggered electron dynamics is coupled to the nuclear motion. A natural and computationally efficient choice to simulate this correlated dynamics is a trajectory-based method where the quantum-mechanical electronic evolution is coupled to a classical-like nuclear dynamics. These methods must approximate the initial correlated electron-nuclear state by associating an initial electronic wavefunction to each classical trajectory in the ensemble. Different possibilities exist that reproduce the initial populations of the exact molecular wavefunction when represented in a basis. We show that different choices yield different dynamics and explore the effect of this choice in Ehrenfest, surface hopping, and exact-factorization-based coupled-trajectory schemes in a one-dimensional two-electronic-state model system that can be solved numerically exactly. This work aims to clarify the problems that standard trajectory-based techniques might have when a coherent superposition of electronic states is created to initialize the dynamics, to discuss what properties and observables are affected by different choices of electronic initial conditions and to point out the importance of quantum-momentum-induced electronic transitions in coupled-trajectory schemes.

Investigating the photo-relaxation mechanism of 6-azauracil through ab initio nonadiabatic molecular dynamics simulations

On-the-fly ab initio molecular dynamics simulations were performed to study the decay dynamics of photo-excited 6-azauracil. The Zhu–Nakamura trajectory surface hopping method was used to determine the nonadiabatic transitions across different electronic states. The lifetime of the photoexcited S2 state was estimated to be 201 fs, which is in line with the experimentally measured lifetime (Hua et al., 2015). The results of the molecular dynamics simulations revealed that the internal conversion from S2 to S1 is facilitated by the destabilization of the ground state caused by molecular ring puckering.

Recovering Marcus Theory Rates and Beyond without the Need for Decoherence Corrections: The Mapping Approach to Surface Hopping.

It is well-known that fewest-switches surface hopping (FSSH) fails to correctly capture the quadratic scaling of rate constants with diabatic coupling in the weak-coupling limit, as expected from Fermi's golden rule and Marcus theory. To address this deficiency, the most widely used approach is to introduce a "decoherence correction", which removes the inconsistency between the wave function coefficients and the active state. Here we investigate the behavior of a new nonadiabatic trajectory method, called the mapping approach to surface hopping (MASH), on systems that exhibit an incoherent rate behavior. Unlike FSSH, MASH hops between active surfaces deterministically and can never have an inconsistency between the wave function coefficients and the active state. We show that MASH not only can describe rates for intermediate and strong diabatic coupling but also can accurately reproduce the results of Marcus theory in the golden-rule limit, without the need for a decoherence correction. MASH is therefore a significant improvement over FSSH in the simulation of nonadiabatic reactions.

Recommendations for Velocity Adjustment in Surface Hopping.

This study investigates velocity adjustment directions after hopping in surface hopping dynamics. Using fulvene and a protonated Schiff base (PSB4) as case studies, we investigate the population decay and reaction yields of different sets of dynamics with the velocity adjusted in either the nonadiabatic coupling, gradient difference, or momentum directions. For the latter, in addition to the conventional algorithm, we investigated the performance of a reduced kinetic energy reservoir approach recently proposed. Our evaluation also considered velocity adjustment in the directions of approximate nonadiabatic coupling vectors. While results for fulvene are susceptible to the adjustment approach, PSB4 is not. We correlated this dependence to the topography near the conical intersections. When nonadiabatic coupling vectors are unavailable, the gradient difference direction is the best adjustment option. If the gradient difference is also unavailable, a semiempirical vector direction or the momentum direction with a reduced kinetic energy reservoir becomes an excellent option to prevent an artificial excess of back hoppings. The precise velocity adjustment direction is less crucial for describing the nonadiabatic dynamics than the kinetic energy reservoir's size.

Which Electronic Structure Method to Choose in Trajectory Surface Hopping Dynamics Simulations? Azomethane as a Case Study.

Nonadiabatic dynamics simulations have become a standard approach to explore photochemical reactions. Such simulations require underlying potential energy surfaces and couplings between them, calculated at a chosen level of theory, yet this aspect is rarely assessed. Here, in combination with the popular trajectory surface hopping dynamics method, we use a high-accuracy XMS-CASPT2 electronic structure level as a benchmark for assessing the performances of various post-Hartree-Fock methods (namely, CIS, ADC(2), CC2, and CASSCF) and exchange-correlation functionals (PBE, PBE0, and CAM-B3LYP) in a TD-DFT/TDA context, using the isomerization around a double bond as test case. Different relaxation pathways are identified, and the ability of the different methods to reproduce their relative importance and time scale is discussed. The results show that multireference electronic structure methods should be preferred, when studying nonadiabatic decay between excited and ground states. If not affordable, TD-DFT with TDA and hybrid functionals and ADC(2) are efficient alternatives but overestimate the nonradiative decay yield and thus may miss deexcitation pathways.

Nonadiabatic Dynamics near Metal Surfaces with Periodic Drivings: A Generalized Surface Hopping in Floquet Representation.

With light-matter interaction extending into the strong regime, as well as rapid development of laser technology, systems subjecting to a time-periodic perturbation have attracted broad attention. Floquet theorem and Floquet time-independent Hamiltonian are powerful theoretical frameworks to investigate the systems subjected to time-periodic drivings. In this study, we extend the previous generalized surface hopping (SH) algorithm near a metal surface (J. Chem. Theory Comput. 2017, 13, 6, 2430-2439) to the Floquet space, and hence, we develop a generalized Floquet representation-based SH (FR-SH) algorithm. Here, we consider an open quantum system with fast drivings. We expect that the present algorithm will be useful for understanding the chemical processes of molecules under time-periodic driving near the metal surface.

