Recent Advances and Perspectives on Nonadiabatic Mixed Quantum–Classical Dynamics

Tuning Electronic Relaxation of Nanorings Through Their Interlocking

Electronic and vibrational relaxation processes can be optimized and tuned by introducing alternative pathways that channel excess energy more efficiently. An ensemble of interacting molecular systems can help overcome the bottlenecks caused by large energy gaps between intermediate excited states involved in the relaxation process. By employing this strategy, catenanes composed of mechanically interlocked carbon nanostructures show great promise as new materials for achieving higher efficiencies in electronic devices. Herein, we perform nonadiabatic excited state molecular dynamics on different all-benzene catenanes. We observe that catenanes experience faster relaxations than individual units. Coupled catenanes present overlapping energy manifolds that include several electronic excited states spatially localized on the different moieties, increasing the density of states that ultimately improve the efficiency in the energy relaxation. This result suggests the use of catenanes as a viable strategy for tuning the internal conversion rates in a quest for their utilization for new optoelectronic applications.

SHARC meets TEQUILA: mixed quantum-classical dynamics on a quantum computer using a hybrid quantum-classical algorithm

Recent developments in quantum computing are highly promising, particularly in the realm of quantum chemistry. Due to the noisy nature of currently available quantum hardware, hybrid quantum-classical algorithms have emerged as a reliable option for near-term simulations. Mixed quantum-classical dynamics methods effectively capture nonadiabatic effects by integrating classical nuclear dynamics with quantum chemical computations of the electronic properties. However, these methods face challenges due to the high computational cost of the quantum chemistry part. To mitigate the computational demand, we propose a method where the required electronic properties are computed through a hybrid quantum-classical approach that combines classical and quantum hardware. This framework employs the variational quantum eigensolver and variational quantum deflation algorithms to obtain ground and excited state energies, gradients, nonadiabatic coupling vectors, and transition dipole moments. These quantities are used to propagate the nonadiabatic molecular dynamics using the Tully's fewest switches surface hopping method, although the implementation is also compatible with other molecular dynamics approaches. The approach, implemented by integrating the molecular dynamics program package SHARC with the TEQUILA quantum computing framework, is validated by studying the cis-trans photoisomerization of methanimine and the electronic relaxation of ethylene. The results show qualitatively accurate molecular dynamics that align with experimental findings and other computational studies. This work is expected to mark a significant step towards achieving a "quantum advantage" for realistic chemical simulations.

First-principles simulations of the fluorescence modulation of a COX-2-specific fluorogenic probe upon protein dimerization for cancer discrimination

Cyclooxygenase-2 (COX-2) plays a crucial role in inflammation and has been implicated in cancer development. Understanding the behavior of COX-2 in different cellular contexts is essential for developing targeted therapeutic strategies. In this study, we investigate the fluorescence spectrum of a fluorogenic probe, NANQ-IMC6, when bound to the active site of human COX-2 in both its monomeric and homodimeric forms. We employ a multiscale first-principles simulation protocol that combines ground state MM-MD simulations with multiple excited state adiabatic QM/MM Born-Oppenheimer MD simulations based on linear response TD-DFT, which allows to account for protein heterogeneity effects on excited-state properties. Emission is then estimated from polarizable embedding TD-DFT QM/MMPol calculations. Our findings indicate that the emission shift arises from dimerization of the highly overexpressed COX-2 in cancer tissues, in contrast to the monomer structure present in inflammatory lesions and in normal cells with constitutive COX-2. This spectral shift is linked to changes in specific protein-probe interactions upon dimerization due to changes in the environment, whereas steric effects related to modulation of the NANQ geometry by the protein scaffold are found to be minor. This research paves the way for detailed investigations on the impact of environment structural transitions on the spectral properties of fluorogenic probes. Moreover, the fact that COX-2 exists as homodimer just in cancer tissues, but as monomer elsewhere, gives novel hints for therapeutical avenues to fight cancer and contributes to the development of drugs targeted to COX-2 dimer in cancer, but without affecting constitutive COX-2, thus minimizing off-target effects.

Photoisomerization Dynamics of Azo-Escitalopram Using Surface Hopping and a Semiempirical Method

The photoisomerization dynamics of azo-escitalopram, a synthetic photoswitchable inhibitor of the human serotonin transporter, is investigated in both gas-phase and water. We use the trajectory surface hopping method─as implemented in SHARC─interfaced with the floating occupation molecular orbital-configuration interaction semiempirical method to calculate on-the-fly energies, forces, and couplings. The inclusion of explicit water molecules is enabled using an electrostatic quantum mechanics/molecular mechanics framework. We find that the photoisomerization quantum yield of trans-azo-escitalopram is wavelength- and environment-dependent, with n → π* excitation yielding higher quantum yields than π → π* excitation. Additionally, we observe the formation of two distinct cis-isomers in the photoisomerization from the most thermodynamically stable trans-isomer, with formation rates influenced by both the excitation window and the surrounding environment. We predict longer excited-state lifetimes than those reported for azobenzene, suggesting that the escitalopram moiety contributes to prolonged lifetimes and slower torsional motions.

Assessing Nonadiabatic Dynamics Methods in Long Timescales

Nonadiabatic dynamics simulations complement time-resolved experiments by revealing ultrafast excited-state mechanistic information in photochemical reactions. Understanding the relaxation mechanisms of photoexcited molecules finds application in energy, material, and medicinal research. However, with substantial computational costs, the nonadiabatic dynamics simulations have been restricted to ultrafast timescales, typically less than a few picoseconds, thus neglecting a wide range of photoactivated processes occurring in much longer timescales. Before developing new methodologies, we must ask: How well do the popular nonadiabatic dynamics methods perform in a long timescale simulation? In this study, we employ the multiconfiguration time-dependent Hartree (MCTDH) and its multilayer variants (ML-MCTDH), ab initio multiple spawning (AIMS), and fewest-switches surface hopping (FSSH) methodologies to simulate the excited-states dynamics of a weakly coupled multidimensional Spin-Boson model Hamiltonian designed for a long timescale decay behavior. Our study assures that despite having very different theoretical backgrounds, all the above methods deliver qualitatively similar results. While quantum dynamics would be very costly for long timescale simulations, the trajectory-based approaches are paving the way for future advancements.

