Approximate switching algorithms for trajectory surface hopping

Simultaneously improving the efficiencies of photo- and thermal isomerization of an oxindole-based light-driven molecular rotary motor by a structural redesign

We designed a novel highly efficient light-driven molecular rotary motor theoretically by using electronic structure calculations and nonadiabatic dynamics simulations, and it showed excellent performance for both photo- and thermal isomerization processes simultaneously. By the small structural modification based on 3-(2,7-dimethyl-2,3-dihydro-1H-inden-1-ylidene)-1-methylindolin-2-one (DDIYM) synthesized by Feringa et al. recently, an oxindole-based light-driven molecular rotary motor, 3-(1,5-dimethyl-4,5-dihydrocyclopenta[b]pyrrol-6(1H)-ylidene)-1-methylindolin-2-one (DDPYM), is proposed, which displays a significant electronic push-pull character and weak steric hindrance for double-bond isomerization. The newly designed motor DDPYM shows a remarkable improvement of the quantum yield for both EP → ZM and ZP → EM photoisomerization processes, compared to the original motor DDIYM. Furthermore, the rotary motion in photoisomerization processes of DDPYM behaves more like a pure axial rotational motion approximately, while that of DDIYM is an obvious precessional motion. The weakness of the steric hindrance reduces the energy barriers of the thermal helix EM → EP and ZM → ZP inversion steps, and would accelerate two ground-state isomerization steps significantly. Our results confirm the feasibility of simultaneously improving the efficiencies of photo- and thermal isomerization of oxindole-based light-driven molecular rotary motors and this design idea sheds light on the future development of more efficient molecular motors.

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 S0→S1 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 S1 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.

Multilayer Subsystem Surface Hopping Method for Large-Scale Nonadiabatic Dynamics Simulation with Hundreds of Thousands of States

We present a multilayer subsystem surface hopping (MSSH) method to deal with nonadiabatic dynamics in large-scale systems. A small subsystem instead of the full system is adopted for surface hopping and is updated on-the-fly to achieve a reliable description of important adiabatic states and the wave function evolution. Additional subsystems for molecular dynamics and statistical description are introduced to further improve the simulation reliability. The global flux hopping probabilities with optimal state assignments are utilized to treat the complex surface crossings. As demonstrated in a series of one- and two-dimensional Holstein models with up to hundreds of thousands of states, MSSH shows weak parameter dependence in all investigated systems. Especially, the computational costs are reduced by 2-6 orders of magnitude compared to traditional surface hopping simulations in full systems, and size-independent results are achieved with a large time-step size of 2-5 fs. The new method is compatible with different decoherence correction strategies and achieves a much better balance between efficiency and reliability, thus promising for applications in general charge and exciton dynamics simulations.

Design and Nonadiabatic Photoisomerization Dynamics Study of a Three-Stroke Light-Driven Molecular Rotary Motor

Working cycle of conventional light-driven molecular rotary motors (LDMRMs), especially Feringa-type motors, usually have four steps, two photoisomerization steps, and two thermal helix inversion (THI) steps. THI steps hinder the ability of the motor to operate at lower temperatures and limit the rotation speed of LDMRMs. A three-stroke LDMRM, 2-(2,7-dimethyl-2,3-dihydro-1H-inden-1-ylidene)-1,2-dihydro-3H-pyrrol-3-one (DDIY), is proposed, which is capable of completing an unidirectional rotation by two photoisomerization steps and one thermal helix inversion step at room temperature. On the basis of trajectory surface-hopping simulation at the semi-empirical OM2/MRCI level, the EP→ZP and ZP→EM nonadiabatic photoisomerization dynamics of DDIY were systematically analyzed. Quantum yields of EP→ZP and ZP→EM photoisomerization of DDIY are ca. 34% and 18%, respectively. Both EP→ZP and ZP→EM photoisomerization processes occur on an ultrafast time scale (ca. 100-300 fs). This three-stroke LDMRM may stimulate further research for the development of new families of more efficient LDMRMs.

