Surface Hopping Research Articles

Toward a Correct Description of Initial Electronic Coherence in Nonadiabatic Dynamics Simulations.

The recent improvement in experimental capabilities for interrogating and controlling molecular systems with ultrafast coherent light sources calls for the development of theoretical approaches that can accurately and efficiently treat electronic coherence. However, the most popular and practical nonadiabatic molecular dynamics techniques, Tully's fewest-switches surface hopping and Ehrenfest mean-field dynamics, are unable to describe the dynamics proceeding from an initial electronic coherence. While such issues are not encountered with the analogous coupled-trajectory algorithms or numerically exact quantum dynamics methods, applying such techniques necessarily comes with a higher computational cost. Here we show that a correct description of initial electronic coherence can indeed be achieved using independent-trajectory methods derived from the semiclassical mapping formalism. The key is the introduction of an initial sampling over the electronic phase space and a means of incorporating phase interference between trajectories, both of which are naturally achieved when working within the semiclassical mapping framework.

Non-adiabatic coupling matrix elements in a magnetic field: Geometric gauge dependence and Berry phase.

Non-adiabatic coupling matrix elements (NACMEs) are important in quantum chemistry, particularly for molecular dynamics methods such as surface hopping. However, NACMEs are gauge dependent. This presents a difficulty for their calculation in general, where there are no restrictions on the gauge function except that it be differentiable. These cases are relevant for complex-valued electronic wave functions, such as those that arise in the presence of a magnetic field or spin-orbit coupling. In addition, the Berry curvature and Berry force play an important role in molecular dynamics in a magnetic field and are also relevant in the context of spin-orbit coupling. For methods such as surface hopping, excited-state Berry curvatures will also be of interest. With this in mind, we have developed a scheme for the calculation of continuous, differentiable NACMEs as a function of the molecular geometry for complex-valued wave functions. We demonstrate the efficacy of the method using the H2 molecule at the full configuration-interaction (FCI) level of theory. In addition, ground- and excited-state Berry curvatures are computed for the first time using FCI theory. Finally, Berry phases are computed directly in terms of diagonal NACMEs.

Nonadiabatic Excited-State Molecular Dynamics with an Explicit Solvent: NEXMD-SANDER Implementation.

In this article, the nonadiabatic excited-state Molecular dynamics (NEXMD) package is linked with the SANDER package, provided by AMBERTOOLS. The combination of these software packages enables the simulation of photoinduced dynamics of large multichromophoric conjugated molecules involving several coupled electronic excited states embedded in an explicit solvent by using the quantum/mechanics/molecular mechanics (QM/MM) methodology. The fewest switches surface hopping algorithm, as implemented in NEXMD, is used to account for quantum transitions among the adiabatic excited-state simulations of the photoexcitation and subsequent nonadiabatic electronic transitions, and vibrational energy relaxation of a substituted polyphenylenevinylene oligomer (PPV3-NO2) in vacuum and methanol as an explicit solvent has been used as a test case. The impact of including specific solvent molecules in the QM region is also analyzed. Our NEXMD-SANDER QM/MM implementation provides a useful computational tool to simulate qualitatively solvent-dependent effects, like electron transfer, stabilization of charge-separated excited states, and the role of solvent reorganization in the molecular optical properties, observed in solution-based spectroscopic experiments.

Design of Functional Gyroid Minimal Surfaces Transporting Proton Based Solely on Surface Hopping Conduction Mechanism.

Surface proton hopping conduction (SPHC) mechanisms is an important proton conduction mechanism in conventional polymer electrolytes, along with the Grotthuss and vehicle mechanisms. Due to the small diffusion coefficient of protons in the SPHC mechanism, few studies have focused on the SPHC mechanism. Recently, it has been found that a dense alignment of SO3 - groups significantly lowers the activation energy in the SPHC mechanism, enabling fast proton conduction. In this study, a series of polymerizable amphiphilic-zwitterions is prepared, forming bicontinuous cubic liquid-crystalline assemblies with gyroid symmetry in the presence of suitable amounts of bis(trifluoromethanesulfonyl) imide (HTf2N) and water. In situ polymerization of these compounds yields gyroid-nanostructured polymer films, as confirmed by synchrotron small-angle X-ray scattering experiments. The high proton conductivity of the films on the order of 10-2 S cm-1 at 40 °C and relative humidity of 90% is based solely on the SPHC mechanism.