Non-adiabatic Couplings in Surface Hopping with Tight Binding Density Functional Theory: The Case of Molecular Motors

Nonadiabatic molecular dynamics (NAMD) has become an essential computational technique for studying the photophysical relaxation of molecular systems after light absorption. These phenomena require approximations that go beyond the Born-Oppenheimer approximation, and the accuracy of the results heavily depends on the electronic structure theory employed. Sophisticated electronic methods, however, make these techniques computationally expensive, even for medium size systems. Consequently, simulations are often performed on simplified models to interpret the experimental results. In this context, a variety of techniques have been developed to perform NAMD using approximate methods, particularly density functional tight binding (DFTB). Despite the use of these techniques on large systems, where ab initio methods are computationally prohibitive, a comprehensive validation has been lacking. In this work, we present a new implementation of trajectory surface hopping combined with DFTB, utilizing nonadiabatic coupling vectors. We selected the methaniminium cation and furan systems for validation, providing an exhaustive comparison with the higher-level electronic structure methods. As a case study, we simulated a system from the class of molecular motors, which has been extensively studied experimentally but remains challenging to simulate with ab initio methods due to its inherent complexity. Our approach effectively captures the key photophysical mechanism of dihedral rotation after the absorption of light. Additionally, we successfully reproduced the transition from the bright to dark states observed in the time-dependent fluorescence experiments, providing valuable insights into this critical part of the photophysical behavior in molecular motors.

Electronic Coherences in Molecules: The Projected Nuclear Quantum Momentum as a Hidden Agent

Electronic coherences are key to understanding and controlling photoinduced molecular transformations. We identify a crucial quantum-mechanical feature of electron-nuclear correlation, the projected nuclear quantum momenta, essential to capture the correct coherence behavior. For simulations, we show that, unlike traditional trajectory-based schemes, exact-factorization-based methods approximate these correlation terms and correctly capture electronic coherences in a range of situations, including their spatial dependence, an important aspect that influences subsequent electron dynamics and that is becoming accessible in more experiments.

Theoretical elucidation of the structure, bonding, and reactivity of the CaMn4Ox clusters in the whole Kok cycle for water oxidation embedded in the oxygen evolving center of photosystem II. New molecular and quantum insights into the mechanism of the O-O bond formation

This paper reviews our historical developments of broken-symmetry (BS) and beyond BS methods that are applicable for theoretical investigations of metalloenzymes such as OEC in PSII. The BS hybrid DFT (HDFT) calculations starting from high-resolution (HR) XRD structure in the most stable S1 state have been performed to elucidate structure and bonding of whole possible intermediates of the CaMn4Ox cluster (1) in the Si (i = 0 ~ 4) states of the Kok cycle. The large-scale HDFT/MM computations starting from HR XRD have been performed to elucidate biomolecular system structures which are crucial for examination of possible water inlet and proton release pathways for water oxidation in OEC of PSII. DLPNO CCSD(T0) computations have been performed for elucidation of scope and reliability of relative energies among the intermediates by HDFT. These computations combined with EXAFS, XRD, XFEL, and EPR experimental results have elucidated the structure, bonding, and reactivity of the key intermediates, which are indispensable for understanding and explanation of the mechanism of water oxidation in OEC of PSII. Interplay between theory and experiments have elucidated important roles of four degrees of freedom, spin, charge, orbital, and nuclear motion for understanding and explanation of the chemical reactivity of 1 embedded in protein matrix, indicating the participations of the Ca(H2O)n ion and tyrosine(Yz)-O radical as a one-electron acceptor for the O-O bond formation. The Ca-assisted Yz-coupled O-O bond formation mechanisms for water oxidation are consistent with recent XES and very recent time-resolved SFX XFEL and FTIR results.

Accelerating Molecular Dynamics Simulations Using Socket-Based Interprocess Communication

Molecular dynamics (MD) simulations are essential for studying the time evolution of molecular systems. Still, their efficiency is often bottlenecked by file-based interprocess communication (IPC) between MD and electronic structure programs. We present a socket-based IPC implementation that dramatically accelerates MD simulations, reducing the computational time by >10-fold compared to those of traditional file-based methods. Our approach, applied to nonadiabatic molecular dynamics with the Newton-X program, eliminates disk read/write overhead, allowing for faster simulations over longer time scales. This method opens the door to more efficient high-throughput simulations, providing new opportunities for exploring complex molecular processes in real time.

QSLE-v1.0: A New Software Package for the Calculation of Coupled Quantum-Classical Dynamics in Condensed Phases Based on a Stochastic Approach

Recently, a stochastic version of the quantum-classical Liouville equation has been proposed [Campeggio, J.; Cortivo, R.; Zerbetto, M. J. Chem. Phys. 2023, 158, 244104], to compute the coupled quantum-classical dynamics of molecules in condensed phases. The approach, called quantum-stochastic Liouville equation (QSLE), is based on coupling the time evolution of electronic states to a stochastic description of the relevant (classical) nuclear coordinates. Natural internal coordinates are used, i.e., bond lengths, bond angles, and dihedral angles. The approach is tailored to directly propagate the populations of the electronic states over time, based on a classical Fokker-Planck equation for the nuclear degrees of freedom coupled to a master equation for the jumps among the electronic states. The QSLE is a multiscale approach requiring many ingredients to be assembled in order to carry out the numerical solution. To make the approach accessible, a software package that handles the main (and most cumbersome) details of the numerical workflow has been implemented into the software package QSLE-v1.0, which is introduced in the present paper. Here, it is considered the case of one torsional nuclear coordinate and two nonadiabatic electronic potential energy surfaces. This is a very basic model for interpreting photoisomerization or charge transfer phenomena, but despite its simplicity, it can be applied even in complex systems where the relevant quantum/classical parts affecting the phenomena under study are highly localized. A sand-box model system for describing photoisomerization processes is reported to demonstrate the usage of the software package. QSLE-v1.0 is open source and distributed under the GPLv2.0 license.

Fully Polarizable Multiconfigurational Self-Consistent Field/Fluctuating Charges Approach

A multiscale model based on the coupling of the multiconfigurational self-consistent field (MCSCF) method and the classical atomistic polarizable fluctuating charges (FQ) force field is presented. The resulting MCSCF/FQ approach is validated by exploiting the CASSCF scheme through application to compute vertical excitation energies of formaldehyde and para-nitroaniline in aqueous solution. The procedure is integrated with molecular dynamics simulations to capture the solute's conformational changes and the dynamic aspects of solvation. Comparative analysis with alternative solvent models, gas-phase calculations, and experimental data provides insights into the model's accuracy in reproducing solute-solvent molecular interactions and spectral signals.