All-Atom Nonadiabatic Dynamics Simulation of Hybrid Graphene Nanoribbons Based on Wannier Analysis and Machine Learning

Trajectory surface hopping combined with ab initio electronic structure calculations is a popular and powerful approach for on-the-fly nonadiabatic dynamics simulations. For large systems, however, this remains a significant challenge because of the unaffordable computational cost of large-scale electronic structure calculations. Here, we present an efficient divide-and-conquer approach to construct the system Hamiltonian based on Wannier analysis and machine learning. In detail, the large system under investigation is first decomposed into small building blocks, and then all possible segments formed by building blocks within a cutoff distance are found out. Ab initio molecular dynamics is carried out to generate a sequence of geometries for each equivalent segment with periodicity. The Hamiltonian matrices in the maximum localized Wannier function (MLWF) basis are obtained for all geometries and utilized to train artificial neural networks (ANNs) for the structure-dependent Hamiltonian elements. Taking advantage of the orthogonality and spatial locality of MLWFs, the one-electron Hamiltonian of a large system at arbitrary geometry can be directly constructed by the trained ANNs. As demonstrations, we study charge transport in a zigzag graphene nanoribbon (GNR), a coved GNR, and a series of hybrid GNRs with a state-of-the-art surface hopping method. The interplay between delocalized and localized states is found to determine the electron dynamics in hybrid GNRs. Our approach has successfully studied GNRs with >10 000 atoms, paving the way for efficient and reliable all-atom nonadiabatic dynamics simulation of general systems.

Nonadiabatic Dynamics with Coupled Trajectories

In this paper, we discuss coupled-trajectory schemes for molecular-dynamics simulations of excited-state processes. New coupled-trajectory strategies to capture decoherence effects, revival of coherence and nonadiabatic interferences in long-time dynamics are proposed, and compared to independent-trajectory schemes. The working framework is provided by the exact factorization of the electron-nuclear wave function, and it exploits ideas emanating from various surface-hopping schemes. The new coupled-trajectory algorithms are tested on a one-dimensional two-state system using different model parameters which allow one to induce different dynamics. The benchmark is provided by the numerically exact solution of the time-dependent Schrödinger equation.

On-the-Fly Symmetrical Quasi-Classical Dynamics with Meyer-Miller Mapping Hamiltonian for the Treatment of Nonadiabatic Dynamics at Conical Intersections

The on-the-fly version of the symmetrical quasi-classical dynamics method based on the Meyer-Miller mapping Hamiltonian (SQC/MM) is implemented to study the nonadiabatic dynamics at conical intersections of polyatomic systems. The current on-the-fly implementation of the SQC/MM method is based on the adiabatic representation and the dressed momentum. To include the zero-point energy (ZPE) correction of the electronic mapping variables, we employ both the γ-adjusted and γ-fixed approaches. Nonadiabatic dynamics of the methaniminium cation (CH₂NH₂⁺) and azomethane are simulated using the on-the-fly SQC/MM method. For CH₂NH₂⁺, both ZPE correction approaches give reasonable and consistent results. However, for azomethane, the γ-adjusted version of the SQC/MM dynamics behaves much better than the γ-fixed version. Further analysis indicates that it is always recommended to use the γ-adjusted SQC/MM dynamics in the on-the-fly simulation of photoinduced dynamics of polyatomic systems, particularly when the excited state is well separated from the ground state in the Franck-Condon region. This work indicates that the on-the-fly SQC/MM method is a powerful simulation protocol to deal with the nonadiabatic dynamics of realistic polyatomic systems.

Non-adiabatic Excited-State Molecular Dynamics: Theory and Applications for Modeling Photophysics in Extended Molecular Materials

Optically active molecular materials, such as organic conjugated polymers and biological systems, are characterized by strong coupling between electronic and vibrational degrees of freedom. Typically, simulations must go beyond the Born-Oppenheimer approximation to account for non-adiabatic coupling between excited states. Indeed, non-adiabatic dynamics is commonly associated with exciton dynamics and photophysics involving charge and energy transfer, as well as exciton dissociation and charge recombination. Understanding the photoinduced dynamics in such materials is vital to providing an accurate description of exciton formation, evolution, and decay. This interdisciplinary field has matured significantly over the past decades. Formulation of new theoretical frameworks, development of more efficient and accurate computational algorithms, and evolution of high-performance computer hardware has extended these simulations to very large molecular systems with hundreds of atoms, including numerous studies of organic semiconductors and biomolecules. In this Review, we will describe recent theoretical advances including treatment of electronic decoherence in surface-hopping methods, the role of solvent effects, trivial unavoided crossings, analysis of data based on transition densities, and efficient computational implementations of these numerical methods. We also emphasize newly developed semiclassical approaches, based on the Gaussian approximation, which retain phase and width information to account for significant decoherence and interference effects while maintaining the high efficiency of surface-hopping approaches. The above developments have been employed to successfully describe photophysics in a variety of molecular materials.

