Fulgides as Light-Driven Molecular Rotary Motors: Computational Design of a Prototype Compound

Nonadiabatic Dynamics with Exact Factorization: Implementation and Assessment

In this work, we report our implementation of several independent-trajectory mixed-quantum-classical (ITMQC) nonadiabatic dynamics methods based on exact factorization (XF) in the Libra package for nonadiabatic and excited-state dynamics. Namely, the exact factorization surface hopping (SHXF), mixed quantum-classical dynamics (MQCXF), and mean-field (MFXF) are introduced. Performance of these methods is compared to that of several traditional surface hopping schemes, such as the fewest-switches surface hopping (FSSH), branching-corrected surface hopping (BCSH), and the simplified decay of mixing (SDM), as well as conventional Ehrenfest (mean-field, MF) method. Based on a comprehensive set of 1D model Hamiltonians, we find the ranking SHXF ≈ MQCXF > BCSH > SDM > FSSH ≫ MF, with the BCSH sometimes outperforming the XF methods in terms of describing coherences. Although the MFXF method can yield reasonable populations and coherences for some cases, it does not conserve the total energy and is therefore not recommended. We also find that the branching correction for auxiliary trajectories is important for the XF methods to yield accurate populations and coherences. However, the branching correction can worsen the quality of the energy conservation in the MQCXF. Finally, we find that using the time-dependent Gaussian width approximation used in the XF methods for computing decoherence correction can improve the quality of energy conservation in the MQCXF dynamics. The parameter-free scheme of Subotnik for computing the Gaussian widths is found to deliver the best performance in situations where such widths are not known a priori.

Advanced theoretical design of light-driven molecular rotary motors: enhancing thermal helix inversion and visible-light activation

In this study, we have advanced the field of light-driven molecular rotary motors (LDMRMs) by achieving two pivotal goals: lowering the thermal helix inversion (THI) barrier and extending the absorption wavelength into the visible spectrum. This study involves the structural reengineering of a second-generation visible LDMRM, resulting in the synthesis of a novel class, specifically, 2-((2S)-5-methoxy-2-methyl-2,3-dihydro-1H-cyclopenta[a]naphthalen-1-yl)-3-oxo-2,3-dihydro-1H-dibenzo[e,g]indole-6,9-dicarbonitrile. This redesigned motor stands out with its two photoisomerization stages and two thermal helix inversions, featuring exceptionally low THI barriers (4.00 and 2.05 kcal mol-1 at the OM2/MRCI level for the EM → EP and ZM → ZP processes, respectively). Moreover, it displays absorption wavelengths in the visible light range (482.98 and 465.76 nm for the EP and ZP isomers, respectively, at the TD-PBE0-D3/6-31G(d,p) level), surpassing its predecessors in efficiency, as indicated by the narrow HOMO-LUMO energy gap. Ultrafast photoisomerization kinetics (approximately 0.8-1.6 ps) and high quantum yields (around 0.3-0.6) were observed through trajectory surface hopping simulations. Additionally, the simulated time-resolved fluorescence emission spectrum indicates a significantly reduced "dark state" duration (0.09-0.26 ps) in these newly designed LDMRMs compared to the original ones, marking a substantial leap forward in the design and efficiency of LDMRMs.

Formulation of transition dipole gradients for non-adiabatic dynamics with polaritonic states

A general formulation of the strong coupling between photons confined in a cavity and molecular electronic states is developed for the state-interaction state-average spin-restricted ensemble-referenced Kohn-Sham method. The light-matter interaction is included in the Jaynes-Cummings model, which requires the derivation and implementation of the analytical derivatives of the transition dipole moments between the molecular electronic states. The developed formalism is tested in the simulations of the nonadiabatic dynamics in the polaritonic states resulting from the strong coupling between the cavity photon mode and the ground and excited states of the penta-2,4-dieniminium cation, also known as PSB3. Comparison with the field-free simulations of the excited-state decay dynamics in PSB3 reveals that the light-matter coupling can considerably alter the decay dynamics by increasing the excited state lifetime and hindering photochemically induced torsion about the C=C double bonds of PSB3. The necessity of obtaining analytical transition dipole gradients for the accurate propagation of the dynamics is underlined.