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.

Reduced density matrix dynamics in multistate harmonic models via time-convolution and time-convolutionless quantum master equations with quantum-mechanical and semiclassical kernels

In this work, we explore the electronic reduced density matrix (RDM) dynamics using time-convolution (TC) and time-convolutionless (TCL) quantum master equations (QMEs) that are based on perturbative electronic couplings within the framework of multistate harmonic (MSH) models. The MSH model Hamiltonian consistently incorporates the electronic-vibrational correlations between all pairs of states by satisfying the pairwise reorganization energies directly obtained from all-atom simulations, representing the globally heterogeneous environments that couple to the multiple states differently. We derive the exact quantum-mechanical and a hierarchy of semiclassical approximate expressions for the kernels in TC and TCL QMEs that project the full RDM for general shifted harmonic systems, including the MSH model. These QMEs are applied to simulate RDM dynamics of photoinduced charge transfer (PICT) in organic photovoltaic carotenoid-porphyrin-fullerene triad solvated in tetrahydrofuran solution and the excitation energy transfer (EET) dynamics in photosynthetic Fenna-Matthews-Olson complexes from C. tepidum and P. aestuarii. Our results show that while both TC and TCL QMEs capture similar phenomena in PICT and EET processes, TC QME generally provides more accurate results than TCL QME, particularly in the initial oscillation of EET population dynamics. This study highlights the effectiveness of the TC and TCL QMEs in modeling RDM dynamics of nonadiabatic processes, offering insights for realistic condensed phase systems.

Fast and accurate nonadiabatic molecular dynamics enabled through variational interpolation of correlated electron wavefunctions

We build on the concept of eigenvector continuation to develop an efficient multi-state method for the rigorous and smooth interpolation of a small training set of many-body wavefunctions through chemical space at mean-field cost. The inferred states are represented as variationally optimal linear combinations of the training states transferred between the many-body bases of different nuclear geometries. We show that analytic multi-state forces and nonadiabatic couplings from the model enable application to nonadiabatic molecular dynamics, developing an active learning scheme to ensure a compact and systematically improvable training set. This culminates in application to the nonadiabatic molecular dynamics of a photoexcited 28-atom hydrogen chain, with surprising complexity in the resulting nuclear motion. With just 22 DMRG calculations of training states from the low-energy correlated electronic structure at different geometries, we infer the multi-state energies, forces and nonadiabatic coupling vectors at 12 000 geometries with provable convergence to high accuracy along an ensemble of molecular trajectories, which would not be feasible with a brute force approach. This opens up a route to bridge the timescales between accurate single-point correlated electronic structure methods and timescales of relevance for photo-induced molecular dynamics.

Simulations of photoinduced processes with the exact factorization: state of the art and perspectives

This perspective offers an overview of the applications of the exact factorization of the electron-nuclear wavefunction to the domain of theoretical photochemistry, where the aim is to gain insights into the ultrafast dynamics of molecular systems via simulations of their excited-state dynamics beyond the Born-Oppenheimer approximation. The exact factorization offers an alternative viewpoint to the Born-Huang representation for the interpretation of dynamical processes involving the electronic ground and excited states as well as their coupling through the nuclear motion. Therefore, the formalism has been used to derive algorithms for quantum molecular-dynamics simulations where the nuclear motion is treated using trajectories and the electrons are treated quantum mechanically. These algorithms have the characteristic features of being based on coupled and on auxiliary trajectories, and have shown excellent performance in describing a variety of excited-state processes, as this perspective illustrates. We conclude with a discussion on the authors' point of view on the future of the exact factorization.

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.

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.

Self-passivation of Halide Interstitial Defects by Organic Cations in Hybrid Lead-Halide Perovskites: Ab Initio Quantum Dynamics

Halide interstitial defects severely hinder the optoelectronic performance of metal halide perovskites, making research on their passivation crucial. We demonstrate, using ab initio nonadiabatic molecular dynamics simulations, that hydrogen vacancies (Hv) at both N and C atoms of the methylammonium (MA) cation in MAPbI3 efficiently passivate iodine interstitials (Ii), providing a self-passivation strategy for dealing with the Hv and Ii defects simultaneously. Hv at the N site (Hv-N) introduces a defect state into the valence band, while the state contributed by Hv at the C site (Hv-C) evolves from a shallow level at 0 K to a deep midgap state at ambient temperature, exhibiting a high environmental activity. Both Hv-N and Hv-C are strong Lewis bases, capable of capturing and passivating Ii defects. Hv-C is a stronger Lewis base, bonds with Ii better, and exhibits a more pronounced passivation effect. The charge carrier lifetimes in the passivated systems are significantly longer than in those containing either Hv or Ii, and even in pristine MAPbI3. Our demonstration of the Hv and Ii defect self-passivation in MAPbI3 suggests that systematic control of the relative concentrations of Hv and Ii can simultaneously eliminate both types of defects, thereby minimizing charge and energy losses. The demonstrated defect self-passivation strategy provides a promising means for defect control in organic-inorganic halide perovskites and related materials and deepens our atomistic understanding of defect chemistry and charge carrier dynamics in solar energy and optoelectronic materials.

Ultrafast dynamics in spatially confined photoisomerization: accelerated simulations through machine learning models

This study sheds light on the exploration of photoresponsive host-guest systems, highlighting the intricate interplay between confined spaces and photosensitive guest molecules. Conducting nonadiabatic molecular dynamics (NAMD) simulations based on electronic structure calculations for such large systems remains a formidable challenge. By leveraging machine learning (ML) as an accelerator for NAMD simulations, we analytically constructed excited-state potential energy surfaces along relevant collective variables to investigate photoisomerization processes efficiently. Combining the quantum mechanics/molecular mechanics (QM/MM) methodology with ML-based NAMD simulations, we elucidated the reaction pathways and identified the key degrees of freedom as reaction coordinates leading to conical intersections. A machine learning-based nonadiabatic dynamics model has been developed to compare the excited-state dynamics of the guest molecule, benzopyran, in both the gas phase and its behavior within the confined space of cucurbit[5]uril. This comparative analysis was designed to determine the influence of the environment on the photoisomerization rate of the guest molecule. The results underscore the effectiveness of ML models in simulating trajectory evolution in a cost-effective manner. This research offers a practical approach to accelerate NAMD simulations in large-scale systems of photochemical reactions, with potential applications in other host-guest complex systems.