Subspace Surface Hopping with Size-Independent Dynamics

We present a subspace surface hopping strategy to deal with complex surface crossings in nonadiabatic dynamics. By focusing on only important adiabatic states, we make subspace crossing correction (SCC) in the framework of the standard fewest switches surface hopping (FSSH) and the global flux surface hopping (GFSH). The resulting SCC-FSSH and SCC-GFSH approaches show much better performance than the counterparts using all adiabatic states for surface hopping. As demonstrated in a series of Holstein models with up to over 1000 molecular sites, both SCC-FSSH and SCC-GFSH show excellent size independence with a large time step size of 1 fs. Especially, SCC-GFSH does not refer to nonadiabatic couplings at all and gives a more proper description of superexchange, and thus, it is promising for realistic applications with complex potential energy surfaces.

Crossing Classified and Corrected Fewest Switches Surface Hopping

In the traditional fewest switches surface hopping (FSSH), trivial crossings between uncoupled or weakly coupled states have highly peaked nonadiabatic couplings and thus are difficult to deal with in the preferred, adiabatic representation. Here, we classify surface crossings into four general types and propose a parameter-free crossing corrected FSSH (CC-FSSH) algorithm, which could treat multiple trivial crossings within a time interval. As examples, Holstein Hamiltonians with different parameters are adopted to mimic electron dynamics in tens to hundreds of molecules, which suffer from severe trivial crossing problems. Using existed surface hopping approaches as references, we show that CC-FSSH exhibits significantly fast time interval convergence and weak system size dependence. In all cases, a reliable description is achieved with a large time interval of 1 fs. With a simple formalism and the ability to describe complex surface crossings, CC-FSSH could potentially simulate general nonadiabatic dynamics in nanoscale materials with a high efficiency.

Ultrafast unidirectional chiral rotation in the Z–E photoisomerization of two azoheteroarene photoswitches

Based on a large number of trajectories starting from the Z-isomer, for both azoheteroarenes, more than 99% of the trajectories decay through conical intersections with the same helicities as their initial geometries.

Incorporating spin–orbit effects into surface hopping dynamics using the diagonal representation: a linear-response time-dependent density functional theory implementation with applications to 2-thiouracil

Evaluation of SOC values employs Casida's wave functions and the Breit–Pauli spin–orbit Hamiltonian with effective charge approximation.

Dynamics of Azobenzene Dimer Photoisomerization: Electronic and Steric Effects

While azobenzenes readily photoswitch in solution, their photoisomerization in densely packed self-assembled monolayers (SAMs) can be suppressed. Reasons for this can be steric hindrance and/or electronic quenching, e.g., by exciton coupling. We address these possibilities by means of nonadiabatic molecular dynamics with trajectory surface hopping calculations, investigating the trans → cis isomerization of azobenzene after excitation into the ππ* absorption band. We consider a free monomer, an isolated dimer and a dimer embedded in a SAM-like environment of additional azobenzene molecules, imitating in this way the gradual transition from an unconstrained over an electronically coupled to an electronically coupled and sterically hindered, molecular switch. Our simulations reveal that in comparison to the single molecule the quantum yield of the trans → cis photoisomerization is similar for the isolated dimer, but greatly reduced in the sterically constrained situation. Other implications of dimerization and steric constraints are also discussed.