Theoretical trends in the dynamics simulations of molecular machines across multiple scales

Over the past few decades, molecular machines have been extensively studied, since they are composed of single molecules for functional materials capable of responding to external stimuli, enabling motion at scales ranging from the microscopic to the macroscopic level within molecular aggregates. This advancement holds the potential to efficiently transform external resources into mechanical movement, achieved through precise control of conformational changes in stimuli-responsive materials. However, the underlying mechanism that links microscopic and macroscopic motions remains unclear, demanding computational development associated with simulating the construction of molecular machines from single molecules. This bottleneck has impeded the design of more efficient functional materials. Advancements in theoretical simulations have successfully been developed in various computational models to unveil the operational mechanisms of stimulus-responsive molecular machines, which could help us reduce the costs in experimental trial-and-error procedures. It opens doors to the computer-aided design of innovative functional materials. In this perspective, we have reviewed theoretical approaches employed in simulating dynamic processes involving conformational changes in molecular machines, spanning different scales and environmental conditions. In addition, we have highlighted current challenges and anticipated future trends in the collective control of aggregates within molecular machines. Our goal is to provide a comprehensive overview of recent theoretical advancements in the field of molecular machines, offering valuable insights for the design of novel smart materials.

A Proof-of-Principle Design for Through-Space Transmission of Unidirectional Rotary Motion by Molecular Photogears

The construction of molecular photogears that can achieve through-space transmission of the unidirectional double-bond rotary motion of light-driven molecular motors onto a remote single-bond axis is a formidable challenge in the field of artificial molecular machines. Here, we present a proof-of-principle design of such photogears that is based on the possibility of using stereogenic substituents to control both the relative stabilities of two helical forms of the photogear and the double-bond photoisomerization reaction that connects them. The potential of the design was verified by quantum-chemical modeling through which photogearing was found to be a favorable process compared to free-standing single-bond rotation ("slippage"). Overall, our study unveils a surprisingly simple approach to realizing unidirectional photogearing.

Extraction of pure component spectra from ex situ illumination UV/Vis and NMR spectroscopy

Obtaining understanding of a photochemical reaction relies on the observation, identification and quantification of the compounds involved. The photochemical properties of the individual components are of particular importance, and their determination, however, is not always trivial. This is also true for the quantitative measure on the ability to absorb light, the extinction coefficient εi if more than one species i is present and two or more species absorb light of the same wavelength. In this work, it is demonstrated how pure component spectra can be obtained with a simple combination of successive and repeated ex situ illumination, UV/Vis and NMR spectroscopy. From the complementary information accessible, the wavelength-dependent extinction coefficients of all species can be calculated yielding the pure component spectra. A comparison with published data shows excellent agreement and thus proves that this approach is highly reliable.

Different flavors of exact-factorization-based mixed quantum-classical methods for multistate dynamics

The exact factorization approach has led to the development of new mixed quantum-classical methods for simulating coupled electron-ion dynamics. We compare their performance for dynamics when more than two electronic states are occupied at a given time, and analyze: (1) the use of coupled versus auxiliary trajectories in evaluating the electron-nuclear correlation terms, (2) the approximation of using these terms within surface-hopping and Ehrenfest frameworks, and (3) the relevance of the exact conditions of zero population transfer away from nonadiabatic coupling regions and total energy conservation. Dynamics through the three-state conical intersection in the uracil radical cation as well as polaritonic models in one dimension are studied.

Ultrafast Photocontrolled Rotation in a Molecular Motor Investigated by Machine Learning-Based Nonadiabatic Dynamics Simulations

The thermal helix inversion (THI) of the overcrowded alkene-based molecular motors determines the speed of the unidirectional rotation due to the high reaction barrier in the ground state, in comparison with the ultrafast photoreaction process. Recently, a phosphine-based motor has achieved all-photochemical rotation experimentally, promising to be controlled without a thermal step. However, the mechanism of this photochemical reaction has not yet been fully revealed. The comprehensive computational studies on photoisomerization still resort to nonadiabatic molecular dynamics (NAMD) simulations based on electronic structure calculations, which remains a high computational cost for large systems such as molecular motors. Machine learning (ML) has become an accelerating tool in NAMD simulations recently, where excited-state potential energy surfaces (PESs) are constructed analytically with high accuracy, providing an efficient approach for simulations in photochemistry. Herein the reaction pathway is explored by a spin-flip time-dependent density functional theory (SF-TDDFT) approach in combination with ML-based NAMD simulations. According to our computational simulations, we notice that one of the key factors of fulfilling all-photochemical rotation in the phosphine-based motor is that the excitation energies of four isomers are similar. Additionally, a shortcut photoinduced transformation between unstable isomers replaces the THI step, which shares the conical intersection (CI) with photoisomerization. In this study, we provide a practical approach to speed up the NAMD simulations in photochemical reactions for a large system that could be extended to other complex systems.

