Time-dependent density functional theory excited state nonadiabatic dynamics combined with quantum mechanical/molecular mechanical approach: Photodynamics of indole in water

Unraveling the Photoionization Dynamics of Indole in Aqueous and Ethanol Solutions

The photoionization dynamics of indole, the ultraviolet-B chromophore of tryptophan, were explored in water and ethanol using ultrafast transient absorption spectroscopy with 292, 268, and 200 nm excitation. By studying the femtosecond-to-nanosecond dynamics of indole in two different solvents, a new photophysical model has been generated that explains many previously unsolved facets of indole's complex solution phase photochemistry. Photoionization is only an active pathway for indole in aqueous solution, leading to a reduction in the fluorescence quantum yield in water-rich environments, which is frequently used in biophysical experiments as a key signature of the protein-folded state. Photoionization of indole in aqueous solution was observed for all three pump wavelengths but via two different mechanisms. For 200 nm excitation, electrons are ballistically ejected directly into the bulk solvent. Conversely, 292 and 268 nm excitation populates an admixture of two 1ππ* states, which form a dynamic equilibrium with a tightly bound indole cation and electron-ion pair. The ion pair dissociates on a nanosecond time scale, generating separated solvated electrons and indole cations. The charged species serve as important precursors to triplet indole production and greatly enhance the overall intersystem crossing rate. Our proposed photophysical model for indole in aqueous solution is the most appropriate for describing photoinduced dynamics of tryptophan in polypeptide sequences; tryptophan in aqueous pH 7 solution is zwitterionic, unlike in peptides, and resultantly has a competitive excited state proton transfer pathway that quenches the tryptophan fluorescence.

The Role of Aqueous Solvation on the Intersystem Crossing of Nitrophenols

The photochemistry of nitrophenols is a source of smog as nitrous acid is formed from their photolysis. Nevertheless, computational studies of the photochemistry of these widespread toxic molecules are scarce. In this work, the initial photodeactivation of ortho-nitrophenol and para-nitrophenol is modeled, both in gas phase and in aqueous solution to simulate atmospheric and aerosol environments. A large number of excited states, six for ortho-nitrophenol and 11 for para-nitrophenol, have been included and were all populated during the decay. Moreover, periodic time-dependent density functional theory (TDDFT) is used for both the explicitly included solvent and the solute. A comparison to periodic QM/MM (TDDFT/MM), with electrostatic embedding, is made, showing notable differences between the decays of solvated nitrophenols simulated with QM/MM and full (TD)DFT. A reduced intersystem crossing in aqueous solution could be observed thanks to the surface hopping approach using explicit, periodic TDDFT solvation including spin-orbit couplings.

Influence of H-bonds on the photoionization of aromatic chromophores in water: The aniline molecule

We have conducted time-resolved experiments (pump-probe and pump-repump-probe) on a model aromatic chromophore, aniline, after excitation in water at 267 nm. In the initial spectra recorded, in addition to the absorption corresponding to the bright ππ* excitation, the fingerprint of a transient state with the electron located on the solvent molecule is identified. We postulate that the latter corresponds to the πσ* state along the N-H bond, whose complete relaxation with a ∼500 ps lifetime results in the formation of the fully solvated electron and cation. This ionization process occurs in parallel with the ππ* photophysical channel that yields the characteristic ∼1 ns fluorescence lifetime. The observed branched pathway is rationalized in terms of the different H-bonds that the water establishes with the amino group. The proposed mechanism could be common for aromatics in water containing N-H or O-H bonds and would allow the formation of separated charges after excitation at the threshold of their electronic absorptions.

Interexcited State Photophysics I: Benchmarking Density Functionals for Computing Nonadiabatic Couplings and Internal Conversion Rate Constants