Recent Progress in Surface Hopping: 2011-2015

Developed 25 years ago, Tully's fewest switches surface hopping (FSSH) has proven to be the most popular approach for simulating quantum-classical dynamics in a broad variety of systems, ranging from the gas phase, to the liquid and solid phases, to biological and nanoscale materials. FSSH is widely adopted as the fundamental platform to introduce modifications as needed. Significant progress has been made recently to enhance the accuracy and efficiency of the surface hopping technique. Various limitations of the standard FSSH-associated with quantum nuclear effects, interference and decoherence, trivial or "unavoided" crossings, superexchange, and representation dependence-have been lifted. These advances are needed to allow one to treat many important phenomena in chemistry, physics, materials, and related disciplines. Examples include charge transport in extended systems such as organic solids, singlet fission in molecular aggregates, Auger-type exciton multiplication, recombination and relaxation in quantum dots and other nanoscale materials, Auger-assisted charge transfer, nonradiative luminescence quenching, and electron-hole recombination. This Perspective summarizes recent advances in the surface hopping formulation of nonadiabatic dynamics and provides an outlook on the future of surface hopping.

Femtosecond structural dynamics drives the trans/cis isomerization in photoactive yellow protein

A variety of organisms have evolved mechanisms to detect and respond to light, in which the response is mediated by protein structural changes after photon absorption. The initial step is often the photoisomerization of a conjugated chromophore. Isomerization occurs on ultrafast time scales and is substantially influenced by the chromophore environment. Here we identify structural changes associated with the earliest steps in the trans-to-cis isomerization of the chromophore in photoactive yellow protein. Femtosecond hard x-ray pulses emitted by the Linac Coherent Light Source were used to conduct time-resolved serial femtosecond crystallography on photoactive yellow protein microcrystals over a time range from 100 femtoseconds to 3 picoseconds to determine the structural dynamics of the photoisomerization reaction.

Nonadiabatic nuclear dynamics of the ammonia cation studied by surface hopping classical trajectory calculations

The Landau-Zener (LZ) type classical-trajectory surface-hopping algorithm is applied to the nonadiabatic nuclear dynamics of the ammonia cation after photoionization of the ground-state neutral molecule to the excited states of the cation. The algorithm employs a recently proposed formula for nonadiabatic LZ transition probabilities derived from the adiabatic potential energy surfaces. The evolution of the populations of the ground state and the two lowest excited adiabatic states is calculated up to 200 fs. The results agree well with quantum simulations available for the first 100 fs based on the same potential energy surfaces. Three different time scales are detected for the nuclear dynamics: Ultrafast Jahn-Teller dynamics between the excited states on a 5 fs time scale; fast transitions between the excited state and the ground state within a time scale of 20 fs; and relatively slow partial conversion of a first-excited-state population to the ground state within a time scale of 100 fs. Beyond 100 fs, the adiabatic electronic populations are nearly constant due to a dynamic equilibrium between the three states. The ultrafast nonradiative decay of the excited-state populations provides a qualitative explanation of the experimental evidence that the ammonia cation is nonfluorescent.

Tracking of azobenzene isomerization by X-ray emission spectroscopy

Cis-trans isomerizations are among the fundamental processes in photochemistry. In azobenzene or its derivatives this dynamics is, due to its reversibility, one of the reactions widely used in photostimulation of molecular motors or in molecular electronics. Though intensively investigated in the optical regime, no detailed study exists in the X-ray regime so far. Because the X-ray emission spectroscopy echoes the electronic structure sensitive to the geometry, this theoretical report based on the density functional theory and its time-dependent version presents different nitrogen K-edge X-ray emission spectra for cis and trans isomers with close interrelation to their electron configuration. Considering the spectrum along the isomerization path, these structural signatures can be utilized to probe the isomerization dynamics in the excited molecule. The scheme can further be generalized to the element specific photoreactions.

Control Mechanisms of Photoisomerization in Protonated Schiff Bases

We performed ab initio excited-state molecular dynamics simulations of a gas-phase photoexcited protonated Schiff base (C1-N2═C3-C4═C5-C6) to search for control mechanisms of its photoisomerization. The excited molecule twists by ∼90° around either the N2C3 bond or the C4C5 bond and relaxes to the ground electronic state through a conical intersection with either a trans or cis outcome. We show that a large initial distortion of several dihedral angles and a specific normal vibrational mode combining pyramidalization and double-bond twisting can lead to a preferential rotation of atoms around the C4C5 bond. We also show that selective pretwisting of several dihedral angles in the initial ground state thermal ensemble (by analogy to a protein pocket) can significantly increase the fraction of photoreactive (cis → trans) trajectories. We demonstrate that new ensembles with higher degrees of control over the photoisomerization reaction can be obtained by a computational directed evolution approach on the ensembles of molecules with the pretwisted geometries.