Photoresponsive Diarylethene-Containing Polymers: Recent Advances and Future Challenges

Photoresponsive polymers have attracted increasing interest owing to their potential applications in anticounterfeiting, information encryption, adhesives, etc. Among them, diarylethene (DAE)-containing polymers are one of the most promising photoresponsive polymers and have unique thermal stability and fatigue resistance compared to azobenzene- and spiropyran-containing polymers. Herein, the design of DAE-containing polymers based on different types of structures, including main chain polymers, side-chain polymers, and crosslinked polymers, is introduced. The mechanism and applications of DAE-containing polymers in anti-counterfeiting, information encryption, light-controllable adhesives, and photoinduced healable materials are reviewed. In addition, the remaining challenges of DAE-containing polymers are also discussed.

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.

Combined QM (MS-CASPT2)/MM studies on photocyclization and photoisomerization of a fulgide derivative in toluene solution

Photocyclization and photoisomerization of fulgides have been extensively studied experimentally and computationally due to their significant potential applications for example as photoswitches in memory devices. However, the reported excited-state decay mechanisms of fulgides do not include the effects of solvation explicitly to date. Herein, calculations using the high-level MS-CASPT2//CASSCF method were conducted to explore the photoinduced excited-state decay processes of the E_α conformer of a fulgide derivative in toluene with solvent effects treated by implicit PCM and explicit QM/MM models, respectively. Several minima and conical intersections were optimized successfully in and between the S₀ and S₁ states; then, two nonadiabatic excited-state decay channels that could efficiently drive the system to the ground state were proposed based on the excited-state ring-closure and isomerization paths. In addition, we also found that in the ring-closure path, the potential energy surface is essentially barrierless before approaching the conical intersection, while it needs to overcome a small energy barrier along the E → Z photoisomerization path for the nonadiabatic S₁ → S₀ internal conversion process. The present computational results could provide useful mechanistic insights into the photoinduced cyclization and isomerization reactions of fulgide and its derivatives.

Towards the engineering of a photon-only two-stroke rotary molecular motor

The rational engineering of photoresponsive materials, e.g., light-driven molecular motors, is a challenging task. Here, we use structure-related design rules to prepare a prototype molecular rotary motor capable of completing an entire revolution using, exclusively, the sequential absorption of two photons; i.e., a photon-only two-stroke motor. The mechanism of rotation is then characterised using a combination of non-adiabatic dynamics simulations and transient absorption spectroscopy measurements. The results show that the rotor moiety rotates axially relative to the stator and produces, within a few picoseconds at ambient T, an intermediate with the same helicity as the starting structure. We discuss how such properties, that include a 0.25 quantum efficiency, can help overcome the operational limitations of the classical overcrowded alkene designs.

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.

Simulation and analysis of the relaxation dynamics of a photochromic furylfulgide

Furylfulgides, a class of photochromic organic compounds, show a complex system of photoinduced reactions. In the present study, the excited-state dynamics of the E_α and E_β isomers of a representative furylfulgide is modelled with the use of nonadiabatic molecular dynamics simulations. Moreover, a pattern recognition algorithm is employed in order to automatically identify relaxation pathways, and to quantify the photoproduct distributions. The simulation results indicate that, despite differing only in the orientation of the furyl group, the two isomers show markedly different photochemical behaviour. The predominant E_α isomer undergoes photocyclisation with a quantum yield (QY) of 0.27 ± 0.10. For this isomer, the undesired E → Z photoisomerisation around the central double bond represents a minor side reaction, with a QY of 0.09 ± 0.07. In contrast, the minority E_β isomer, which is incapable of photocyclisation, undergoes efficient E → Z photoisomerisation, with a QY as high as 0.56 ± 0.14. The relaxation kinetics and the photoproduct distributions are interpreted in the light of the available experimental data.