We present the first benchmarking study of nonadiabatic matrix coupling elements (NACMEs) calculated using different density functionals. Using the S₁ → S₀ transition in perylene solvated in toluene as a case study, we calculate the photophysical properties and corresponding rate constants for a variety of density functionals from each rung of Jacob's ladder. The singlet photoluminescence quantum yield (sPLQY) is taken as a measure of accuracy, measured experimentally here as 0.955. Important quantum chemical parameters such as geometries, absorption, emission, and adiabatic energies, NACMEs, Hessians, and transition dipole moments were calculated for each density functional basis set combination (data set) using density functional theory based multireference configuration interaction (DFT/MRCI) and compared to experiment where possible. We were able to derive simple relations between the TDDFT and DFT/MRCI photophysical properties; with semiempirical damping factors of ∼0.843 ± 0.017 and ∼0.954 ± 0.064 for TDDFT transition dipole moments and energies to DFT/MRCI level approximations, respectively. NACMEs were dominated by out-of-plane derivative components belonging to the center-most ring atoms with weaker contributions from perturbations along the transverse and longitudinal axes. Calculated theoretical spectra compared well to both experiment and literature, with fluorescence lifetimes between 7.1 and 12.5 ns, agreeing within a factor of 2 with experiment. Internal conversion (IC) rates were then calculated and were found to vary wildly between 10⁶-10¹⁶ s^-1 compared with an experimental rate of the order 10⁷ s^-1. Following further testing by mixing data sets, we found a strong dependence on the method used to obtain the Hessian. The 5 characterized data sets ranked in order of most promising are PBE0/def2-TZVP, ωB97XD/def2-TZVP, HCTH407/TZVP, PBE/TZVP, and PBE/def2-TZVP.

Environment-Driven Coherent Population Transfer Governs the Ultrafast Photophysics of Tryptophan

By combining UV transient absorption spectroscopy with sub-30-fs temporal resolution and CASPT2/MM calculations, we present a complete description of the primary photoinduced processes in solvated tryptophan. Our results shed new light on the role of the solvent in the relaxation dynamics of tryptophan. We unveil two consecutive coherent population transfer events involving the lowest two singlet excited states: a sub-50-fs nonadiabatic L_a → L_b transfer through a conical intersection and a subsequent 220 fs reverse L_b → L_a transfer due to solvent-assisted adiabatic stabilization of the L_a state. Vibrational fingerprints in the transient absorption spectra provide compelling evidence of a vibronic coherence established between the two excited states from the earliest times after photoexcitation and lasting until the back-transfer to L_a is complete. The demonstration of response to the environment as a driver of coherent population dynamics among the excited states of tryptophan closes the long debate on its solvent-assisted relaxation mechanisms and extends its application as a local probe of protein dynamics to the ultrafast time scales.

Evaluation of molecular photophysical and photochemical properties using linear response time-dependent density functional theory with classical embedding: Successes and challenges

Time-dependent density functional theory (TDDFT) based approaches have been developed in recent years to model the excited-state properties and transition processes of the molecules in the gas-phase and in a condensed medium, such as in a solution and protein microenvironment or near semiconductor and metal surfaces. In the latter case, usually, classical embedding models have been adopted to account for the molecular environmental effects, leading to the multi-scale approaches of TDDFT/polarizable continuum model (PCM) and TDDFT/molecular mechanics (MM), where a molecular system of interest is designated as the quantum mechanical region and treated with TDDFT, while the environment is usually described using either a PCM or (non-polarizable or polarizable) MM force fields. In this Perspective, we briefly review these TDDFT-related multi-scale models with a specific emphasis on the implementation of analytical energy derivatives, such as the energy gradient and Hessian, the nonadiabatic coupling, the spin-orbit coupling, and the transition dipole moment as well as their nuclear derivatives for various radiative and radiativeless transition processes among electronic states. Three variations of the TDDFT method, the Tamm-Dancoff approximation to TDDFT, spin-flip DFT, and spin-adiabatic TDDFT, are discussed. Moreover, using a model system (pyridine-Ag20 complex), we emphasize that caution is needed to properly account for system-environment interactions within the TDDFT/MM models. Specifically, one should appropriately damp the electrostatic embedding potential from MM atoms and carefully tune the van der Waals interaction potential between the system and the environment. We also highlight the lack of proper treatment of charge transfer between the quantum mechanics and MM regions as well as the need for accelerated TDDFT modelings and interpretability, which calls for new method developments.

The ΔSCF method for non-adiabatic dynamics of systems in the liquid phase

Computational studies of ultrafast photoinduced processes give valuable insights into the photochemical mechanisms of a broad range of compounds. In order to accurately reproduce, interpret, and predict experimental results, which are typically obtained in a condensed phase, it is indispensable to include the condensed phase environment in the computational model. However, most studies are still performed in vacuum due to the high computational cost of state-of-the-art non-adiabatic molecular dynamics (NAMD) simulations. The quantum mechanical/molecular mechanical (QM/MM) solvation method has been a popular model to perform photodynamics in the liquid phase. Nevertheless, the currently used QM/MM embedding techniques cannot sufficiently capture all solute-solvent interactions. In this Perspective, we will discuss the efficient ΔSCF electronic structure method and its applications with respect to the NAMD of solvated compounds, with a particular focus on explicit quantum mechanical solvation. As more research is required for this method to reach its full potential, some challenges and possible directions for future research are presented as well.