Effect of load-resisting force on photoisomerization mechanism of a single second generation light-driven molecular rotary motor.

A pivotal aspect of molecular motors is their capability to generate load capacity from a single entity. However, few studies have directly characterized the load-resisting force of a single light-driven molecular motor. This research provides a simulation analysis of the load-resisting force for a highly efficient, second-generation molecular motor developed by Feringa et al. We investigate the M-to-P photoinduced nonadiabatic molecular dynamics of 9-(2,3-dihydro-2-methyl-1H-benz[e]inden-1-ylidene)-9H-fluorene utilizing Tully's surface hopping method at the semi-empirical OM2/MRCI level under varying load-resisting forces. The findings indicate that the quantum yield remains relatively stable under forces up to 0.003a.u., with the photoisomerization mechanism functioning typically. Beyond this threshold, the quantum yield declines, and an alternative photoisomerization mechanism emerges, characterized by an inversion of the central double bond's twisting direction. The photoisomerization process stalls when the force attains a critical value of 0.012a.u. Moreover, the average lifetime of the excited state oscillates around that of the unperturbed system. The quantum yield and mean lifetime of the S1 excited state in the absence of external force are recorded at 0.54 and 877.9fs, respectively. In addition, we analyze a time-dependent fluorescence radiation spectrum, confirming the presence of a dark state and significant vibrations, as previously observed experimentally by Conyard et al.

Tracking the Electron Density Changes in Excited States: A Computational Study of Pyrazine.

The development of X-ray free-electron lasers has enabled ultrafast X-ray diffraction (XRD) experiments, which are capable of resolving electronic and vibrational transitions and structural changes in molecules or capturing molecular movies. While time-resolved XRD has attracted more attention, the extraction of information from signals is challenging and requires theoretical support. In this work, we combined X-ray scattering theory and a trajectory surface hopping approach to resolve dynamical changes in the electronic structure of photoexcited molecules by studying the time evolution of electron density changes between electronic excited states and ground state. Using the pyrazine molecule as an example, we show that key features of reaction pathways can be identified, enabling the capture of structural changes associated with electronic transitions for a photoexcited molecule.

Including Photoexcitation Explicitly in Trajectory-Based Nonadiabatic Dynamics at No Cost.

Over the last decades, theoretical photochemistry has produced multiple techniques to simulate the nonadiabatic dynamics of molecules. Surprisingly, much less effort has been devoted to adequately describing the first step of a photochemical or photophysical process: photoexcitation. Here, we propose a formalism to include the effect of a laser pulse in trajectory-based nonadiabatic dynamics at the level of the initial conditions, with no additional cost. The promoted density approach (PDA) decouples the excitation from the nonadiabatic dynamics by defining a new set of initial conditions, which include an excitation time. PDA with surface hopping leads to nonadiabatic dynamics simulations in excellent agreement with quantum dynamics using an explicit laser pulse and highlights the strong impact of a laser pulse on the resulting photodynamics and the limits of the (sudden) vertical excitation. Combining PDA with trajectory-based nonadiabatic methods is possible for any arbitrary-sized molecules using a code provided in this work.

Charge transport in organic semiconductors from the mapping approach to surface hopping.