Exact Factorization Adventures: A Promising Approach for Non-Bound States

Modeling the dynamics of non-bound states in molecules requires an accurate description of how electronic motion affects nuclear motion and vice-versa. The exact factorization (XF) approach offers a unique perspective, in that it provides potentials that act on the nuclear subsystem or electronic subsystem, which contain the effects of the coupling to the other subsystem in an exact way. We briefly review the various applications of the XF idea in different realms, and how features of these potentials aid in the interpretation of two different laser-driven dissociation mechanisms. We present a detailed study of the different ways the coupling terms in recently-developed XF-based mixed quantum-classical approximations are evaluated, where either truly coupled trajectories, or auxiliary trajectories that mimic the coupling are used, and discuss their effect in both a surface-hopping framework as well as the rigorously-derived coupled-trajectory mixed quantum-classical approach.

Independent Trajectory Mixed Quantum-Classical Approaches Based on the Exact Factorization

Mixed quantum-classical dynamics based on the exact factorization exploits the "derived" electron-nuclear correlation (ENC) term aiming for the description of quantum coherences. The ENC contains interactions between the phase of electronic states and nuclear quantum momenta which depend on the spatial shape of the nuclear density.The original surface hopping based on the exact factorization (SHXF) [\textit{J. Phys. Chem. Lett.} \textbf{2018}, \textit{9}, 1097] exploits frozen Gaussian functions to construct the nuclear density in the ENC term while the phase of electronic states is approximated as a fictitious nuclear momentum change.However, in reality, the width of nuclear wave packets varies in time depending on the shape of potential energy surfaces.In this work, we present a modified SHXF approach and a newly-developed Ehrenfest dynamics based on the exact factorization (EhXF) with time-dependent Gaussian functions and phases by enforcing total energy conservation.We perform numerical tests for various one-dimensional two-state model Hamiltonians.Overall, the time-dependent width of Gaussian functions and the energy conserving phase show a reliable decoherence compared to the original frozen Gaussian-based SHXF and the exact quantum mechanical calculation.Especially, the energy conserving phase is crucial for EhXF to reproduce the correct quantum dynamics.

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.

Dynamics of Excitons in Conjugated Molecules and Organic Semiconductor Systems

The exciton, an excited electron-hole pair bound by Coulomb attraction, plays a key role in photophysics of organic molecules and drives practically important phenomena such as photoinduced mechanical motions of a molecule, photochemical conversions, energy transfer, generation of free charge carriers, etc. Its behavior in extended π-conjugated molecules and disordered organic films is very different and very rich compared with exciton behavior in inorganic semiconductor crystals. Due to the high degree of variability of organic systems themselves, the exciton not only exerts changes on molecules that carry it but undergoes its own changes during all phases of its lifetime, that is, birth, conversion and transport, and decay. The goal of this review is to give a systematic and comprehensive view on exciton behavior in π-conjugated molecules and molecular assemblies at all phases of exciton evolution with emphasis on rates typical for this dynamic picture and various consequences of the above dynamics. To uncover the rich variety of exciton behavior, details of exciton formation, exciton transport, exciton energy conversion, direct and reverse intersystem crossing, and radiative and nonradiative decay are considered in different systems, where these processes lead to or are influenced by static and dynamic disorder, charge distribution symmetry breaking, photoinduced reactions, electron and proton transfer, structural rearrangements, exciton coupling with vibrations and intermediate particles, and exciton dissociation and annihilation as well.

Exact-Factorization-Based Surface Hopping for Multistate Dynamics

A surface-hopping algorithm recently derived from the exact factorization approach, SHXF [Ha et al. J. Phys. Chem. Lett. 2018, 9, 1097], introduces an additional term in the electronic equation of surface hopping that couples electronic states through the quantum momentum. This term not only provides a first-principles description of decoherence, but here we show it is crucial to accurately capture nonadiabatic dynamics when more than two states are occupied at any given time. Using a vibronic coupling model of the uracil cation, we show that the lack of this term in traditional surface-hopping methods, including those with decoherence corrections, leads to failure to predict the dynamics through a three-state intersection, while SHXF performs similarly to the multiconfiguration time-dependent Hartree quantum dynamics benchmark.

Coupled- and Independent-Trajectory Approaches Based on the Exact Factorization Using the PyUNIxMD Package

We present mixed quantum-classical approaches based on the exact factorization framework. The electron-nuclear correlation term in the exact factorization enables us to deal with quantum coherences by accounting for electronic and nuclear nonadiabatic couplings effectively within classical nuclei approximation. We compare coupled- and independent-trajectory approximations with each other to understand algorithms in description of the bifurcation of nuclear wave packets and the correct spatial distribution of electronic wave functions along with nuclear trajectories. Finally, we show numerical results for comparisons of coupled- and independent-trajectory approaches for the photoisomerization of a protonated Schiff base from excited state molecular dynamics (ESMD) simulations with the recently developed Python-based ESMD code, namely, the PyUNIxMD program.

