Ab Initio Nonadiabatic Quantum Molecular Dynamics

Efficient time-dependent vibrational coupled cluster computations with time-dependent basis sets at the two-mode coupling level: Full and hybrid TDMVCC[2]

The computation of the nuclear quantum dynamics of molecules is challenging, requiring both accuracy and efficiency to be applicable to systems of interest. Recently, theories have been developed for employing time-dependent basis functions (denoted modals) with vibrational coupled cluster theory (TDMVCC). The TDMVCC method was introduced along with a pilot implementation, which illustrated good accuracy in benchmark computations. In this paper, we report an efficient implementation of TDMVCC, covering the case where the wave function and Hamiltonian contain up to two-mode couplings. After a careful regrouping of terms, the wave function can be propagated with a cubic computational scaling with respect to the number of degrees of freedom. We discuss the use of a restricted set of active one-mode basis functions for each mode, as well as two interesting limits: (i) the use of a full active basis where the variational modal determination amounts essentially to the variational determination of a time-dependent reference state for the cluster expansion; and (ii) the use of a single function as an active basis for some degrees of freedom. The latter case defines a hybrid TDMVCC/TDH (time-dependent Hartree) approach that can obtain even lower computational scaling. The resulting computational scaling for hybrid and full TDMVCC[2] is illustrated for polyaromatic hydrocarbons with up to 264 modes. Finally, computations on the internal vibrational redistribution of benzoic acid (39 modes) are used to show the faster convergence of TDMVCC/TDH hybrid computations towards TDMVCC compared to simple neglect of some degrees of freedom.

Twisting Aromaticity and Photoinduced Dynamics in Hexapole Helicenes

Curved aromatic molecules are attractive electronic materials, where an additional internal strain uniquely modifies their structure, aromaticity, dynamics, and optical properties. Helicenes are examples of such twisted conjugated systems. Herein, we analyze the photoinduced dynamics in different stereoisomers of a hexapole helicene by using nonadiabatic excited-state molecular dynamics simulations. We explore how changes in symmetry and structural distortion modulate the intramolecular energy redistribution. We find that distinct helical assembly leads to different rigid distorted structures that in turn impact the nonradiative energy relaxation and ultimately formation of the self-trapped exciton. Subsequently, the value of the twisting angles relative to the central triphenylene core structure controls the global molecular aromaticity and electronic localization during the internal conversion process. Our work sheds light on how the future synthesis of novel curved aromatic compounds can be directed to attain specific desired electronic properties through the modulation of their twisted aromaticity.

Analytical nonadiabatic coupling and state-specific energy gradient for the crystal field Hamiltonian describing lanthanide single-ion magnets

Paramagnetic molecules with a metal ion as an electron spin center are promising building blocks for molecular qubits and high-density memory arrays. However, fast spin relaxation and decoherence in these molecules lead to a rapid loss of magnetization and quantum information. Nonadiabatic coupling (NAC), closely related to spin-vibrational coupling, is the main source of spin relaxation and decoherence in paramagnetic molecules at higher temperatures. Predicting these couplings using numerical differentiation requires a large number of computationally intensive ab initio or crystal field electronic structure calculations. To reduce computational cost and improve accuracy, we derive and implement analytical NAC and state-specific energy gradient for the ab initio parametrized crystal field Hamiltonian describing single-ion molecular magnets. Our implementation requires only a single crystal field calculation. In addition, the accurate NACs and state-specific energy gradients can be used to model spin relaxation using sophisticated nonadiabatic molecular dynamics, which avoids the harmonic approximation for molecular vibrations. To test our implementation, we calculate the NAC values for three lanthanide complexes. The predicted values support the relaxation mechanisms reported in previous studies.

The carbonyl-lock mechanism underlying non-aromatic fluorescence in biological matter

Challenging the basis of our chemical intuition, recent experimental evidence reveals the presence of a new type of intrinsic fluorescence in biomolecules that exists even in the absence of aromatic or electronically conjugated chemical compounds. The origin of this phenomenon has remained elusive so far. In the present study, we identify a mechanism underlying this new type of fluorescence in different biological aggregates. By employing non-adiabatic ab initio molecular dynamics simulations combined with a data-driven approach, we characterize the typical ultrafast non-radiative relaxation pathways active in non-fluorescent peptides. We show that the key vibrational mode for the non-radiative decay towards the ground state is the carbonyl elongation. Non-aromatic fluorescence appears to emerge from blocking this mode with strong local interactions such as hydrogen bonds. While we cannot rule out the existence of alternative non-aromatic fluorescence mechanisms in other systems, we demonstrate that this carbonyl-lock mechanism for trapping the excited state leads to the fluorescence yield increase observed experimentally, and set the stage for design principles to realize novel non-invasive biocompatible probes with applications in bioimaging, sensing, and biophotonics.

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.

What is Missing in the Mean Field Description of Spatial Distribution of Population? Important Role of Auxiliary Wave Packets in Trajectory Branching

When the traditional Ehrenfest mean field approach is employed to simulate nonadiabatic dynamics, an effective wave packet (WP) on the average potential energy surface (PES) is utilized to describe the nuclear motion. In the fully quantum picture, however, the WP components on different adiabatic PESs gradually separate in space because they evolve under different velocities and forces. Due to trajectory branching of the WP components, proper decoherence needs to be taken into account, and the spatial distribution of population cannot be described by a single effective WP. Here, we propose an auxiliary branching corrected mean field (A-BCMF) method, where trajectories of auxiliary WPs on adiabatic PESs are introduced. As benchmarked in the three standard Tully models, A-BCMF not only gives correct channel populations but also captures an accurate time-dependent spatial distribution of population. Thereby, we reveal the important role of auxiliary WPs in solving intrinsic problems of the widely used mean field description of nonadiabatic dynamics.

Advances in Computational Approaches for Estimating Passive Permeability in Drug Discovery

Passive permeation of cellular membranes is a key feature of many therapeutics. The relevance of passive permeability spans all biological systems as they all employ biomembranes for compartmentalization. A variety of computational techniques are currently utilized and under active development to facilitate the characterization of passive permeability. These methods include lipophilicity relations, molecular dynamics simulations, and machine learning, which vary in accuracy, complexity, and computational cost. This review briefly introduces the underlying theories, such as the prominent inhomogeneous solubility diffusion model, and covers a number of recent applications. Various machine-learning applications, which have demonstrated good potential for high-volume, data-driven permeability predictions, are also discussed. Due to the confluence of novel computational methods and next-generation exascale computers, we anticipate an exciting future for computationally driven permeability predictions.

LVC/MM: A Hybrid Linear Vibronic Coupling/Molecular Mechanics Model with Distributed Multipole-Based Electrostatic Embedding for Highly Efficient Surface Hopping Dynamics in Solution

We present a theoretical framework for a hybrid linear vibronic coupling model electrostatically embedded into a molecular mechanics environment, termed the linear vibronic coupling/molecular mechanics (LVC/MM) method, for the surface hopping including arbitrary coupling (SHARC) molecular dynamics package. Electrostatic embedding is realized through the computation of interactions between environment point charges and distributed multipole expansions (DMEs, up to quadrupoles) that represent each electronic state and transition densities in the diabatic basis. The DME parameters are obtained through a restrained electrostatic potential (RESP) fit, which we extended to yield higher-order multipoles. We also implemented in SHARC a scheme for achieving roto-translational invariance of LVC models as well as a general quantum mechanics/molecular mechanics (QM/MM) interface, an OpenMM interface, and restraining potentials for simulating liquid droplets. Using thioformaldehyde in water as a test case, we demonstrate that LVC/MM can accurately reproduce the solvation structure and energetics of rigid solutes, with errors on the order of 1-2 kcal/mol compared to a BP86/MM reference. The implementation in SHARC is shown to be very efficient, enabling the simulation of trajectories on the nanosecond time scale in a matter of days.