We describe how to simulate charge diffusion in organic semiconductors using a recently introduced mixed quantum-classical method, the mapping approach to surface hopping. In contrast to standard fewest-switches surface hopping, this method propagates the classical degrees of freedom deterministically on the most populated adiabatic electronic state. This correctly preserves the equilibrium distribution of a quantum charge coupled to classical phonons, allowing one to time-average along trajectories to improve the statistical convergence of the calculation. We illustrate the method with an application to a standard model for the charge transport in the direction of maximum mobility in crystalline rubrene. Because of its consistency with the equilibrium distribution, the present method gives a time-dependent diffusion coefficient that plateaus correctly to a long-time limiting value. The resulting mobility is somewhat higher than that of the relaxation time approximation, which uses a phenomenological relaxation parameter to obtain a non-zero diffusion coefficient from a calculation with static phonon disorder. However, it is very similar to the mobility obtained from Ehrenfest dynamics, at least in the parameter regimes we have investigated here. This is somewhat surprising because Ehrenfest dynamics overheats the electronic subsystem and is, therefore, inconsistent with the equilibrium distribution.

Nonadiabatic Photodynamics of Amantadine and 1-Cyanoadamantane Cations.

Cations of diamondoids and derivatives thereof have recently become the subject of experimental, spectroscopic studies due to their potential role in astrochemistry. In particular, their electronic spectra and photoinduced dynamics trigger great interest. Here, we report on computational investigations of two nitrogen-containing derivatives of the adamantane cation (Ada+, ), the amantadine cation (Ama+, ) and the 1-cyanoadamantane cation (Ada-CN+, C10H15CN+). Specifically, we study electronic (vibrationally resolved) spectra and nonadiabatic molecular dynamics (modeled using the surface hopping approach based on semiempirical electronic structure theory) of these radical cations. The internal conversion time constants as well as reactive relaxation outcomes (cage-opening and hydrogen loss) are compared for the two derivatives and also with the case of Ada+.[29] Remarkably, we find a longer ground-state recovery time for Ada-CN+ than for Ama+ (for the same excitation energy window), despite a smaller excitation energy for the former. Thus, a static energy gap law cannot be used to rationalize nonadiabatic dynamics and excited state lifetimes in this case: Dynamics and details of the couplings between several states play a decisive role.

Theoretical Investigation on Proton Transfer Directionality and Dynamics Behavior of 3-(Benzo[d]thiazol-2-yl)-2-hydroxy-5-methoxybenzaldehyde with Two Asymmetric Proton Acceptors.

A detailed theoretical investigation on the excited state intramolecular proton transfer (ESIPT) directionality and dynamics behavior of 3-(benzo[d]thiazol-2-yl)-2-hydroxy-5-methoxybenzaldehyde (BTHMB) with two unsymmetric proton acceptors (N and O2) has been performed. The hydrogen bond O1-H···N in BTHMB-a formed by the O1-H group with the N atom or O1-H···O2 in BTHMB-b formed by the O1-H group with the O2 atom is enhanced upon photoexcitation, and the strength of the O1-H···N bond is stronger, which will drive the O1-H proton to the N atom. Potential energy curves further confirm that ESIPT occurs in the N atom because of the smaller energy barrier (0.39 kcal/mol). Results of dynamics simulations manifest that no surface hopping exists between the S0 and S1 states within 300 fs, and ESIPT time constants of BTHMB-a and BTHMB-b are 48 and 151 fs, respectively. While the reverse ESIPT is observed in BTHMB-b at 294 fs, implying that the O1-H proton is transferred to the N atom instead of the O2 atom. The consistency of the calculated absorption (390 nm) and fluorescence spectra (443 and 602 nm) of BTHMB-a with the experimental values (390, 410, and 605 nm) confirms this conclusion again. The charge distribution analysis shows that the charge on the proton acceptors increases, and the O2 atom has higher electronegativity because it has more negative charges. The minimum surface electrostatic potential on the N atom in BTHMB-b correlating with the pKb value is -47.38 kcal/mol, indicating that the N atom has strong basicity. Therefore, the basicity of the N atom dominates the ESIPT process rather than the electronegativity of the O2 atom.