Photoinduced Nonadiabatic Dynamics of a Single-Walled Carbon Nanotube-Porphyrin Complex

Single-walled carbon nanotubes (SWCNTs) have gained a lot of attention in the past few decades due to their promising optoelectronic properties. In addition, SWCNTs can form complexes that have good chemical stability and transport properties with other optical functional materials through noncovalent interactions. Elucidating the detailed mechanism of these complexes is of great significance for improving their optoelectronic properties. Nevertheless, simulating the photoinduced dynamics of these complexes accurately is rather challenging since they usually contain hundreds of atoms. To save computational efforts, most of the previous works have ignored the excitonic effects by employing nonadiabatic carrier (electron and hole) dynamics simulations. To properly consider the influence of excitonic effects on the photoinduced ultrafast processes of the SWCNT-tetraphenyl porphyrin (H2TPP) complex and to further improve the computational efficiency, we developed the nonadiabatic molecular dynamics (NAMD) method based on the extended tight binding-based simplified Tamm-Dancoff approximation (sTDA-xTB), which is applied to study the ultrafast photoinduced dynamics of the noncovalent SWCNT-porphyrin complex. In combination with statically electronic structure calculations, the present work successfully reveals the detailed microscopic mechanism of the ultrafast excitation energy transfer process of the complex. Upon local excitation on the H2TPP molecule, an ultrafast energy transfer process occurs from H2TPP (SWCNT-H2TPP*) to SWCNT (SWCNT*-H2TPP) within 10 fs. Then, two slower processes corresponding to the energy transfer from H2TPP to SWCNT and hole transfer from H2TPP to SWCNT take place in the 1 ps time scale. The sTDA-xTB-based electronic structure calculation and NAMD simulation results not only match the previous experimental observations from static and transient spectra but also provide more insights into the detailed information on the complex's photoinduced dynamics. Therefore, the sTDA-xTB-based NAMD method is a powerful theoretical tool for studying the ultrafast photoinduced dynamics in large extended systems with a large number of electronically excited states, which could be helpful for the subsequent design of SWCNT-based functional materials.

AtmoSpec-A Tool to Calculate Photoabsorption Cross-Sections for Atmospheric Volatile Organic Compounds

Characterizing the photolysis processes undergone by transient volatile organic compounds (VOCs) in the troposphere requires the knowledge of their photoabsorption cross-section-quantities often challenging to determine experimentally, particularly due to the reactivity of these molecules. We present a computational tool coined AtmoSpec, which can predict a quantitative photoabsorption cross-section for volatile organic compounds by using computational photochemistry. The user enters the molecule of interest as a SMILES code and, after selecting a level of theory for the electronic structure (and waiting for the calculations to take place), is presented with a photoabsorption cross-section for the low-energy conformers and an estimate of the photolysis rate coefficient for different standardized actinic fluxes. More specifically, AtmoSpec is an automated workflow for the nuclear ensemble approach, an efficient technique to approximate the absolute intensities and excitation wavelengths of a photoabsorption cross-section for a molecule in the gas phase of interest in atmospheric chemistry and astrochemistry. This work provides background information on the nuclear ensemble approach, a guided example of a typical AtmoSpec calculation, details about the architecture of the code, and the current limitations and future developments of this tool.

Unsupervised Machine Learning in the Analysis of Nonadiabatic Molecular Dynamics Simulation

The all-atomic full-dimensional-level simulations of nonadiabatic molecular dynamics (NAMD) in large realistic systems has received high research interest in recent years. However, such NAMD simulations normally generate an enormous amount of time-dependent high-dimensional data, leading to a significant challenge in result analyses. Based on unsupervised machine learning (ML) methods, considerable efforts were devoted to developing novel and easy-to-use analysis tools for the identification of photoinduced reaction channels and the comprehensive understanding of complicated molecular motions in NAMD simulations. Here, we tried to survey recent advances in this field, particularly to focus on how to use unsupervised ML methods to analyze the trajectory-based NAMD simulation results. Our purpose is to offer a comprehensive discussion on several essential components of this analysis protocol, including the selection of ML methods, the construction of molecular descriptors, the establishment of analytical frameworks, their advantages and limitations, and persistent challenges.

Machine Learning-Assisted Mixed Quantum-Classical Dynamics without Explicit Nonadiabatic Coupling: Application to the Photodissociation of Peroxynitric Acid

We have devised a hybrid quantum-classical scheme utilizing machine-learned potential energy surfaces (PES), which circumvents the need for explicit computation of nonadiabatic coupling elements. The quantities necessary to account for the nonadiabatic effects are directly obtained from the PESs. The simulation of dynamics is based on the fewest-switches surface-hopping method. We applied this scheme to model the photodissociation of both N-O and O-O bonds in a conformer of peroxynitric acid (HO2NO2). Adiabatic PES data for the six lowest states of this molecule were computed at the CASSCF level for various nuclear configurations. These served as the training data for the machine-learning models for the PESs. The dynamics simulation was initiated on the lowest optically bright singlet excited state (S4) and propagated along the two Jacobi coordinates J → 1 and J → 2 while accounting for the nonadiabatic effects through transitions between PESs. Our analysis revealed that there is a very high chance of dissociation of the N-O bond leading to the HO2 and NO2 fragments.

Nonadiabatic Hydrogen Tunneling Dynamics for Multiple Proton Transfer Processes with Generalized Nuclear-Electronic Orbital Multistate Density Functional Theory

Proton transfer and hydrogen tunneling play key roles in many processes of chemical and biological importance. The generalized nuclear-electronic orbital multistate density functional theory (NEO-MSDFT) method was developed in order to capture hydrogen tunneling effects in systems involving the transfer and tunneling of one or more protons. The generalized NEO-MSDFT method treats the transferring protons quantum mechanically on the same level as the electrons and obtains the delocalized vibronic states associated with hydrogen tunneling by mixing localized NEO-DFT states in a nonorthogonal configuration interaction scheme. Herein, we present the derivation and implementation of analytical gradients for the generalized NEO-MSDFT vibronic state energies and the nonadiabatic coupling vectors between these vibronic states. We use this methodology to perform adiabatic and nonadiabatic dynamics simulations of the double proton transfer reactions in the formic acid dimer and the heterodimer of formamidine and formic acid. The generalized NEO-MSDFT method is shown to capture the strongly coupled synchronous or asynchronous tunneling of the two protons in these processes. Inclusion of vibronically nonadiabatic effects is found to significantly impact the double proton transfer dynamics. This work lays the foundation for a variety of nonadiabatic dynamics simulations of multiple proton transfer systems, such as proton relays and hydrogen-bonding networks.