Charge carrier dynamics in conducting polymer PEDOT using ab initio molecular dynamics simulations

As conducting polymers become increasingly important in electronic devices, understanding their charge transport is essential for material and device development. Various semi-empirical approaches have been used to describe temporal charge carrier dynamics in these materials, but there have yet to be any theoretical approaches utilizing ab initio molecular dynamics. In this work, we develop a computational technique based on ab initio Car-Parrinello molecular dynamics to trace charge carrier temporal motion in archetypical conducting polymer poly(3,4-ethylenedioxythiophene) (PEDOT). Particularly, we analyze charge dynamics in a single PEDOT chain and in two coupled chains with different degrees of coupling and study the effect of temperature. In our model we first initiate a positively charged polaron (compensated by a negative counterion) at one end of the chain, and subsequently displace the counterion to the other end of the chain and trace polaron dynamics in the system by monitoring bond length alternation in the PEDOT backbone and charge density distribution. We find that at low temperature (T = 1 K) the polaron distortion gradually disappears from its initial location and reappears near the new position of the counterion. At the room temperature (T = 300 K), we find that the distortions induced by polaron, and atomic vibrations are of the same magnitude, which makes tracking the polaron distortion challenging because it is hidden behind the temperature-induced vibrations. The novel approach developed in this work can be used to study polaron mobility along and between the chains, investigate charge transport in highly doped polymers, and explore other flexible polymers, including n-doped ones.

Multiple k-Point Nonadiabatic Molecular Dynamics for Ultrafast Excitations in Periodic Systems: The Example of Photoexcited Silicon

With the rapid development of ultrafast experimental techniques for the research of carrier dynamics in solid-state systems, a microscopic understanding of the related phenomena, particularly a first-principle calculation, is highly desirable. Nonadiabatic molecular dynamics (NAMD) offers a real-time direct simulation of the carrier transfer or carrier thermalization. However, when applied to a periodic supercell, there is no cross-k-point transitions during the NAMD simulation. This often leads to a significant underestimation of the transition rate with the single-k-point band structure in a supercell. In this work, based on the surface hopping scheme used for NAMD, we propose a practical method to enable the cross-k transitions for a periodic system. We demonstrate our formalism by showing that the hot electron thermalization process by the multi-k-point NAMD in a small silicon supercell is equivalent to such simulation in a large supercell with a single Γ point. The simulated hot carrier thermalization process of the bulk silicon is compared with the recent ultrafast experiments, which shows excellent agreements. We have also demonstrated our method for the hot carrier coolings in the amorphous silicons and the GaAlAs_{2} solid solutions with the various cation distributions.

A Discrete-Variable Local Diabatic Representation of Conical Intersection Dynamics

Conical intersections (CIs) are ubiquitous in polyatomic molecules and are responsible for a wide range of phenomena in photochemistry and photophysics. Modeling the conical intersection dynamics with adiabatic electronic states is hindered by the divergence of the first- and second-order derivative couplings at CIs due to electronic degeneracy. We introduce and implement a novel diabatic representation for exact correlated electron-nuclear wave packet dynamics through conical intersections. It directly employs the adiabatic electronic states but avoids the singular first- and second-order derivative couplings and is robust to different gauge choices of the electronic wave function phases. The reference nuclear geometries defining the adiabatic electronic states are determined by a discrete-variable representation of the nuclear coordinates. The nonadiabatic effects are accounted for by the electronic overlap matrix instead of derivative couplings as in the adiabatic representation. Illustrated by a two-mode conical intersection model, this representation captures all nonadiabatic effects, including electronic transitions, electronic coherence, and geometric phases. Thus, this representation provides a singularity-free framework for modeling ab initio conical intersection wave packet dynamics.

Nonadiabatic simulations of photoisomerization and dissociation in ethylene using ab initio classical trajectories

We simulate the nonadiabatic dynamics of photo-induced isomerization and dissociation in ethylene using ab initio classical trajectories in an extended phase space of nuclear and electronic variables. This is achieved by employing the linearized semiclassical initial value representation method for nonadiabatic dynamics, where discrete electronic states are mapped to continuous classical variables using either the Meyer-Miller-Stock-Thoss representation or a more recently introduced spin mapping approach. Trajectory initial conditions are sampled by constraining electronic state variables to a single initial excited state and by drawing nuclear phase space configurations from a Wigner distribution at a finite temperature. An ensemble of classical ab initio trajectories is then generated to compute thermal population correlation functions and analyze the mechanisms of isomerization and dissociation. Our results serve as a demonstration that this parameter-free semiclassical approach is computationally efficient and accurate, identifying mechanistic pathways in agreement with previous theoretical studies and also uncovering dissociation pathways observed experimentally.

Efficient Modeling of Quantum Dynamics of Charge Carriers in Materials Using Short Nonequilibrium Molecular Dynamics

Nonadiabatic molecular dynamics provides essential insights into excited-state processes, but it is computationally intense and simplifications are needed. The classical path approximation provides critical savings. Still, long heating and equilibration steps are required. We demonstrate that practical results can be obtained with short, partially equilibrated ab initio trajectories. Once the system's structure is adequate and essential fluctuations are sampled, the nonadiabatic Hamiltonian can be constructed. Local structures require only 1-2 ps trajectories, as demonstrated with point defects in metal halide perovskites. Short trajectories represent anharmonic motions common in defective structures, an essential improvement over the harmonic approximation around the optimized geometry. Glassy systems, such as grain boundaries, require different simulation protocols, e.g., involving machine learning force fields. 10-fold shorter trajectories generate 10-20% time scale errors, which are acceptable, given experimental uncertainties and other approximations. The practical NAMD protocol enables fast screening of excited-state dynamics for rapid exploration of new materials.

Analytic Evaluation of Nonadiabatic Couplings within the Complex Absorbing Potential Equation-of-Motion Coupled-Cluster Method

We present the theory for the evaluation of nonadiabatic couplings (NACs) involving resonance states within the complex absorbing potential equation-of-motion coupled-cluster (CAP-EOM-CC) framework implemented within the singles and doubles approximation. Resonance states are embedded in the continuum and undergo rapid decay through autodetachment. In addition, nuclear motion can facilitate transitions between different resonances and between resonances and bound states. These nonadiabatic transitions affect the chemical fate of resonances and have distinct spectroscopic signatures. The NAC vector is a central quantity needed to model such effects. In the CAP-EOM-CC framework, resonance states are treated on the same footing as bound states. Using the example of fumaronitrile, which supports a bound radical anion and several anionic resonances, we analyze the NAC between bound states and pseudocontinuum states, between bound states and resonances, and between two resonances. We find that the NAC between a bound state and a resonance is nearly independent of the CAP strength and thus straightforward to evaluate, whereas the NAC between two resonance states or between a bound state and a pseudocontinuum state is more difficult to evaluate.