Designing light-driven rotary molecular motors

The ability to induce and amplify motion at the molecular scale has seen tremendous progress ranging from simple molecular rotors to responsive materials. In the two decades since the discovery of light-driven rotary molecular motors, the development of these molecules has been extensive; moving from the realm of molecular chemistry to integration into dynamic molecular systems. They have been identified as actuators holding great potential to precisely control the dynamics of nanoscale devices, but integrating molecular motors effectively into evermore complex artificial molecular machinery is not trivial. Maximising efficiency without compromising function requires conscious and judicious selection of the structures used. In this perspective, we focus on the key aspects of motor design and discuss how to manipulate these properties without impeding motor integrity. Herein, we describe these principles in the context of molecular rotary motors featuring a central double bond axle and emphasise the strengths and weaknesses of each design, providing a comprehensive evaluation of all artificial light-driven rotary motor scaffolds currently present in the literature. Based on this discussion, we will explore the trajectory of research into the field of molecular motors in the coming years, including challenges to be addressed, potential applications, and future prospects.

Study of the Decoherence Correction Derived from the Exact Factorization Approach for Nonadiabatic Dynamics

We present a detailed study of the decoherence correction to surface hopping that was recently derived from the exact factorization approach. Ab initio multiple spawning calculations that use the same initial conditions and the same electronic structure method are used as a reference for three molecules: ethylene, the methaniminium cation, and fulvene, for which nonadiabatic dynamics follows a photoexcitation. A comparison with the Granucci–Persico energy-based decoherence correction and the augmented fewest-switches surface-hopping scheme shows that the three decoherence-corrected methods operate on individual trajectories in a qualitatively different way, but the results averaged over trajectories are similar for these systems.

PyUNIxMD: A Python-based excited state molecular dynamics package

Theoretical/computational description of excited state molecular dynamics is nowadays a crucial tool for understanding light-matter interactions in many materials. Here we present an open-source Python-based nonadiabatic molecular dynamics program package, namely PyUNIxMD, to deal with mixed quantum-classical dynamics for correlated electron-nuclear propagation. The PyUNIxMD provides many interfaces for quantum chemical calculation methods with commercial and noncommercial ab initio and semiempirical quantum chemistry programs. In addition, the PyUNIxMD offers many nonadiabatic molecular dynamics algorithms such as fewest-switch surface hopping and its derivatives as well as decoherence-induced surface hopping based on the exact factorization (DISH-XF) and coupled-trajectory mixed quantum-classical dynamics (CTMQC) for general purposes. Detailed structures and flows of PyUNIxMD are explained for the further implementations by developers. We perform a nonadiabatic molecular dynamics simulation for a molecular motor system as a simple demonstration.

On the Transition from a Biomimetic Molecular Switch to a Rotary Molecular Motor

The experimental investigation of the unidirectional motion characterizing the photoisomerization of single-molecule rotary motors requires accessible lab prototypes featuring an electronic circular dichroism (ECD) signal that is sensitive to the geometrical and electronic changes occurring during an ultrafast reactive process. Here we report a combined experimental/computational study of a candidate obtained via the asymmetrization of a light-driven biomimetic molecular switch. We show that the achieved motor has an ECD band that is remarkably sensitive to the isomerization motion, and it is therefore suitable for time-resolved ECD studies. However, we also find that, unexpectedly, the synthesized motor isomerizes on a time scale longer than the subpicosecond time measured for the achiral parent, a result that points to alternative candidates conserving a high reaction speed.