Frustrated charge transfer in vibrationally inelastic Ar++N2 collisions via hard collision glory scattering

Vibrational energy transfer in collisions between ions and neutrals is a fundamental process in interstellar media, planetary atmospheres, and plasmas. The conventional wisdom is that glancing collisions with large impact parameters are forward-scattered with low vibrational excitation, while hard collisions with small impact parameters are sideway- or backward-scattered with relatively high vibrational excitation. Here, we report experimental observations with a three-dimensional velocity-map imaging crossed-beam apparatus in the inelastic scattering process Ar++N2(v′′ = 0, J′′)→Ar++N2(v′, J′), where all the vibrationally excited N2 products are dominated by forward scattering, contradicting the textbook model. Trajectory surface hopping calculations not only reproduced the experimental observation qualitatively, but also revealed that the vibrational excitation mainly occurs through a transient charge-transfer process. The hard collision glory mechanism, which has so far only been observed in inelastic rotational energy transfer between neutrals, is shown to play a major role for vibrational excitation in the inelastic Ar++N2 collision, via the frustrated charge transfer process.

Excitonic Approach for Nonadiabatic Dynamics: Extending Beyond the Frenkel Exciton Model.

We report the formulation and implementation of an extended Frenkel exciton model (EFEM) designed for simulating the dynamics of multichromophoric systems, taking into account the possible presence of interchromophore charge transfer states, as well as other states in which two chromophores are simultaneously excited. Our approach involves constructing a Hamiltonian based on calculations performed on monomers and selected dimers within the multichromophoric aggregate. Nonadiabatic molecular dynamics is addressed using a surface hopping approach, while the electronic wave functions and energies required for constructing the EFEM are computed utilizing the semiempirical floating occupation molecular orbitals-configuration interaction (FOMO-CI) electronic structure method. To validate our approach, we simulate the singlet fission process in a trimer of 2,5-bis(fluorene-9-ylidene)-2,5-dihydrothiophene (ThBF) molecules, embedded in their crystal environment, comparing the results of the EFEM to the standard "supermolecule" approach.

Multiconfigurational Surface Hopping: a Time-Dependent Variational Approach with Momentum-Jump Trajectories.

The Ehrenfest mean field dynamics and trajectory surface hopping have been widely used in nonadiabatic dynamics simulations. Based on the time-dependent variational principle (TDVP), the multiconfigurational Ehrenfest (MCE) method has also been developed and can be regarded as a multiconfigurational extension of the traditional Ehrenfest dynamics. However, it is not straightforward to apply the TDVP to surface hopping trajectories because there exists momentum jump during surface hops. To solve this problem, we here propose a multiconfigurational surface hopping (MCSH) method, where continuous momenta are obtained by linear interpolation and the interpolated trajectories are used to construct the basis functions for TDVP in a postprocessing manner. As demonstrated in a series of representative spin-boson models, MCSH achieves high accuracy with only several hundred trajectory bases and can uniformly improve the performance of surface hopping. In principle, MCSH can be combined with all kinds of mixed quantum-classical trajectories and thus has the potential to properly describe general nonadiabatic dynamics.

Exact factorization of the photon-electron-nuclear wavefunction: Formulation and coupled-trajectory dynamics.

We employ the exact-factorization formalism to study the coupled dynamics of photons, electrons, and nuclei at the quantum mechanical level, proposing illustrative examples of model situations of nonadiabatic dynamics and spontaneous emission of electron-nuclear systems in the regime of strong light-matter coupling. We make a particular choice of factorization for such a multi-component system, where the full wavefunction is factored as a conditional electronic amplitude and a marginal photon-nuclear amplitude. Then, we apply the coupled-trajectory mixed quantum-classical (CTMQC) algorithm to perform trajectory-based simulations, by treating photonic and nuclear degrees of freedom on equal footing in terms of classical-like trajectories. The analysis of the time-dependent potentials of the theory along with the assessment of the performance of CTMQC allows us to point out some limitations of the current approximations used in CTMQC. Meanwhile, comparing CTMQC with other trajectory-based algorithms, namely multi-trajectory Ehrenfest and Tully surface hopping, demonstrates the better quality of CTMQC predictions.