Deciphering the Influence of Ground-State Distributions on the Calculation of Photolysis Observables

Nonadiabatic molecular dynamics offers a powerful tool for studying the photochemistry of molecular systems. Key to any nonadiabatic molecular dynamics simulation is the definition of its initial conditions (ICs), ideally representing the initial molecular quantum state of the system of interest. In this work, we provide a detailed analysis of how ICs may influence the calculation of experimental observables by focusing on the photochemistry of methylhydroperoxide (MHP), the simplest and most abundant organic peroxide in our atmosphere. We investigate the outcome of trajectory surface hopping simulations for distinct sets of ICs sampled from different approximate quantum distributions, namely harmonic Wigner functions and ab initio molecular dynamics using a quantum thermostat (QT). Calculating photoabsorption cross-sections, quantum yields, and translational kinetic energy maps from the results of these simulations reveals the significant effect of the ICs, in particular when low-frequency (∼ a few hundred cm-1) normal modes are connected to the photophysics of the molecule. Overall, our results indicate that sampling ICs from ab initio molecular dynamics using a QT is preferable for flexible molecules with photoactive low-frequency modes. From a photochemical perspective, our nonadiabatic dynamics simulations offer an explanation for a low-energy tail observed at high excitation energy in the translational kinetic energy map of MHP.

Isolated and solvated chiroptical behavior in conformationally flexible butanamines

The nonresonant optical activity of two highly flexible aliphatic amines, (2R)-3-methyl-2-butanamine (R-MBA) and (2R)-(3,3)-dimethyl-2-butanamine (R-DMBA), has been probed under isolated and solvated conditions to examine the roles of conformational isomerism and to explore the influence of extrinsic perturbations. The optical rotatory dispersion (ORD) measured in six solvents presented uniformly negative rotatory powers over the 320-590 nm region, with the long-wavelength magnitude of chiroptical response growing nearly monotonically as the dielectric constant of the surroundings diminished. The intrinsic specific optical rotation,α λ T (in deg dm-1 [g/mL]-1 ), extracted for ambient vapor-phase samples of R-MBA [-11.031(98) and -2.29 (11)] and R-DMBA [-9.434 (72) and -1.350 (48)] at 355 and 633 nm were best reproduced by counterintuitive solvents of high polarity (yet low polarizability) like acetonitrile and methanol. Attempts to interpret observed spectral signatures quantitatively relied on the linear-response frameworks of density-functional theory (B3LYP, cam-B3LYP, and dispersion-corrected analogs) and coupled-cluster theory (CCSD), with variants of the polarizable continuum model (PCM) deployed to account for the effects of implicit solvation. Building on the identification of several low-lying equilibrium geometries (nine for R-MBA and three for R-DMBA), ensemble-averaged ORD profiles were calculated at T = 300 K by means of the independent-conformer ansatz, which enabled response properties predicted for the optimized structure of each isomer to be combined through Boltzmann-weighted population fractions derived from corresponding relative internal-energy or free-energy values, the latter of which stemmed from composite CBS-APNO and G4 analyses. Although reasonable accord between theory and experiment was realized for the isolated (vapor-phase) species, the solution-phase results were less satisfactory and tended to degrade progressively as the solvent polarity increased. These trends were attributed to solvent-mediated changes in structural parameters and energy metrics for the transition states that separate and putatively isolate the equilibrium conformations supported by the ground electronic potential-energy surface, with the resulting displacement of barrier locations and/or decrease of barrier heights compromising the underlying premise of the independent-conformer ansatz.

Theoretical Advances in Polariton Chemistry and Molecular Cavity Quantum Electrodynamics

When molecules are coupled to an optical cavity, new light-matter hybrid states, so-called polaritons, are formed due to quantum light-matter interactions. With the experimental demonstrations of modifying chemical reactivities by forming polaritons under strong light-matter interactions, theorists have been encouraged to develop new methods to simulate these systems and discover new strategies to tune and control reactions. This review summarizes some of these exciting theoretical advances in polariton chemistry, in methods ranging from the fundamental framework to computational techniques and applications spanning from photochemistry to vibrational strong coupling. Even though the theory of quantum light-matter interactions goes back to the midtwentieth century, the gaps in the knowledge of molecular quantum electrodynamics (QED) have only recently been filled. We review recent advances made in resolving gauge ambiguities, the correct form of different QED Hamiltonians under different gauges, and their connections to various quantum optics models. Then, we review recently developed ab initio QED approaches which can accurately describe polariton states in a realistic molecule-cavity hybrid system. We then discuss applications using these method advancements. We review advancements in polariton photochemistry where the cavity is made resonant to electronic transitions to control molecular nonadiabatic excited state dynamics and enable new photochemical reactivities. When the cavity resonance is tuned to the molecular vibrations instead, ground-state chemical reaction modifications have been demonstrated experimentally, though its mechanistic principle remains unclear. We present some recent theoretical progress in resolving this mystery. Finally, we review the recent advances in understanding the collective coupling regime between light and matter, where many molecules can collectively couple to a single cavity mode or many cavity modes. We also lay out the current challenges in theory to explain the observed experimental results. We hope that this review will serve as a useful document for anyone who wants to become familiar with the context of polariton chemistry and molecular cavity QED and thus significantly benefit the entire community.

NEXMD v2.0 Software Package for Nonadiabatic Excited State Molecular Dynamics Simulations

We present NEXMD version 2.0, the second release of the NEXMD (Nonadiabatic EXcited-state Molecular Dynamics) software package. Across a variety of new features, NEXMD v2.0 incorporates new implementations of two hybrid quantum-classical dynamics methods, namely, Ehrenfest dynamics (EHR) and the Ab-Initio Multiple Cloning sampling technique for Multiconfigurational Ehrenfest quantum dynamics (MCE-AIMC or simply AIMC), which are alternative options to the previously implemented trajectory surface hopping (TSH) method. To illustrate these methodologies, we outline a direct comparison of these three hybrid quantum-classical dynamics methods as implemented in the same NEXMD framework, discussing their weaknesses and strengths, using the modeled photodynamics of a polyphenylene ethylene dendrimer building block as a representative example. We also describe the expanded normal-mode analysis and constraints for both the ground and excited states, newly implemented in the NEXMD v2.0 framework, which allow for a deeper analysis of the main vibrational motions involved in vibronic dynamics. Overall, NEXMD v2.0 expands the range of applications of NEXMD to a larger variety of multichromophore organic molecules and photophysical processes involving quantum coherences and persistent couplings between electronic excited states and nuclear velocity.

Probing the sensitivity of ab initio multiple spawning to its parameters

Full multiple spawning (FMS) offers a strategy to simulate the nonadiabatic dynamics of molecular systems by describing their nuclear wavefunctions by a linear combination of coupled trajectory basis functions (TBFs). Applying a series of controlled approximations to the full multiple spawning (FMS) equations leads to the ab initio multiple spawning (AIMS), which is compatible with an on-the-fly propagation of the TBFs and an accurate description of nonadiabatic processes. The AIMS strategy and its numerical implementations, however, rely on a series of user-defined parameters. Herein, we investigate the influence of these parameters on the electronic-state population of two molecular systems- trans-azomethane and a two-dimensional model of the butatriene cation. This work highlights the stability of AIMS with respect to most of its parameters, underlines the specific parameters that require particular attention from the user of the method, and offers prescriptions for an informed selection of their value.