Singlet Oxygen Photophysics: From Liquid Solvents to Mammalian Cells

Molecular oxygen, O2, has long provided a cornerstone for studies in chemistry, physics, and biology. Although the triplet ground state, O2(X3Σg-), has garnered much attention, the lowest excited electronic state, O2(a1Δg), commonly called singlet oxygen, has attracted appreciable interest, principally because of its unique chemical reactivity in systems ranging from the Earth's atmosphere to biological cells. Because O2(a1Δg) can be produced and deactivated in processes that involve light, the photophysics of O2(a1Δg) are equally important. Moreover, pathways for O2(a1Δg) deactivation that regenerate O2(X3Σg-), which address fundamental principles unto themselves, kinetically compete with the chemical reactions of O2(a1Δg) and, thus, have practical significance. Due to technological advances (e.g., lasers, optical detectors, microscopes), data acquired in the past ∼20 years have increased our understanding of O2(a1Δg) photophysics appreciably and facilitated both spatial and temporal control over the behavior of O2(a1Δg). One goal of this Review is to summarize recent developments that have broad ramifications, focusing on systems in which oxygen forms a contact complex with an organic molecule M (e.g., a liquid solvent). An important concept is the role played by the M+•O2-• charge-transfer state in both the formation and deactivation of O2(a1Δg).

Simulation of the non-adiabatic dynamics of an enone-Lewis acid complex in an explicit solvent

Unlocking the full potential of Lewis acid catalysis for photochemical transformations requires a comprehensive understanding of the ultrafast dynamics of substrate-Lewis acid complexes. In a previous article [Peschel et al., Angew. Chem. Int. Ed., 2021, 60, 10155], time-resolved spectroscopy supported by static calculations revealed that the Lewis acid remains attached during the relaxation of the model complex cyclohexenone-BF3. In contrast to the experimental observation, surface-hopping dynamics in the gas phase predicted ultrafast heterolytic dissociation. We attributed the discrepancy to missing solvent interactions. Thus, in this work, we present an interface between the SHARC and FermiONs++ program packages, which enables us to investigate the ultrafast dynamics of cyclohexenone-BF3 in an explicit solvent environment. Our simulations demonstrate that the solvent prevents the dissociation of the complex, leading to an intriguing dissociation-reassociation mechanism. Comparing the dynamics with and without triplet states highlights their role in the relaxation process and shows that the Lewis acid inhibits intersystem crossing. These findings provide a clear picture of the relaxation process, which may aid in designing future Lewis acid catalysts for photochemical applications. They underscore that an explicit solvent model is required to describe relaxation processes in weakly bound states, as energy transfer to the solvent is crucial for the system to reach its minimum geometries.

Interconnection between Polarization-Detected and Population-Detected Signals: Theoretical Results and Ab Initio Simulations

Most of spectroscopic signals are specified by the nonlinear laser-induced polarization. In recent years, population-detection of signals becomes a trend in femtosecond spectroscopy. Polarization-detected (PD) and population-detected signals are fundamentally different, because they are determined by photoinduced processes acting on disparate time scales. In this work, we consider the fluorescence-detected (FD) N-wave-mixing (NWM) signal as a representative example of population-detected signals, derive a rigorous expression for this signal, and discuss its approximate variants suitable for numerical simulations. This leads us to the definition of the phenomenological FD (PFD) signal, which contains as a special case all definitions of FD signals available in the literature. Then we formulate and prove the population-polarization equivalence (PPE) theorem, which states that PFD NWM signals produced by (possibly strong) laser pulses can be evaluated as conventional PD signals in which the effective polarization is determined by the PFD transition dipole moment operator. We use the PPE theorem for the construction of the ab initio protocol for the simulation of PFD 4WM signals. As an example, we calculate electronic two-dimensional (2D) PFD spectra of the gas-phase pyrazine and compare them with the corresponding PD 2D spectra.

Semiclassical dynamics in Wigner phase space II: Nonadiabatic hybrid Wigner dynamics

We present an approximate semiclassical (SC) framework for mixed quantized dynamics in Wigner phase space in a two-part series. In the first article, we introduced the Adiabatic Hybrid Wigner Dynamics (AHWD) method that allows for a few important "system" degrees of freedom to be quantized using high-level double Herman-Kluk SC theory while describing the rest (the "bath") using classical-limit linearized SC theory. In this second article, we extend our hybrid Wigner dynamics to nonadiabatic processes. The resulting Nonadiabatic Hybrid Wigner Dynamics (NHWD) has two variants that differ in the choice of degrees of freedom to be quantized. Specifically, we introduce NHWD(E) where only the electronic state variables are quantized and the NHWD(V) where both electronic state variables and a handful of strongly coupled nuclear modes are quantized. We show that while NHWD(E) proves accurate for a wide range of scattering models and spin-boson models, systems where a few nuclear modes are strongly coupled to electronic states require NHWD(V) to accurately capture the long-time dynamics. Taken together, we show that AHWD and NHWD represent a new framework for SC simulations of high-dimensional systems with significant quantum effects.

Discriminating Clockwise and Counterclockwise Photoisomerization Paths in Achiral Photoswitches by Excited-State Electronic Circular Dichroism

Despite the numerous investigations of photoisomerization reactions from both the computational and experimental points of view, even in complex environments, to date there is no direct demonstration of the direction of rotation of the retinal chromophore, initiating the vision process in several organisms, occurring upon light irradiation. In the literature, many proposals have been formulated to shed light on the details of this process, most of which are extracted from semiclassical simulations. Although high hopes are held in the development of time-resolved X-ray spectroscopy, I argue in this work that simpler but less known techniques can be used to unravel the details of this fascinating photochemical process. In fact, chiroptical spectroscopy would unambiguously prove the direction of the rotatory motion of the chromophore during the photoisomerization process by probing excited state chirality, a piece of information that, so far, has been exclusively extracted from atomistic simulations. I demonstrate this statement by computing the expected chiroptical response along photoisomerization pathways for several models of the retinal chromophores that are found in nature bound to rhodopsins, including nuclear ensemble spectra from semiclassical dynamics simulations, that can be compared with time-resolved experiments.