On-the-Fly Simulation of Two-Dimensional Fluorescence-Excitation Spectra.

Two-dimensional (2D) fluorescence-excitation (2D-FLEX) spectroscopy is a recently proposed nonlinear femtosecond technique for the detection of photoinduced dynamics. The method records a time-resolved fluorescence signal in its excitation- and detection-frequency dependence and hence combines the exclusive detection of excited state dynamics (fluorescence) with signals resolved in both excitation and emission frequencies (2D electronic spectroscopy). In this work, we develop an on-the-fly protocol for the simulation of 2D-FLEX spectra of molecular systems, which is based on interfacing the classical doorway-window representation of spectroscopic responses with trajectory surface hopping simulations. Applying this methodology to gas-phase pyrazine, we show that femtosecond 2D-FLEX spectra can deliver detailed information that is otherwise obtainable via attosecond spectroscopy.

Decoherence ensures convergence of non-adiabatic molecular dynamics with number of states.

Non-adiabatic (NA) molecular dynamics (MD) is a powerful approach for studying far-from-equilibrium quantum dynamics in photophysical and photochemical systems. Most NA-MD methods are developed and tested with few-state models, and their validity with complex systems involving many states is not well studied. By modeling intraband equilibration and interband recombination of charge carriers in MoS2, we investigate the convergence of three popular NA-MD algorithms, fewest switches surface hopping (FSSH), global flux surface hopping (GFSH), and decoherence induced surface hopping (DISH) with the number of states. Only the standard DISH algorithm converges with the number of states and produces Boltzmann equilibrium. Unitary propagation of the wave function in FSSH and GFSH violates the Boltzmann distribution, leads to internal inconsistency between time-dependent Schrödinger equation state populations and trajectory counts, and produces non-convergent results. Introducing decoherence in FSSH and GFSH by collapsing the wave function fixes these problems. The simplified version of DISH that omits projecting out the occupied state and is applicable to few-state systems also causes problems when the number of states is increased. We discuss the algorithmic application of wave function collapse and Boltzmann detailed balance and provide detailed FSSH, GFSH, and DISH flow charts. The use of convergent NA-MD methods is highly important for modeling complicated quantum processes involving multiple states. Our findings provide the basis for investigating quantum dynamics in realistic complex systems.

Influence of Singlet Oxygen in H + O2 Collision Reaction.

The collision reaction of H + O2 = OH + O is a pivotal step in combustion. To investigate the influence of singlet oxygen on this reaction, we computed potential energy surfaces (PESs) for all six lowest states using high-level ab initio methods and coupled them with embedded atom neural network (EANN) fitting. By integrating quasi-classical trajectory (QCT) with trajectory surface hopping (TSH) based on the fitted PESs, we simulated the dynamics of both ground- and excited-states to derive the reaction rate constants for the forward and reverse processes. The results reveal that the forward reaction facilitates radical generation, promoting combustion reactions. Furthermore, calculations of reverse reaction rate constants indicate that all electronic states ultimately yield ground-state oxygen, leading to radical deactivation and exerting an inhibitory effect on combustion processes.

Exciton energy transfer inside cavity-A benchmark study of polaritonic dynamics using the surface hopping method.

Strong coupling between the molecular system and photon inside the cavity generates polaritons, which can alter reaction rates by orders of magnitude. In this work, we benchmark the surface hopping method to simulate non-adiabatic dynamics in a cavity. The comparison is made against a numerically exact method (the hierarchical equations of motion) for a model system investigating excitonic energy transfer for a broad range of parameters. Surface hopping captures the effects of the radiation mode well, both at resonance and off-resonance. We have further investigated parameters that can increase or decrease the rate of population transfer, and we find that surface hopping in general can capture both effects well. Finally, we show that the dipole self-energy term within our parameter regime does not significantly affect the system's dynamics.

Photophysics in Biomembranes: Computational Insight into the Interaction between Lipid Bilayers and Chromophores.