Supplementary Information

The online version contains supplementary material available at 10.1007/s00214-023-03004-w.

Charge Migration in HCCI Cations Probed by Strong Field Ionization: Time-Dependent Configuration Interaction and Vibrational Wavepacket Simulations

Strong field ionization of neutral iodoacetylene (HCCI) can produce a coherent superposition of the X and A cations and results in charge migration between the CC π orbital and the iodine π-type lone pair. This charge migration causes oscillations in the rate of strong field ionization of the cation to the dication that can be monitored using intense few-cycle probe pulses. The dynamics and strong field ionization of the coherent superposition the X and A states of HCCI⁺ have been modeled by time-dependent configuration interaction (TDCI) simulations. When the nuclei are allowed to move, the electronic wavefunctions need to be multiplied by vibrational wavefunctions. Nuclear motion has been modeled by vibrational packets moving on quadratic approximations to the potential energy surfaces for the X and A states of the cation. The overlap of the vibrational wavepackets decays in about 10-15 fs. Consequently, the oscillations in the strong field ionization decay on the same time scale. A revival of the vibrational overlap and in the oscillations of the strong field ionization is seen at 60-110 fs. TDCI simulations show that the decay and revival of the charge migration can be monitored by strong field ionization with intense 2- and 4-cycle linearly polarized 800 nm pulses. The revival is also seen with 7-cycle pulses.

Molecular photodissociation dynamics revealed by Coulomb explosion imaging

Coulomb explosion imaging (CEI) methods are finding ever-growing use as a means of exploring and distinguishing the static stereo-configurations of small quantum systems (molecules, clusters, etc). CEI experiments initiated by ultrafast (femtosecond-duration) laser pulses also allow opportunities to track the time-evolution of molecular structures, and thereby advance understanding of molecular fragmentation processes. This Perspective illustrates two emerging families of dynamical studies. 'One-colour' studies (employing strong field ionisation driven by intense near infrared or single X-ray or extreme ultraviolet laser pulses) afford routes to preparing multiply charged molecular cations and exploring how their fragmentation progresses from valence-dominated to Coulomb-dominated dynamics with increasing charge and how this evolution varies with molecular size and composition. 'Two-colour' studies use one ultrashort laser pulse to create electronically excited neutral molecules (or monocations), whose structural evolution is then probed as a function of pump-probe delay using an ultrafast ionisation pulse along with time and position-sensitive detection methods. This latter type of experiment has the potential to return new insights into not just molecular fragmentation processes but also charge transfer processes between moieties separating with much better defined stereochemical control than in contemporary ion-atom and ion-molecule charge transfer studies.

Computational Design of Molecular Probes for Electronic Preresonance Raman Scattering Microscopy

Recently developed electronic preresonance stimulated Raman scattering (epr-SRS) microscopy, in which the Raman signal of a dye is significantly boosted by setting the incident laser frequency near the electronic excitation energy, has pushed the sensitivity of SRS microscopy close to that offered by confocal fluorescence microscopy. Prominently, the maintained narrow line-width of epr-SRS also offers high multiplexity that breaks the "color barrier" in optical microscopy. However, detailed understanding of the fundamental mechanism in these epr-SRS dyes still remains elusive. Here, we combine experiments with theoretical modeling to investigate the structure-function relationship, aiming to facilitate the design of new probes and expanding epr-SRS palettes. Our ab initio approach employing the displaced harmonic oscillator (DHO) model provides a consistent agreement between simulated and experimental SRS intensities of various triple-bond bearing epr-SRS probes with distinct scaffolds. We further review two popular approximate expressions for epr-SRS, namely the short-time and Albrecht A-term equations, and compare them to the DHO model. Overall, the theory allows us to illustrate how the observed intensity differences between molecular scaffolds stem from the coupling strength between the electronic excitation and the targeted vibrational mode, leading to a general design strategy for highly sensitive next-generation vibrational imaging probes.

Excited-State Dynamics during Primary C-I Homolysis in Acetyl Iodide Revealed by Ultrafast Core-Level Spectroscopy

In typical carbonyl-containing molecules, bond dissociation events follow initial excitation to nπC═O* states. However, in acetyl iodide, the iodine atom gives rise to electronic states with mixed nπC═O* and nσC-I* character, leading to complex excited-state dynamics, ultimately resulting in dissociation. Using ultrafast extreme ultraviolet (XUV) transient absorption spectroscopy and quantum chemical calculations, we present an investigation of the primary photodissociation dynamics of acetyl iodide via time-resolved spectroscopy of core-to-valence transitions of the I atom after 266 nm excitation. The probed I 4d-to-valence transitions show features that evolve on sub-100-fs time scales, reporting on excited-state wavepacket evolution during dissociation. These features subsequently evolve to yield spectral signatures corresponding to free iodine atoms in their spin-orbit ground and excited states with a branching ratio of 1.1:1 following dissociation of the C-I bond. Calculations of the valence excitation spectrum via equation-of-motion coupled cluster with single and double substitutions (EOM-CCSD) show that initial excited states are of spin-mixed character. From the initially pumped spin-mixed state, we use a combination of time-dependent density functional theory (TDDFT)-driven nonadiabatic ab initio molecular dynamics and EOM-CCSD calculations of the N4,5 edge to reveal a sharp inflection point in the transient XUV signal that corresponds to rapid C-I homolysis. By examining the molecular orbitals involved in the core-level excitations at and around this inflection point, we are able to piece together a detailed picture of C-I bond photolysis in which d → σ* transitions give way to d → p excitations as the bond dissociates. We also report theoretical predictions of short-lived, weak 4d → 5d transitions in acetyl iodide, validated by weak bleaching in the experimental transient XUV spectra. This joint experimental-theoretical effort has thus unraveled the detailed electronic structure and dynamics of a strongly spin-orbit coupled system.

An on-the-fly deep neural network for simulating time-resolved spectroscopy: predicting the ultrafast ring opening dynamics of 1,2-dithiane

Revolutionary developments in ultrafast light source technology are enabling experimental spectroscopists to probe the structural dynamics of molecules and materials on the femtosecond timescale. The capacity to investigate ultrafast processes afforded by these resources accordingly inspires theoreticians to carry out high-level simulations which facilitate the interpretation of the underlying dynamics probed during these ultrafast experiments. In this Article, we implement a deep neural network (DNN) to convert excited-state molecular dynamics simulations into time-resolved spectroscopic signals. Our DNN is trained on-the-fly from first-principles theoretical data obtained from a set of time-evolving molecular dynamics. The train-test process iterates for each time-step of the dynamics data until the network can predict spectra with sufficient accuracy to replace the computationally intensive quantum chemistry calculations required to produce them, at which point it simulates the time-resolved spectra for longer timescales. The potential of this approach is demonstrated by probing dynamics of the ring opening of 1,2-dithiane using sulphur K-edge X-ray absorption spectroscopy. The benefits of this strategy will be more markedly apparent for simulations of larger systems which will exhibit a more notable computational burden, making this approach applicable to the study of a diverse range of complex chemical dynamics.