Quantum Dynamics from Classical Trajectories

Nonadiabatic molecular dynamics plays an essential role in exploring the time evolution of molecular systems. Various methods have been developed for this study, with varying accuracy and computational cost. One very successful among them is trajectory surface hopping, which propagates nuclei as classical trajectories using forces from a quantum description of the electrons and incorporates nonadiabatic effects through stochastic state changes during each trajectory propagation. A statistical analysis of an ensemble of the independent trajectories recovers the simulated system's behavior. This approach can give good results, but it is known to overlook nuclear quantum effects, leading to inaccurate predictions. Here, we present quantum dynamics from classical trajectories (QDCT), a new protocol to recover the quantum wavepacket from the classical trajectories generated by surface hopping. In this first QDCT implementation, we apply it to recover results at the multiple spawning level from postprocessing surface hopping precomputed trajectories. With a series of examples, we demonstrate QDCT's potential to improve the accuracy of the dynamics, correct decoherence effects, and diagnose problems or increase confidence in surface hopping results. All that comes at virtually no computational cost since no new electronic calculation is required.

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.

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.

Transient-absorption spectroscopy of dendrimers via nonadiabatic excited-state dynamics simulations

The efficiency of light-harvesting and energy transfer in multi-chromophore ensembles underpins natural photosynthesis. Dendrimers are highly branched synthetic multi-chromophoric conjugated supra-molecules that mimic these natural processes. After photoexcitation, their repeated units participate in a number of intramolecular electronic energy relaxation and redistribution pathways that ultimately funnel to a sink. Here, a model four-branched dendrimer with a pyrene core is theoretically studied using nonadiabatic molecular dynamics simulations. We evaluate excited-state photoinduced dynamics of the dendrimer, and demonstrate on-the-fly simulations of its transient absorption pump-probe (TA-PP) spectra. We show how the evolutions of the simulated TA-PP spectra monitor in real time photoinduced energy relaxation and redistribution, and provide a detailed microscopic picture of the relevant energy-transfer pathways. To the best of our knowledge, this is the first of this kind of on-the-fly atomistic simulation of TA-PP signals reported for a large molecular system.

Perspective on Theoretical and Experimental Advances in Atmospheric Photochemistry

Research that explores the chemistry of Earth's atmosphere is central to the current understanding of global challenges such as climate change, stratospheric ozone depletion, and poor air quality in urban areas. This research is a synergistic combination of three established domains: earth observation, for example, using satellites, and in situ field measurements; computer modeling of the atmosphere and its chemistry; and laboratory measurements of the properties and reactivity of gas-phase molecules and aerosol particles. The complexity of the interconnected chemical and photochemical reactions which determine the composition of the atmosphere challenges the capacity of laboratory studies to provide the spectroscopic, photochemical, and kinetic data required for computer models. Here, we consider whether predictions from computational chemistry using modern electronic structure theory and nonadiabatic dynamics simulations are becoming sufficiently accurate to supplement quantitative laboratory data for wavelength-dependent absorption cross-sections, photochemical quantum yields, and reaction rate coefficients. Drawing on presentations and discussions from the CECAM workshop on Theoretical and Experimental Advances in Atmospheric Photochemistry held in March 2024, we describe key concepts in the theory of photochemistry, survey the state-of-the-art in computational photochemistry methods, and compare their capabilities with modern experimental laboratory techniques. From such considerations, we offer a perspective on the scope of computational (photo)chemistry methods based on rigorous electronic structure theory to become a fourth core domain of research in atmospheric chemistry.

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.

Analogies and Differences in the Photoactivation Mechanism of Bathy and Canonical Bacteriophytochromes Revealed by Multiscale Modeling

Bacteriophytochromes are light-sensing biological machines that switch between two photoreversible states, Pr and Pfr. Their relative stability is opposite in canonical and bathy bacteriophytochromes, but in both cases the switch between them is triggered by the photoisomerization of an embedded bilin chromophore. We applied an integrated multiscale strategy of excited-state QM/MM nonadiabatic dynamics and (QM/)MM molecular dynamics simulations with enhanced sampling techniques to the Agrobacterium fabrum bathy phytochrome and compared the results with those obtained for the canonical phytochrome Deinococcus radiodurans. Contrary to what recently suggested, we found that photoactivation in both phytochromes is triggered by the same hula-twist motion of the bilin chromophore. However, only in the bathy phytochrome, the bilin reaches the final rotated structure already in the first intermediate. This allows a reorientation of the binding pocket in a microsecond time scale, which can propagate through the entire protein causing the spine to tilt.

Gravitationally-induced wave function collapse time for molecules

The Diósi-Penrose model states that the wave function collapse ending a quantum superposition occurs due to the instability of coexisting gravitational potentials created by distinct geometric conformations of the system in different states. The Heisenberg time-energy principle can be invoked to estimate the collapse time for the energy associated with this instability, the gravitational self-energy. This paper develops atomistic models to calculate the Diósi-Penrose collapse time. It applies them to a range of systems, from small molecules to large biological structures and macroscopic systems. An experiment is suggested to test the Diósi-Penrose hypothesis, and we critically examine the model, highlighting challenges from an atomistic perspective, such as gravitational self-energy saturation and limited extensivity.

Mixed quantum-classical modeling of exciton-phonon scattering in solids: Application to optical linewidths of monolayer MoS2

We present a mixed quantum-classical framework for the microscopic and non-Markovian modeling of exciton-phonon scattering in solid-state materials and apply it to calculate the optical linewidths of monolayer MoS2. Within this framework, we combine reciprocal-space mixed quantum-classical dynamics with models for the quasiparticle band structure as well as the electron-hole and carrier-phonon interactions, parametrized against ab initio calculations, although noting that a direct interfacing with ab initio calculations is straightforward in principle. We introduce various parameters for truncating the Brillouin zone to select regions of interest. Variations of these parameters allow us to determine linewidths in the limit of asymptotic material sizes. The obtained asymptotic linewidths are found to agree favorably with experimental measurements across a range of temperatures. As such, our framework establishes itself as a promising route toward unraveling the non-Markovian and microscopic principles governing the nonadiabatic dynamics of solids.

A Multipronged Bioengineering, Spectroscopic and Theoretical Approach in Unravelling the Excited-State Dynamics of the Archetype Mycosporine Amino Acid

Mycosporine glycine (MyG) was produced by the fermentation of a purposely engineered bacterial strain and isolated from this sustainable source. The ultrafast spectroscopy of MyG was then investigated in its native, zwitterionic form (MyGzwitter), via femtosecond transient electronic absorption spectroscopy. Complementary nonadiabatic (NAD) simulations suggest that, upon photoexcitation to the lowest excited singlet state (S1), MyGzwitter undergoes efficient nonradiative decay to repopulate the electronic ground state (S0). We propose an initial ultrafast ring-twisting mechanism toward an S1/S0 conical intersection, followed by internal conversion to S0 and subsequent vibrational cooling. This study illuminates the workings of the archetype mycosporine, providing photoprotection, in the UV-B range, to organisms such as corals, macroalgae, and cyanobacteria. This study also contributes to our growing understanding of the photoprotection mechanisms of life.