Machine Learning-Assisted Excited State Molecular Dynamics with the State-Interaction State-Averaged Spin-Restricted Ensemble-Referenced Kohn-Sham Approach

We present a machine learning-assisted excited state molecular dynamics (ML-ESMD) based on the ensemble density functional theory framework. Since we represent a diabatic Hamiltonian in terms of generalized valence bond ansatz within the state-interaction state-averaged spin-restricted ensemble-referenced Kohn-Sham (SI-SA-REKS) method, we can avoid singularities near conical intersections, which are crucial in excited state molecular dynamics simulations. We train the diabatic Hamiltonian elements and their analytical gradients with the SchNet architecture to construct machine learning models, while the phase freedom of off-diagonal elements of the Hamiltonian is cured by introducing the phase-less loss function. Our machine learning models show reasonable accuracy with mean absolute errors of ∼0.1 kcal/mol and ∼0.5 kcal/mol/Å for the diabatic Hamiltonian elements and their gradients, respectively, for penta-2,4-dieniminium cation. Moreover, by exploiting the diabatic representation, our models can predict correct conical intersection structures and their topologies. In addition, our ML-ESMD simulations give almost identical result with a direct dynamics at the same level of theory.

Case studies of the time-dependent potential energy surface for dynamics in cavities

The exact time-dependent potential energy surface driving the nuclear dynamics was recently shown to be a useful tool to understand and interpret the coupling of nuclei, electrons, and photons in cavity settings. Here, we provide a detailed analysis of its structure for exactly solvable systems that model two phenomena: cavity-induced suppression of proton-coupled electron-transfer and its dependence on the initial state, and cavity-induced electronic excitation. We demonstrate the inadequacy of simply using a weighted average of polaritonic surfaces to determine the dynamics. Such a weighted average misses a crucial term that redistributes energy between the nuclear and the polaritonic systems, and this term can in fact become a predominant term in determining the nuclear dynamics when several polaritonic surfaces are involved. Evolving an ensemble of classical trajectories on the exact potential energy surface reproduces the nuclear wavepacket quite accurately, while evolving on the weighted polaritonic surface fails after a short period of time. The implications and prospects for application of mixed quantum-classical methods based on this surface are discussed.

Light-Gated Modulation of Electronic Mobility of a Dihydropyrene-Based Photochromic Coordination Polymer

Photo-induced modulation of electronic conductance has been achieved by employing an Ag^I-based two-dimensional coordination polymer (CP) having pyridine-functionalized photochromic dimethyldihydropyrene-cyclophanediene (DHP-CPD) π-switch. Both the coordination polymer and the organic photochromic core were characterized by single-crystal X-ray diffraction studies. The coordination polymer displayed an excellent conductance in the ON state of the switch in the closed form of DHP. Upon exposure to visible light, the π-switch in the CPD form loses its planarity, turning the switch OFF, which is reflected in the drastic reduction of the conductance. Exposure to UV light turns the switch back ON wherein the high electronic conductance of the polymer can be restored.

Molecular Photochemistry: Recent Developments in Theory

Photochemistry is a fascinating branch of chemistry that is concerned with molecules and light. However, the importance of simulating light-induced processes is reflected also in fields as diverse as biology, material science, and medicine. This Minireview highlights recent progress achieved in theoretical chemistry to calculate electronically excited states of molecules and simulate their photoinduced dynamics, with the aim of reaching experimental accuracy. We focus on emergent methods and give selected examples that illustrate the progress in recent years towards predicting complex electronic structures with strong correlation, calculations on large molecules, describing multichromophoric systems, and simulating non-adiabatic molecular dynamics over long time scales, for molecules in the gas phase or in complex biological environments.

Synthesis of Core-Modified Third-Generation Light-Driven Molecular Motors

The synthesis and characterization of a series of light-driven third-generation molecular motors featuring various structural modifications at the central aromatic core are presented. We explore a number of substitution patterns, such as 1,2-dimethoxybenzene, naphthyl, 1,2-dichlorobenzene, 1,1':2',1″-terphenyl, 4,4″-dimethoxy-1,1':2',1″-terphenyl, and 1,2-dicarbomethoxybenzene, considered essential for designing future responsive systems. In many cases, the synthetic routes for both synthetic intermediates and motors reported here are modular, allowing for their post-functionalization. The structural modifications introduced in the core of the motors result in improved solubility and a bathochromic shift of the absorption maxima. These features, in combination with a structural design that presents remote functionalization of the stator with respect to the fluorene rotors, make these novel motors particularly promising as light-responsive actuators in covalent and supramolecular materials.

Unidirectional Rotary Motion in Isotopically Chiral Molecular Motors: A Computational Analysis

Molecular dynamics simulations are performed to explore if isotopic chirality can induce unidirectional rotary motion in molecular motors operated through double-bond photoisomerizations. Using a high-quantum yield motor featuring a chemically asymmetric carbon atom as reference, it is found that isotopically chiral counterparts of this motor sustain such motion almost equally well. Overall, the study reveals a previously unexplored role for isotopic chirality in the design of rotary molecular motors.