Impact of the core on the inter-branch exciton exchange in dendrimers

Organic dendrimers with π conjugated systems are capable of capturing solar energy as a renewable source for human use. Nonetheless, further study regarding the relationship between the structure and the energy transfer mechanism in these types of molecules is still necessary. In this work, nonadiabatic excited state molecular dynamics (NEXMD) were carried out to study the intra- and inter-branch exciton migration in two tetra-branched dendrimers, C(dSSB)₄ and Ad(BuSSB)₄, which differ in their respective carbon and adamantane core. Both systems undergo a ladder decay mechanism between excited states, with back-and-forth transitions between S₁ and S₂. Despite presenting very similar absorption-emission spectra, differences in the photoinduced energy relaxation are observed. The size of the core impacts the inter-branch energy exchange and transient exciton localization/delocalization, which ultimately condition the relative energy relaxation rates, being faster in Ad(BuSSB)₄ with respect to C(dSSB)₄. Nevertheless, the photoinduced processes lead to a progressive final exciton-self-trapping in one of the branches of both dendrimers, which is a desirable feature in organic photovoltaic applications. Our results can inspire the design of more efficient dendrimers with the desired magnitude of inter-branch exciton exchange and localization/delocalization according to changes in their core.

New Gradient Correction Scheme for Electronically Nonadiabatic Dynamics Involving Multiple Spin States

It has been recommended that the best representation to use for trajectory surface hopping (TSH) calculations is the fully adiabatic basis in which the Hamiltonian is diagonal. Simulations of intersystem crossing processes with conventional TSH methods require an explicit computation of nonadiabatic coupling vectors (NACs) in the molecular-Coulomb-Hamiltonian (MCH) basis, also called the spin-orbit-free basis, in order to compute the gradient in the fully adiabatic basis (also called the diagonal representation). This explicit requirement destroys some of the advantages of the overlap-based algorithms and curvature-driven algorithms that can be used for the most efficient TSH calculations. Therefore, although these algorithms allow one to perform NAC-free simulations for internal conversion processes, one still requires NACs for intersystem crossing. Here, we show that how the NAC requirement is circumvented by a new computation scheme called the time-derivative-matrix scheme.

Fluorescence in quantum dynamics: Accurate spectra require post-mean-field approaches

Real time modeling of fluorescence with vibronic resolution entails the representation of the light-matter interaction coupled to a quantum-mechanical description of the phonons and is therefore a challenging problem. In this work, taking advantage of the difference in timescales characterizing internal conversion and radiative relaxation-which allows us to decouple these two phenomena by sequentially modeling one after the other-we simulate the electron dynamics of fluorescence through a master equation derived from the Redfield formalism. Moreover, we explore the use of a recent semiclassical dissipative equation of motion [C. M. Bustamante et al., Phys. Rev. Lett. 126, 087401 (2021)], termed coherent electron electric-field dynamics (CEED), to describe the radiative stage. By comparing the results with those from the full quantum-electrodynamics treatment, we find that the semiclassical model does not reproduce the right amplitudes in the emission spectra when the radiative process involves the de-excitation to a manifold of closely lying states. We argue that this flaw is inherent to any mean-field approach and is the case with CEED. This effect is critical for the study of light-matter interaction, and this work is, to our knowledge, the first one to report this problem. We note that CEED reproduces the correct frequencies in agreement with quantum electrodynamics. This is a major asset of the semiclassical model, since the emission peak positions will be predicted correctly without any prior assumption about the nature of the molecular Hamiltonian. This is not so for the quantum electrodynamics approach, where access to the spectral information relies on knowledge of the Hamiltonian eigenvalues.

Quantum and Semiclassical Dynamics of Nonadiabatic Electronic Excitation of C(3P) to C1D) by Hyperthermal Collisions with N2

The dynamics and kinetics of nonadiabatic excitation of C(3P) to C(1D) induced by hyperthermal collisions with N2 molecules are investigated using a quantum mechanical and two semiclassical nonadiabatic methods. The full-dimensional interaction potential energy surfaces and spin-orbit coupling, which facilitates the spin-forbidden process, are represented by a recently constructed diabatic potential energy matrix. The multistate quantum dynamics for selected partial waves found small transition probabilities due to the weak spin-orbit coupling. The spin-flip transition is the most favored near the threshold due to effective curve crossing. Strong oscillations are also found in the probabilities, which are attributable to resonances supported by the deep well in the singlet-state potential. Vibrational state-specified rate coefficients are reported from J-shifted quantum dynamics calculations, and they follow the Arrhenius form. Vibrational excitation in the N2 collision partner is found to increase the excitation rate at low temperatures, but the trend is reversed at high temperatures. The two semiclassical methods qualitatively reproduce the quantum rate coefficients.

On-the-Fly Nonadiabatic Dynamics Simulations of Single-Walled Carbon Nanotubes with Covalent Defects

Single-walled carbon nanotubes (SWCNTs) with covalent surface defects have been explored recently due to their promise for use in single-photon telecommunication emission and in spintronic applications. The all-atom dynamic evolution of electrostatically bound excitons (the primary electronic excitations) in these systems has only been loosely explored from a theoretical perspective due to the size limitations of these large systems (>500 atoms). In this work, we present computational modeling of nonradiative relaxation in a variety of SWCNT chiralities with single-defect functionalizations. Our excited-state dynamics modeling uses a trajectory surface hopping algorithm accounting for excitonic effects with a configuration interaction approach. We find a strong chirality and defect-composition dependence on the population relaxation (varying over 50-500 fs) between the primary nanotube band gap excitation E₁₁ and the defect-associated, single-photon-emitting E₁₁* state. These simulations give direct insight into the relaxation between the band-edge states and the localized excitonic state, in competition with dynamic trapping/detrapping processes observed in experiment. Engineering fast population decay into the quasi-two-level subsystem with weak coupling to higher-energy states increases the effectiveness and controllability of these quantum light emitters.

Exploring Proton-Coupled Electron Transfer at Multiple Scales

The coupling of electron and proton transfer is critical for chemical and biological processes spanning a wide range of length and time scales and often occurring in complex environments. Thus, diverse modeling strategies, including analytical theories, quantum chemistry, molecular dynamics, and kinetic modeling, are essential for a comprehensive understanding of such proton-coupled electron transfer reactions. Each of these computational methods provides one piece of the puzzle, and all these pieces must be viewed together to produce the full picture.

Quantitative Evaluation of the Carrier Separation Performance of Heterojunction Photocatalysts: The Case of g-C3N4/SrTiO3

Heterojunction photocatalysts are of great interest in the energy and environmental fields, because of their potential to significantly increase the efficiency of harvesting solar energy. Advances in design have been hampered by the continued use of only qualitative analyses. Quantitative evaluation of the carrier separation performance is urgently needed for the design and application of heterojunction photocatalysts. Taking the g-C₃N₄/SrTiO₃ heterojunction as an example, we address the conventional energy band and electronic structure issues by first-principles analysis. After interface coupling, the band edge alignment reverses from that of the respective isolated states of the heterojunction components, suggesting new ways of thinking about the catalytic mechanism of the heterojunction. More significantly, we show the carrier separation performance of heterojunction photocatalysts can be quantitatively predicted by the nonadiabatic molecular dynamics method, enabling more precisely directed research and promoting the quantified design and application of heterojunction photocatalysis, making a contribution of great scientific significance.