ConspectusLight is ubiquitously available to probe the structure and dynamics of biomolecules and biological tissues. Generally, this cannot be done directly with visible light, because of the absence of absorption by those biomolecules. This problem can be overcome by incorporating organic molecules (chromophores) that show an optical response in the vicinity of those biomolecules. Since those optical properties are strongly dependent on the chromophore's environment, time-resolved spectroscopic studies can provide a wealth of information on biosystems at the molecular scale in a nondestructive way. In this work, we give an overview on the multiscale computational strategy developed by us in the last eight years and prove that theoretical studies and simulations are needed to explain, guide, and predict observations in fluorescence experiments. As we challenge the accepted views on existing probes, we discover unexplored abilities that can discriminate surrounding lipid bilayers and their temperature-dependent as well as solvent-dependent properties. We focus on three archetypal chromophores: diphenylhexatriene (DPH), Laurdan, and azobenzene. Our method shows that conformational changes should not be neglected for the prototype rod-shaped molecule DPH. They determine its position and orientation in a liquid-ordered (Lo) sphingomyelin/cholesterol (SM/Chol) bilayer and are responsible for a strong differentiation of its absorption spectra and fluorescence decay times in dioleoylphosphatidylcholine (DOPC) and dipalmitoylphosphatidylcholine (DPPC) membranes, which are at room temperature in liquid-disordered (Ld) and solid-gel (So) phases, respectively. Thanks to its pronounced first excited state dipole moment, Laurdan has long been known as a solvatochromic probe. Since this molecule has however two conformers, we prove that they exhibit different properties in different lipid membrane phases. We see that the two conformers are only blocked in one phase but not in another. Supported by fluorescence anisotropy decay simulations, Laurdan can therefore be regarded as a molecular rotor. Finally, the conformational versatility of azobenzene in saturated Ld lipid bilayers is simulated, along with its photoisomerization pathways. By means of nonadiabatic QM/MM surface hopping analyses (QM/MM-SH), a dual mechanism is found with a torsional mechanism and a slow conversion for trans-to-cis. For cis-to-trans, simulations show a much higher quantum yield and a so-called "pedal-like" mechanism. The differences are related to the different potential energy surfaces as well as the interactions with the surrounding alkyl chains. When tails of increased length are attached to this probe, cis is pushed toward the polar surface, while trans is pulled toward the center of the membrane.

Exciton Transport in the Nonfullerene Acceptor O-IDTBR from Nonadiabatic Molecular Dynamics.

Theory, computation, and experiment have given strong evidence that charge carriers in organic molecular crystals form partially delocalized quantum objects that diffuse very efficiently via a mechanism termed transient delocalization. It is currently unclear how prevalent this mechanism is for exciton transport. Here we carry out simulation of singlet Frenkel excitons (FE) in a molecular organic semiconductor that belongs to the class of nonfullerene acceptors, O-IDTBR, using the recently introduced FE surface hopping nonadiabatic molecular dynamics method. We find that FE are, on average, localized on a single molecule in the crystal due to sizable reorganization energy and moderate excitonic couplings. Yet, our simulations suggest that the diffusion mechanism is more complex than simple local hopping; in addition to hopping, we observe frequent transient delocalization events where the exciton wave function expands over 10 or more molecules for a short period of time in response to thermal excitations within the excitonic band, followed by de-excitation and contraction onto a single molecule. The transient delocalization events lead to an increase in the diffusion constant by a factor of 3-4, depending on the crystallographic direction as compared to the situation where only local hopping events are considered. Intriguingly, O-IDTBR appears to be a moderately anisotropic 3D "conductor" for excitons but a highly anisotropic 2D conductor for electrons. Taken together with previous simulation results, two trends seem to emerge for molecular organic crystals: excitons tend to be more localized and slower than charge carriers due to higher internal reorganization energy, while exciton transport tends to be more isotropic than charge transport due to the weaker distance dependence of excitonic versus electronic coupling.