Investigating the Photodynamics of trans-Azobenzene with Coupled Trajectories.

In this work, we present the first implementation of coupled-trajectory Tully surface hopping (CT-TSH) suitable for applications to molecular systems. We combine CT-TSH with the semiempirical floating occupation molecular orbital-configuration interaction electronic structure method to investigate the photoisomerization dynamics of trans-azobenzene. Our study shows that CT-TSH can capture correctly decoherence effects in this system, yielding consistent electronic and nuclear dynamics in agreement with (standard) decoherence-corrected TSH. Specifically, CT-TSH is derived from the exact factorization and the electronic coefficients' evolution is directly influenced by the coupling of trajectories, resulting in the improvement of internal consistency if compared to standard TSH.

SpaiNN: equivariant message passing for excited-state nonadiabatic molecular dynamics.

Excited-state molecular dynamics simulations are crucial for understanding processes like photosynthesis, vision, and radiation damage. However, the computational complexity of quantum chemical calculations restricts their scope. Machine learning offers a solution by delivering high-accuracy properties at lower computational costs. We present SpaiNN, an open-source Python software for ML-driven surface hopping nonadiabatic molecular dynamics simulations. SpaiNN combines the invariant and equivariant neural network architectures of SchNetPack with SHARC for surface hopping dynamics. Its modular design allows users to implement and adapt modules easily. We compare rotationally-invariant and equivariant representations in fitting potential energy surfaces of multiple electronic states and properties arising from the interaction of two electronic states. Simulations of the methyleneimmonium cation and various alkenes demonstrate the superior performance of equivariant SpaiNN models, improving accuracy, generalization, and efficiency in both training and inference.

Surface proton hopping conduction mechanism dominant polymer electrolytes created by self-assembly of bicontinuous cubic liquid crystals.

For the development of the next generation of fuel cells, it is essential to create an innovative design principle of polymer electrolytes that is beyond extension of the existing strategy. In the present study, we focused on the surface hopping proton conduction mechanism where an activation energy for proton conduction is greatly reduced by decreasing the distance between SO3- groups. Our gyroid nanostructured polymer film (Film-G), with a hydrophilic surface where the SO3- groups are aligned densely and precisely, shows high proton conductivity of the order of 10-2 S cm-1 when the water content is about 15 wt%. We reveal that the high proton conductivity of Film-G is attributed to the exhibition of an extremely-fast surface hopping conduction mechanism due to the reduced activation energy barrier along the gyroid minimal surface. This finding should introduce a game-changing novel opportunity in polymer electrolyte design.

Surface hopping simulations on charge photogeneration in conjugated polymers.

The mechanism of charge photogeneration in neat conjugated polymers has long been controversial and a unified explanation has not been achieved so far. In this paper, we use a surface hopping method to simulate the excited-state dynamics of a system composed of five π-stacked polymer chains. In this system, polaron pairs (PPs) with large electron-hole distance can be seen as free charges. The surface hopping method is based on the Pariser-Parr-Pople (PPP) Hamiltonian and the excited states of the system are calculated with configuration interaction singles (CIS) formalism. During the simulations, the yields of PPs and free charges are calculated using a statistical method. By comparison, it is found that impurity and excess energy have significant effects on the yields of PPs and free charges. Free charges are difficult to be generated in neat systems with small excess energy. Free charges come from direct dissociation of high-energy excitons.

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

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

Effect of Sb-Bi alloying on electron-hole recombination time of Cs2AgBiBr6 double perovskite.

The double perovskite material Cs2AgBiBr6, characterized by high stability, low toxicity, and excellent optoelectronic properties, has emerged as a promising alternative to lead-based halide perovskites in photovoltaic applications. However, its photovoltaic conversion efficiency after integration into solar cell devices is less than 3%, significantly lower than that of traditional perovskite solar cells. While alloying methods have been widely applied in the design of photovoltaic materials, their specific role in modulating the lifetime of photo-generated charge carriers in double-perovskite solar cells remains inadequately explored. In this study, through nonadiabatic molecular dynamics (NAMD) simulations, the excited-state dynamics properties of Cs2AgBiBr6 and alloyed Cs2AgSb0.375Bi0.625Br6 samples were compared. The results revealed that the introduction of Sb ions into the double perovskite structure induces lattice deformation upon heating to 300 K, leading to distortion of Bi-Br bonds and enhanced valence band delocalization. Using the decoherence-induced surface hopping method, the capture and recombination processes of charge carriers between different states were simulated. It was suggested that hole lifetime serves as the primary limiting factor for carrier lifetime in Cs2AgBiBr6, and replacing 0.375 proportion of Bi with Sb can decelerate the hole capture rate, extending carrier lifetime by 3-4 times. This study demonstrates that alloying offers a viable approach to optimizing the optoelectronic performance of the Cs2AgBiBr6 perovskite, thereby advancing the application of double perovskite materials in the field of photovoltaics.

Nonadiabatic molecular dynamics simulations shed light on the timescale of furylfulgide photocyclisation

Furylfulgide photocyclisation is one of the fastest known photoisomerisation reactions. In this study, I use surface hopping simulations aided by pattern recognition analysis to verify spectroscopic estimates of its timescale.