Nonadiabatic Forward Flux Sampling for Excited-State Rare Events

We present a rare event sampling scheme applicable to coupled electronic excited states. In particular, we extend the forward flux sampling (FFS) method for rare event sampling to a nonadiabatic version (NAFFS) that uses the trajectory surface hopping (TSH) method for nonadiabatic dynamics. NAFFS is applied to two dynamically relevant excited-state models that feature an avoided crossing and a conical intersection with tunable parameters. We investigate how nonadiabatic couplings, temperature, and reaction barriers affect transition rate constants in regimes that cannot be otherwise obtained with plain, traditional TSH. The comparison with reference brute-force TSH simulations for limiting cases of rareness shows that NAFFS can be several orders of magnitude cheaper than conventional TSH and thus represents a conceptually novel tool to extend excited-state dynamics to time scales that are able to capture rare nonadiabatic events.

Semiclassical Dynamics on Machine-Learned Coupled Multireference Potential Energy Surfaces: Application to the Photodissociation of the Simplest Criegee Intermediate

Determination of high-dimensional potential energy surfaces (PESs) and nonadiabatic couplings have always been quite challenging. To this end, machine learning (ML) models, trained with a finite set of ab initio data, allow accurate prediction of such properties. To express the PESs in terms of atomic contributions is the cornerstone of any ML based technique because it can be easily scaled to large systems. In this work, we have constructed high fidelity PESs and nonadiabatic coupling terms at the CASSCF level of ab initio data using a machine learning technique, namely, kernel-ridge regression. Additional MRCI-level calculations were carried out to assess the quality of the PESs. We use these machine-learned PESs and nonadiabatic couplings to simulate excited-state molecular dynamics based on Tully's fewest-switches surface hopping method (FSSH). FSSH is a semiclassical method in which nuclei move on the PESs due to the electrons according to the laws of classical mechanics. Nonadiabatic effects are taken into account in terms of transitions between PESs. We apply this scheme to study the O-O photodissociation of the simplest Criegee intermediate (CH₂OO). The FSSH trajectories were initiated on the lowest optically bright singlet excited state (S₂) and propagated along the three most important internal coordinates, namely, O-O and C-O bond distances and the COO bond angle. Some of the trajectories end up on energetically lower PESs as a result of radiationless transfer through conical intersections. All of the trajectories lead to the dissociation of the O-O bond due to the dissociative nature of the excited PESs through one of the two dissociative channels. The simulation reveals that there is about 88.4% probability of dissociation through the lower channel leading to the H₂CO (X¹A₁) and O (¹D) products, whereas there is only 11.6% probability of dissociation through the upper channel leading to H₂CO (a³A″) and O (³P) products.

A Nitrogen Out-of-Plane (NOOP) Mechanism for Imine-Based Light-Driven Molecular Motors

Light-driven molecular motors have generated considerable interest due to their potential applications in material and biological systems. Recently, Greb and Lehn reported a new class of molecular motors, chiral N-alkyl imines, which undergo unidirectional rotation induced by light and heat. The mechanism of unidirectional motion in molecular motors containing a C═N group has been assumed to consist of photoinduced torsion about the double bond. In this work, we present a computational study of the photoisomerization dynamics of a chiral N-alkyl imine motor. We find that the location and energetics of minimal energy conical intersections (MECIs) alone are insufficient to understand the mechanism of the motor. Furthermore, a key part of the mechanism consists of out-of-plane distortions of the N atom (followed by isomerization about the double bond). Dynamic effects and out-of-plane distortions are critical to understand the observed (rather low) quantum yield for photoisomerization. Our results provide hints as to how the photoisomerization quantum yield might be increased, improving the efficiency of this class of molecular motors.

Monitoring vibronic coherences and molecular aromaticity in photoexcited cyclooctatetraene with an X-ray probe: a simulation study

Understanding conical intersection (CI) dynamics and subsequent conformational changes is key for exploring and controlling photo-reactions in aromatic molecules. Monitoring of their time-resolved dynamics remains a formidable experimental challenge. In this study, we simulate the photoinduced S₃ to S₁ non-adiabatic dynamics of cyclooctatetraene (COT), involving multiple CIs with relaxation times in good agreement with experiment. We further investigate the possibility to directly probe the CI passages in COT by off-resonant X-ray Raman spectroscopy (TRUECARS) and time-resolved X-ray diffraction (TRXD). We find that these signals sensitively monitor key chemical features during the ultrafast dynamics. First, we distinguish two CIs by using TRUECARS signals with their appearances at different Raman shifts. Second, we demonstrate that TRXD, where X-ray photons scatter off electron densities, can resolve ultrafast changes in the aromaticity of COT. It can further distinguish between planar and non-planar geometries explored during the dynamics, as e.g. two different tetraradical-type CIs. The knowledge gained from these measurements can give unique insight into fundamental chemical properties that dynamically change during non-adiabatic passages.

Mind the GAP: quantifying the breakdown of the linear vibronic coupling Hamiltonian

Excited state dynamics play a critical role across a broad range of scientific fields. Importantly, the highly non-equilibrium nature of the states generated by photoexcitation means that excited state simulations should usually include an accurate description of the coupled electronic-nuclear motion, which often requires solving the time-dependent Schrödinger equation (TDSE). One of the biggest challenges for these simulations is the requirement to calculate the PES over which the nuclei evolve. An effective approach for addressing this challenge is to use the approximate linear vibronic coupling (LVC) Hamiltonian, which enables a model potential to be parameterised using relatively few quantum chemistry calculations. However, this approach is only valid provided there are no large amplitude motions in the excited state dynamics. In this paper we introduce and deploy a metric, the global anharmonicity parameter (GAP), which can be used to assess the accuracy of an LVC potential. Following its derivation, we illustrate its utility by applying it to three molecules exhibiting different rigidity in their excited states.

Direct Nonadiabatic Dynamics of Ammonia with Curvature-Driven Coherent Switching with Decay of Mixing and with Fewest Switches with Time Uncertainty: An Illustration of Population Leaking in Trajectory Surface Hopping Due to Frustrated Hops

Mixed quantum-classical nonadiabatic dynamics is a widely used approach to simulate molecular dynamics involving multiple electronic states. There are two main categories of mixed quantum-classical nonadiabatic dynamics algorithms, namely, trajectory surface hopping (TSH) in which the trajectory propagates on a single potential energy surface, interrupted by hops, and self-consistent-potential (SCP) methods, such as semiclassical Ehrenfest, in which propagation occurs on a mean-field surface without hops. In this work, we will illustrate an example of severe population leaking in TSH. We emphasize that such leaking is a combined effect of frustrated hops and long-time simulations that drive the final excited-state population toward zero as a function of time. We further show that such leaking can be alleviated-but not eliminated-by the fewest switches with time uncertainty TSH algorithm (here implemented in the SHARC program); the time uncertainty algorithm slows down the leaking process by a factor of 4.1. The population leaking is not present in coherent switching with decay of mixing (CSDM), which is an SCP method with non-Markovian decoherence included. Another result in this paper is that we find very similar results with the original CSDM algorithm, with time-derivative CSDM (tCSDM), and with curvature-driven CSDM (κCSDM). Not only do we find good agreement for electronically nonadiabatic transition probabilities but also we find good agreement of the norms of the effective nonadiabatic couplings (NACs) that are derived from the curvature-driven time-derivative couplings as implemented in κCSDM with the time-dependent norms of the nonadiabatic coupling vectors computed by state-averaged complete-active-space self-consistent field theory.