Computation of Molecular Ionization Energies Using an Ensemble Density Functional Theory Method

Computation of the ionization energies and of the respective Dyson orbitals based on the use of the extended Koopmans theorem (EKT) is implemented in connection with an ensemble density functional theory (eDFT) method, the state-interaction state-averaged spin-restricted ensemble-referenced Kohn-Sham (SI-SA-REKS or SSR) method. The new methodology enables fast computation of the ionization energies and evaluation of the respective Dyson orbitals, the square norms of which are related with the ionization probabilities, in the ground and excited electronic states of molecules. As the application of EKT recycles the intermediate quantities from the SSR analytical energy gradient, evaluation of the ionization energies and probabilities can be carried out on-the-fly during the nonadiabatic molecular dynamics simulations. This opens up a perspective for fast theoretical simulation of the time-resolved photoelectron spectroscopy observations. In the present work, the new methodology is tested in the computation of the ionization energies and Dyson orbitals of several molecules in the ground and excited electronic states, including strongly correlated species, such as the ozone molecule, dissociating chemical bonds, and conical intersections.

Photo- and Redox-Driven Artificial Molecular Motors

Directed motion at the nanoscale is a central attribute of life, and chemically driven motor proteins are nature's choice to accomplish it. Motivated and inspired by such bionanodevices, in the past few decades chemists have developed artificial prototypes of molecular motors, namely, multicomponent synthetic species that exhibit directionally controlled, stimuli-induced movements of their parts. In this context, photonic and redox stimuli represent highly appealing modes of activation, particularly from a technological viewpoint. Here we describe the evolution of the field of photo- and redox-driven artificial molecular motors, and we provide a comprehensive review of the work published in the past 5 years. After an analysis of the general principles that govern controlled and directed movement at the molecular scale, we describe the fundamental photochemical and redox processes that can enable its realization. The main classes of light- and redox-driven molecular motors are illustrated, with a particular focus on recent designs, and a thorough description of the functions performed by these kinds of devices according to literature reports is presented. Limitations, challenges, and future perspectives of the field are critically discussed.

Bile Acid Binding Protein Functionalization Leads to a Fully Synthetic Rhodopsin Mimic

Rhodopsins are photoreceptive proteins using light to drive a plethora of biological functions such as vision, proton and ion pumping, cation and anion channeling, and gene and enzyme regulation. Here we combine organic synthesis, NMR structural studies, and photochemical characterization to show that it is possible to prepare a fully synthetic mimic of rhodopsin photoreceptors. More specifically, we conjugate a bile acid binding protein with a synthetic mimic of the rhodopsin protonated Schiff base chromophore to achieve a covalent complex featuring an unnatural protein host, photoswitch, and photoswitch-protein linkage with a reverse orientation. We show that, in spite of its molecular-level diversity, light irradiation of the prepared mimic fuels a photochromic cycle driven by sequential photochemical and thermal Z/E isomerizations reminiscent of the photocycles of microbial rhodopsins.

Recent Implementations of Molecular Photoswitches into Smart Materials and Biological Systems

Light is a nearly ideal stimulus for molecular systems. It delivers information encoded in the form of wavelengths and their intensities with high precision in space and time. Light is a mild trigger that does not permanently contaminate targeted samples. Its energy can be reversibly transformed into molecular motion, polarity, or flexibility changes. This leads to sophisticated functions at the supramolecular and macroscopic levels, from light-triggered nanomaterials to photocontrol over biological systems. New methods and molecular adapters of light are reported almost daily. Recently reported applications of photoresponsive systems, particularly azobenzenes, spiropyrans, diarylethenes, and indigoids, for smart materials and photocontrol of biological setups are described herein with the aim to demonstrate that the 21st century has become the Age of Enlightenment-"Le siècle des Lumières"-in molecular sciences.

Design of photo-activated molecular machines: highlights from the past ten years

Researchers continue to generate ingenious (supra)molecular structures in which light can trigger controlled and directed movements of the components.

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

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

Theoretical modelling of the dynamics of primary photoprocess of cyclopropanone

Photodecomposition of cyclopropanone is investigated by static quantum chemical calculations and non-adiabatic molecular dynamics (NAMD) simulations.