Ultrafast Excited-State Energy Transfer in Phenylene Ethynylene Dendrimer: Quantum Dynamics with the Tensor Network Method

Photoinduced excited-state energy transfer (EET) processes play an important role in solar energy conversions. Owing to their excellent photoharvesting and exciton-transport properties, phenylene ethynylene (PE) dendrimers display great potential for improving the efficiency of solar cells. In this work, we investigated the intramolecular EET dynamics in a dendrimer composed of two linear PE units (2-ring and 3-ring) using a fully quantum description based on the tensor network method. We first constructed a diabatic model Hamiltonian based on the electronic structure calculations. Using this diabatic vibronic coupling model, we tried to obtain the main features of the EET dynamics in terms of the several diabatic models with different numbers of vibrational modes (from 4 modes to 129 modes) and to explore the corresponding vibronic coupling interactions. The results show that the EET in this PE dendrimer is ultrafast. Four modes of A' symmetry play dominant roles in the dynamics; the remaining 86 modes of A' symmetry can dampen the electronic coherence; and the modes of A″ symmetry do not exhibit significant influence on the EET process. Overall, the first-order intrastate vibronic coupling terms show the dominant role in the EET dynamics, while the second-order intrastate vibronic coupling terms cause damping of the electronic coherence and slow down the overall EET process. This work provides a microscopic understanding of the EET dynamics in PE dendrimers.

Ultrafast Photoinduced Dynamics in 1,3-Cyclohexadiene: A Comparison of Trajectory Surface Hopping Schemes†

Photoinduced nonadiabatic processes play a crucial role in a wide range of disciplines, from fundamental steps in biology to modern applications in advanced materials science. A theoretical understanding of these processes is highly desirable, and trajectory surface hopping (TSH) has proven to be a well-suited framework for a wide range of systems. In this work, we present a comprehensive comparison between two TSH algorithms, the conventional Tully's fewest switches surface hopping (FSSH) scheme and the Landau-Zener surface hopping (LZSH), to study the photoinduced ring-opening of 1,3-cyclohexadiene (CHD) to 1,3,5-hexatriene at the spin-flip time-dependent density functional theory (SF-TDDFT) level of theory. Additionally, we compare our results with a literature study at the extended multistate complete active space second-order perturbation theory method (XMS-CASPT2) level of theory. Our results show that the average population and lifetimes estimated with LZSH using SF-TDDFT are closer to the literature (using multireference methods) than those estimated with FSSH using SF-TDDFT. The latter speaks in favor of applying LZSH in combination with the SF-TDDFT method to study larger and more complex systems such as molecular photoswitches where the CHD molecule acts as a backbone. In addition, we present an implementation of Tully's FSSH algorithm as an extension to the PySurf software package.

Mixed Quantum-Classical Dynamics under Arbitrary Unitary Basis Transformations

A common approach to minimizing the cost of quantum computations is by unitarily transforming a quantum system into a basis that can be optimally truncated. Here, we derive classical equations of motion subjected to similar unitary transformations and propose their integration into mixed quantum-classical dynamics, allowing this class of methods to be applied within arbitrary bases for both the quantum and classical coordinates. To this end, canonical positions and momenta of the classical degrees of freedom are combined into a set of complex-valued coordinates amenable to unitary transformations. We demonstrate the potential of the resulting approach by means of surface hopping calculations of an electronic carrier scattering onto a single impurity in the presence of phonons. Appropriate basis transformations, capturing both the localization of the impurity and the delocalization of higher-energy excitations, are shown to faithfully capture the dynamics within a fraction of the classical and quantum basis sets.

Mean-Field Ring Polymer Rates Using a Population Dividing Surface

Mean-field ring polymer molecular dynamics offers a computationally efficient method for the simulation of reaction rates in multilevel systems. Previous work has established that, to model a nonadiabatic state-to-state reaction accurately, it is necessary to ensure reactive trajectories form kinked ring polymer configurations at the dividing surface. Building on this idea, we introduce a population difference coordinate and a reactive flux expression modified to only include contributions from kinked configurations. We test the accuracy of the resulting mean-field rate theory on a series of linear vibronic coupling model systems. We demonstrate that this new kMF-RP rate approach is efficient to implement and quantitatively accurate for models over a wide range of driving forces, coupling strengths, and temperatures.

Non-adiabatic molecular dynamics simulations provide new insights into the exciton transfer in the Fenna-Matthews-Olson complex

A trajectory surface hopping approach, which uses machine learning to speed up the most time-consuming steps, has been adopted to investigate the exciton transfer in light-harvesting systems. The present neural networks achieve high accuracy in predicting both Coulomb couplings and excitation energies. The latter are predicted taking into account the environment of the pigments. Direct simulation of exciton dynamics through light-harvesting complexes on significant time scales is usually challenging due to the coupled motion of nuclear and electronic degrees of freedom in these rather large systems containing several relatively large pigments. In the present approach, however, we are able to evaluate a statistically significant number of non-adiabatic molecular dynamics trajectories with respect to exciton delocalization and exciton paths. The formalism is applied to the Fenna-Matthews-Olson complex of green sulfur bacteria, which transfers energy from the light-harvesting chlorosome to the reaction center with astonishing efficiency. The system has been studied experimentally and theoretically for decades. In total, we were able to simulate non-adiabatically more than 30 ns, sampling also the relevant space of parameters within their uncertainty. Our simulations show that the driving force supplied by the energy landscape resulting from electrostatic tuning is sufficient to funnel the energy towards site 3, from where it can be transferred to the reaction center. However, the high efficiency of transfer within a picosecond timescale can be attributed to the rather unusual properties of the BChl a molecules, resulting in very low inner and outer-sphere reorganization energies, not matched by any other organic molecule, e.g., used in organic electronics. A comparison with electron and exciton transfer in organic materials is particularly illuminating, suggesting a mechanism to explain the comparably high transfer efficiency.