Grid-based methods for chemistry simulations on a quantum computer

First-quantized, grid-based methods for chemistry modeling are a natural and elegant fit for quantum computers. However, it is infeasible to use today's quantum prototypes to explore the power of this approach because it requires a substantial number of near-perfect qubits. Here, we use exactly emulated quantum computers with up to 36 qubits to execute deep yet resource-frugal algorithms that model 2D and 3D atoms with single and paired particles. A range of tasks is explored, from ground state preparation and energy estimation to the dynamics of scattering and ionization; we evaluate various methods within the split-operator QFT (SO-QFT) Hamiltonian simulation paradigm, including protocols previously described in theoretical papers and our own techniques. While we identify certain restrictions and caveats, generally, the grid-based method is found to perform very well; our results are consistent with the view that first-quantized paradigms will be dominant from the early fault-tolerant quantum computing era onward.

The hierarchy of Davydov's Ansätze: From guesswork to numerically "exact" many-body wave functions

This Perspective presents an overview of the development of the hierarchy of Davydov's Ansätze and a few of their applications in many-body problems in computational chemical physics. Davydov's solitons originated in the investigation of vibrational energy transport in proteins in the 1970s. Momentum-space projection of these solitary waves turned up to be accurate variational ground-state wave functions for the extended Holstein molecular crystal model, lending unambiguous evidence to the absence of formal quantum phase transitions in Holstein systems. The multiple Davydov Ansätze have been proposed, with increasing Ansatz multiplicity, as incremental improvements of their single-Ansatz parents. For a given Hamiltonian, the time-dependent variational formalism is utilized to extract accurate dynamic and spectroscopic properties using Davydov's Ansätze as its trial states. A quantity proven to disappear for large multiplicities, the Ansatz relative deviation is introduced to quantify how closely the Schrödinger equation is obeyed. Three finite-temperature extensions to the time-dependent variation scheme are elaborated, i.e., the Monte Carlo importance sampling, the method of thermofield dynamics, and the method of displaced number states. To demonstrate the versatility of the methodology, this Perspective provides applications of Davydov's Ansätze to the generalized Holstein Hamiltonian, variants of the spin-boson model, and systems of cavity-assisted singlet fission, where accurate dynamic and spectroscopic properties of the many-body systems are given by the Davydov trial states.

Accurate Relativistic Real-Time Time-Dependent Density Functional Theory for Valence and Core Attosecond Transient Absorption Spectroscopy

First principles theoretical modeling of out-of-equilibrium processes observed in attosecond pump-probe transient absorption spectroscopy (TAS) triggering pure electron dynamics remains a challenging task, especially for heavy elements and/or core excitations containing fingerprints of scalar and spin-orbit relativistic effects. To address this, we formulate a methodology for simulating TAS within the relativistic real-time, time-dependent density functional theory (RT-TDDFT) framework, for both the valence and core energy regimes. Especially for TAS, full four-component (4c) RT simulations are feasible but computationally demanding. Therefore, in addition to the 4c approach, we also introduce the atomic mean-field exact two-component (amfX2C) Hamiltonian accounting for one- and two-electron picture-change corrections within RT-TDDFT. amfX2C preserves the accuracy of the parent 4c method at a fraction of its computational cost. Finally, we apply the methodology to study valence and near-L_2,3-edge TAS processes of experimentally relevant systems and provide additional physical insights using relativistic nonequilibrium response theory.

Excited-state intramolecular proton transfer (ESIPT)-based fluorescent probes for biomarker detection: design, mechanism, and application

Biomarkers are essential in biology, physiology, and pharmacology; thus, their detection is of extensive importance. Fluorescent probes provide effective tools for detecting biomarkers exactly. Excited state intramolecular proton transfer (ESIPT), one of the significant photophysical processes that possesses specific photoisomerization between Keto and Enol forms, can effectively avoid annoying interference from the background with a large Stokes shift. Hence, ESIPT is an excellent choice for biomarker monitoring. Based on the ESIPT process, abundant probes were designed and synthesized using three major design methods. In this review, we conclude probes for 14 kinds of biomarkers based on ESIPT explored in the past five years, summarize these general design methods, and highlight their application for biomarker detection in vitro or in vivo.

TeraChem protocol buffers (TCPB): Accelerating QM and QM/MM simulations with a client-server model

The routine use of electronic structures in many chemical simulation applications calls for efficient and easy ways to access electronic structure programs. We describe how the graphics processing unit (GPU) accelerated electronic structure program TeraChem can be set up as an electronic structure server, to be easily accessed by third-party client programs. We exploit Google's protocol buffer framework for data serialization and communication. The client interface, called TeraChem protocol buffers (TCPB), has been designed for ease of use and compatibility with multiple programming languages, such as C++, Fortran, and Python. To demonstrate the ease of coupling third-party programs with electronic structures using TCPB, we have incorporated the TCPB client into Amber for quantum mechanics/molecular mechanics (QM/MM) simulations. The TCPB interface saves time with GPU initialization and I/O operations, achieving a speedup of more than 2× compared to a prior file-based implementation for a QM region with ∼250 basis functions. We demonstrate the practical application of TCPB by computing the free energy profile of p-hydroxybenzylidene-2,3-dimethylimidazolinone (p-HBDI^-)-a model chromophore in green fluorescent proteins-on the first excited singlet state using Hamiltonian replica exchange for enhanced sampling. All calculations in this work have been performed with the non-commercial freely-available version of TeraChem, which is sufficient for many QM region sizes in common use.

Quantum-classical dynamics of vibration-induced autoionization in molecules

We present a novel method for the simulation of the vibration-induced autoionization dynamics in molecular anions in the framework of the quantum-classical surface hopping approach. Classical trajectories starting from quantum initial conditions are propagated on a quantum-mechanical potential energy surface while allowing for autoionization through transitions into discretized continuum states. These transitions are induced by the couplings between the electronic states of the bound anionic system and the electron-detached system composed of the neutral molecule and the free electron. A discretization scheme for the detached system is introduced, and a set of formulas is derived that enable the approximate calculation of couplings between the bound and free-electron states. We demonstrate our method on the example of the anion of vinylidene, a high-energy isomer of acetylene, for which detailed experimental data are available. Our results provide information on the time scale of the autoionization process and give insight into the energetic and angular distribution of the ejected electrons, as well as the associated changes in the molecular geometry. We identify the formation of structures with reduced C-C bond lengths and T-like conformations through bending of the CH₂ group with respect to the C-C axis and point out the role of autoionization as a driving process for the isomerization to acetylene.

Unraveling the Nature of Hydrogen Bonds of "Proton Sponges" Based on Car-Parrinello and Metadynamics Approaches

The nature of intra- and intermolecular non-covalent interactions was studied in four naphthalene derivatives commonly referred to as "proton sponges". Special attention was paid to an intramolecular hydrogen bond present in the protonated form of the compounds. The unsubstituted "proton sponge" served as a reference structure to study the substituent influence on the hydrogen bond (HB) properties. We selected three compounds substituted by methoxy, amino, and nitro groups. The presence of the substituents either retained the parent symmetry or rendered the compounds asymmetric. In order to reveal the non-covalent interaction properties, the Hirshfeld surface (HS) was computed for the crystal structures of the studied compounds. Next, quantum-chemical simulations were performed in vacuo and in the crystalline phase. Car-Parrinello molecular dynamics (CPMD), Path Integral Molecular Dynamics (PIMD), and metadynamics were employed to investigate the time-evolution changes of metric parameters and free energy profile in both phases. Additionally, for selected snapshots obtained from the CPMD trajectories, non-covalent interactions and electronic structure were studied. Quantum theory of atoms in molecules (QTAIM) and the Density Overlap Regions Indicator (DORI) were applied for this purpose. It was found based on Hirshfeld surfaces that, besides intramolecular hydrogen bonds, other non-covalent interactions are present and have a strong impact on the crystal structure organization. The CPMD results obtained in both phases showed frequent proton transfer phenomena. The proton was strongly delocalized in the applied time-scale and temperature, especially in the PIMD framework. The use of metadynamics allowed for tracing the free energy profiles and confirming that the hydrogen bonds present in "proton sponges" are Low-Barrier Hydrogen Bonds (LBHBs). The electronic and topological analysis quantitatively described the temperature dependence and time-evolution changes of the electronic structure. The covalency of the hydrogen bonds was estimated based on QTAIM analysis. It was found that strong hydrogen bonds show greater covalency, which is additionally determined by the proton position in the hydrogen bridge.

Classical Nuclear Motion: Comparison to Approaches with Quantum Mechanical Nuclear Motion

Ab initio molecular dynamics combines a classical description of nuclear motion with a density-functional description of the electronic cloud. This approach nicely describes chemical reactions. A possible conclusion is that a quantum mechanical description of nuclear motion is not needed. Using Occam’s razor, this means that, being the simpler approach, classical nuclear motion is preferable. In this paper, it is claimed that nuclear motion is classical, and this hypothesis will be tested in comparison to methods with quantum mechanical nuclear motion. In particular, we apply ab initio molecular dynamics to two photoreactions involving hydrogen. Hydrogen, as the lightest element, is often assumed to show quantum mechanical tunneling. We will see that the classical picture is fully sufficient. The quantum mechanical view leads to phenomena that are difficult to understand, such as the entanglement of nuclear motion. In contrast, it is easy to understand the simple classical picture which assumes that nuclear motion is steady and uniform unless a force is acting. Of course, such a hypothesis must be verified for many systems and phenomena, and this paper is one more step in this direction.

Extending the Applicability of the Multiple-Spawning Framework for Nonadiabatic Molecular Dynamics

Ab initio multiple-spawning (AIMS) describes the nonadiabatic dynamics of molecules by expanding nuclear wave functions in a basis of traveling multidimensional Gaussians called trajectory basis functions (TBFs). New TBFs can be spawned whenever nuclear amplitude is transferred between electronic states due to nonadiabatic transitions. While the adaptive size of the TBF basis grants AIMS its characteristic accuracy in describing nonadiabatic processes, it also leads to a fast and uncontrolled growth of the number of TBFs, penalizing computational efficiency. A different flavor of AIMS, called AIMS with informed stochastic selections (AIMSWISS), has recently been proposed to reduce the number of TBFs dramatically. Herein, we test the performance of AIMSWISS for a series of challenging nonadiabatic processes─photodynamics of two-dimensional model systems, 1,2-dithiane and chromium (0) hexacarbonyl─and show that this method is robust and extends the range of molecular systems that can be simulated within the multiple-spawning framework.

Equation-of-Motion Methods for the Calculation of Femtosecond Time-Resolved 4-Wave-Mixing and N-Wave-Mixing Signals

Femtosecond nonlinear spectroscopy is the main tool for the time-resolved detection of photophysical and photochemical processes. Since most systems of chemical interest are rather complex, theoretical support is indispensable for the extraction of the intrinsic system dynamics from the detected spectroscopic responses. There exist two alternative theoretical formalisms for the calculation of spectroscopic signals, the nonlinear response-function (NRF) approach and the spectroscopic equation-of-motion (EOM) approach. In the NRF formalism, the system-field interaction is assumed to be sufficiently weak and is treated in lowest-order perturbation theory for each laser pulse interacting with the sample. The conceptual alternative to the NRF method is the extraction of the spectroscopic signals from the solutions of quantum mechanical, semiclassical, or quasiclassical EOMs which govern the time evolution of the material system interacting with the radiation field of the laser pulses. The NRF formalism and its applications to a broad range of material systems and spectroscopic signals have been comprehensively reviewed in the literature. This article provides a detailed review of the suite of EOM methods, including applications to 4-wave-mixing and N-wave-mixing signals detected with weak or strong fields. Under certain circumstances, the spectroscopic EOM methods may be more efficient than the NRF method for the computation of various nonlinear spectroscopic signals.

Trajectory Propagation of Symmetrical Quasi-classical Dynamics with Meyer-Miller Mapping Hamiltonian Using Machine Learning

The long short-term memory recurrent neural network (LSTM-RNN) approach is applied to realize the trajectory-based nonadiabatic dynamics within the framework of the symmetrical quasi-classical dynamics method based on the Meyer-Miller mapping Hamiltonian (MM-SQC). After construction, the LSTM-RNN model allows us to propagate the entire trajectory evolutions of all involved degrees of freedoms (DOFs) from initial conditions. The proposed idea is proven to be reliable and accurate in the simulations of the dynamics of several site-exciton electron-phonon coupling models and three Tully's scattering models. It indicates that the LSTM-RNN model perfectly captures the dynamical information on the trajectory evolution in the MM-SQC dynamics. Our work proposes a novel machine learning approach in the simulation of trajectory-based nonadiabatic dynamic of complex systems with a large number of DOFs.

Bivariational time-dependent wave functions with biorthogonal adaptive basis sets: General formulation and regularization of equations of motion through polar decomposition

We derive general bivariational equations of motion (EOMs) for time-dependent wave functions with biorthogonal time-dependent basis sets. The time-dependent basis functions are linearly parameterized and their fully variational time evolution is ensured by solving a set of so-called constraint equations, which we derive for arbitrary wave function expansions. The formalism allows division of the basis set into an active basis and a secondary basis, ensuring a flexible and compact wave function. We show how the EOMs specialize to a few common wave function forms, including coupled cluster and linearly expanded wave functions. It is demonstrated, for the first time, that the propagation of such wave functions is not unconditionally stable when a secondary basis is employed. The main signature of the instability is a strong increase in non-orthogonality, which eventually causes the calculation to fail; specifically, the biorthogonal active bra and ket bases tend toward spanning different spaces. Although formally allowed, this causes severe numerical issues. We identify the source of this problem by reparametrizing the time-dependent basis set through polar decomposition. Subsequent analysis allows us to remove the instability by setting appropriate matrix elements to zero. Although this solution is not fully variational, we find essentially no deviation in terms of autocorrelation functions relative to the variational formulation. We expect that the results presented here will be useful for the formal analysis of bivariational time-dependent wave functions for electronic and nuclear dynamics in general and for the practical implementation of time-dependent CC wave functions in particular.