Benchmarking various nonadiabatic semiclassical mapping dynamics methods with tensor-train thermo-field dynamics

Accurate quantum dynamics simulations of nonadiabatic processes are important for studies of electron transfer, energy transfer, and photochemical reactions in complex systems. In this comparative study, we benchmark various approximate nonadiabatic dynamics methods with mapping variables against numerically exact calculations based on the tensor-train (TT) representation of high-dimensional arrays, including TT-KSL for zero-temperature dynamics and TT-thermofield dynamics for finite-temperature dynamics. The approximate nonadiabatic dynamics methods investigated include mixed quantum-classical Ehrenfest mean-field and fewest-switches surface hopping, linearized semiclassical mapping dynamics, symmetrized quasiclassical dynamics, the spin-mapping method, and extended classical mapping models. Different model systems were evaluated, including the spin-boson model for nonadiabatic dynamics in the condensed phase, the linear vibronic coupling model for electronic transition through conical intersections, the photoisomerization model of retinal, and Tully's one-dimensional scattering models. Our calculations show that the optimal choice of approximate dynamical method is system-specific, and the accuracy is sensitively dependent on the zero-point-energy parameter and the initial sampling strategy for the mapping variables.

Non-adiabatic dynamics of photoexcited cyclobutanone: Predicting structural measurements from trajectory surface hopping with XMS-CASPT2 simulations

Over the years, theoretical calculations and scalable computer simulations have complemented ultrafast experiments, as they offer the advantage of overcoming experimental restrictions and having access to the whole dynamics. This synergy between theory and experiment promises to yield a deeper understanding of photochemical processes, offering valuable insights into the behavior of complex systems at the molecular level. However, the ability of theoretical models to predict ultrafast experimental outcomes has remained largely unexplored. In this work, we aim to predict the electron diffraction signals of an upcoming ultrafast photochemical experiment using high-level electronic structure calculations and non-adiabatic dynamics simulations. In particular, we perform trajectory surface hopping with extended multi-state complete active space with second order perturbation simulations for understanding the photodissociation of cyclobutanone (CB) upon excitation at 200 nm. Spin-orbit couplings are considered for investigating the role of triplet states. Our simulations capture the bond cleavage after ultrafast relaxation from the 3s Rydberg state, leading to the formation of the previously observed primary photoproducts: CO + cyclopropane/propene (C3 products), ketene, and ethene (C2 products). The ratio of the C3:C2 products is found to be about 1:1. Within 700 fs, the majority of trajectories transition to their electronic ground state, with a small fraction conserving the initial cyclobutanone ring structure. We found a minimal influence of triplet states during the early stages of the dynamics, with their significance increasing at later times. We simulate MeV-ultrafast electron diffraction (UED) patterns from our trajectory results, linking the observed features with specific photoproducts and the underlying structural dynamics. Our analysis reveals highly intense features in the UED signals corresponding to the photochemical processes of CB. These features offer valuable insights into the experimental monitoring of ring opening dynamics and the formation of C3 and C2 photoproducts.

Complex Fluid Models of Mixed Quantum-Classical Dynamics

Several methods in nonadiabatic molecular dynamics are based on Madelung's hydrodynamic description of nuclear motion, while the electronic component is treated as a finite-dimensional quantum system. In this context, the quantum potential leads to severe computational challenges and one often seeks to neglect its contribution, thereby approximating nuclear motion as classical. The resulting model couples classical hydrodynamics for the nuclei to the quantum motion of the electronic component, leading to the structure of a complex fluid system. This type of mixed quantum-classical fluid models has also appeared in solvation dynamics to describe the coupling between liquid solvents and the quantum solute molecule. While these approaches represent a promising direction, their mathematical structure requires a certain care. In some cases, challenging higher-order gradients make these equations hardly tractable. In other cases, these models are based on phase-space formulations that suffer from well-known consistency issues. Here, we present a new complex fluid system that resolves these difficulties. Unlike common approaches, the current system is obtained by applying the fluid closure at the level of the action principle of the original phase-space model. As a result, the system inherits a Hamiltonian structure and retains energy/momentum balance. After discussing some of its structural properties and dynamical invariants, we illustrate the model in the case of pure-dephasing dynamics. We conclude by presenting some invariant planar models.

Prediction of photodynamics of 200 nm excited cyclobutanone with linear response electronic structure and ab initio multiple spawning

Simulations of photochemical reaction dynamics have been a challenge to the theoretical chemistry community for some time. In an effort to determine the predictive character of current approaches, we predict the results of an upcoming ultrafast diffraction experiment on the photodynamics of cyclobutanone after excitation to the lowest lying Rydberg state (S2). A picosecond of nonadiabatic dynamics is described with ab initio multiple spawning. We use both time dependent density functional theory (TDDFT) and equation-of-motion coupled cluster singles and doubles (EOM-CCSD) theory for the underlying electronic structure theory. We find that the lifetime of the S2 state is more than a picosecond (with both TDDFT and EOM-CCSD). The predicted ultrafast electron diffraction spectrum exhibits numerous structural features, but weak time dependence over the course of the simulations.

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.

MLatom Software Ecosystem for Surface Hopping Dynamics in Python with Quantum Mechanical and Machine Learning Methods

We present an open-source MLatom@XACS software ecosystem for on-the-fly surface hopping nonadiabatic dynamics based on the Landau-Zener-Belyaev-Lebedev algorithm. The dynamics can be performed via Python API with a wide range of quantum mechanical (QM) and machine learning (ML) methods, including ab initio QM (CASSCF and ADC(2)), semiempirical QM methods (e.g., AM1, PM3, OMx, and ODMx), and many types of ML potentials (e.g., KREG, ANI, and MACE). Combinations of QM and ML methods can also be used. While the user can build their own combinations, we provide AIQM1, which is based on Δ-learning and can be used out-of-the-box. We showcase how AIQM1 reproduces the isomerization quantum yield of trans-azobenzene at a low cost. We provide example scripts that, in dozens of lines, enable the user to obtain the final population plots by simply providing the initial geometry of a molecule. Thus, those scripts perform geometry optimization, normal mode calculations, initial condition sampling, parallel trajectories propagation, population analysis, and final result plotting. Given the capabilities of MLatom to be used for training different ML models, this ecosystem can be seamlessly integrated into the protocols building ML models for nonadiabatic dynamics. In the future, a deeper and more efficient integration of MLatom with Newton-X will enable a vast range of functionalities for surface hopping dynamics, such as fewest-switches surface hopping, to facilitate similar workflows via the Python API.