The quantum chemical solvation of indole: accounting for strong solute-solvent interactions using implicit/explicit models

In this paper, we investigate the efficacy of different quantum chemical solvent modelling methods of indole in both water and methylcyclohexane solutions. The goal is to show that one can yield good photophysical properties in strongly coupled solute-solvent systems using standard DFT methods. We use standard and linearly-corrected Polarisable Continuum Models (PCM), as well as explicit solvation models, and compare the different model parameters, including the choice of density functional, basis set, and number of explicit solvent molecules. We demonstrate that implicit models overestimate energies and oscillator strengths. In particular, for indole-water, no level inversion is observed, suggesting a dielectric medium on its own is insufficient. In contrast, energies are seen to converge fairly rapidly with respect to cluster size towards experimentally measured properties in the explicit models. We find that the use of B3LYP with a diffuse basis set can adequately represent the photophysics of the system with a cluster size of between 9-12 explicit water molecules. Sampling of configurations from a molecular dynamics simulation suggests that the single point results are suitably representative of the solvated ensemble. For indole-water, we show that solvent reorganisation plays a significant role in stabilisation of the excited state energies. It is hoped that the findings and observations of this study will aid in the choice of solvation model parameters in future studies.

Prediction of the excited-state reaction channels in photo-induced processes of nitrofurantoin using first-principle calculations and dynamics simulations

The understanding of the photochemistry of antibiotic compounds is important because it gives the direct information on the possible environmental pollution caused by them. Due to their large size, the theoretical studies of their excited-state reactions are rather challenging. In current work, we combined the on-the-fly trajectory surface-hopping dynamics, conical-intersection optimizations and excited-state pathway calculations to study the photochemistry of the trans-isomer of nitrofurantoin, a widely-used drug to treat the urinary tract infections. The dynamics-then-pathway approach was taken. First the trajectory surface hopping dynamics at the state-averaged complete-active-space self-consistent-field (SA-CASSCF) level with small active space and small basis sets were run. Second, the minimum-energy conical-intersection optimizations were performed. Finally the excited pathways from the Frank-Condon region to different reaction channels were built at the multi-state multi-reference second-order perturbation (MS-CASPT2) level with large active space and large basis set. Several possible channels responsible for the photo-induced reaction mechanism of the trans-nitrofurantoin were obtained, including the cleavage of the NO bond of the NO₂ moiety, the photoisomerization at the central CN bond, and other internal conversion channels. Our findings give some preliminary explanations on available experimental observations. It is also demonstrates that the current theoretical approach is a powerful tool to explore the excited-state reactions in the photochemistry of media-sized or large-sized drug compounds.

Electronic relaxation of aqueous aminoazobenzenes studied by time-resolved photoelectron spectroscopy and surface hopping TDDFT dynamics calculations

Studies of ultrafast relaxation of molecular chromophores are complicated by the fact that most chromophores of biological and technological importance are rather large molecules and are strongly affected by their environment, either solvent or a protein cage. Here we present an approach which allows us to follow transient electronic structure of complex photoexcited molecules. We use the method of time-resolved photoelectron spectroscopy in solution to follow relaxation of two prototypical aqueous chromophores, Methyl Orange and Metanil Yellow, both of which are aminoazobenzene derivatives. Using excitation by 400 nm laser pulses and ionization by wavelength-selected 46.7 nm XUV pulses from high-order harmonic generation we follow relaxation of both molecules via the dark S1 state. The photoelectron spectra yield binding energies of both ground and excited states. We combine the experimental results with surface hopping time-dependent density functional theory (TDDFT) calculations employing B3LYP+D3 and ωB97X-D functionals. The results demonstrate that the method is generally suitable for description of ultrafast dynamics in these molecules and can recover absolute binding energies observed in the experiment. The B3LYP+D3 functional appears to be better suited for these systems, especially in the case of Metanil Yellow, where it indicates the importance of an intramolecular charge transfer state. Our results pave the way towards quantitative understanding of evolving electronic structure in photo-induced relaxation processes.

Quantum and semiclassical dynamical studies of nonadiabatic processes in solution: achievements and perspectives

We concisely review the main methodological approaches to model nonadiabatic dynamics in isotropic solutions and their applications. Three general classes of models are identified as the most used to include solvent effects in the simulations. The first model describes the solvent as a set of harmonic collective modes coupled to the solute degrees of freedom, and the second as a continuum, while the third explicitly includes solvent molecules in the calculations. The issues related to the use of these models in semiclassical and quantum dynamical simulations are discussed, as well as the main limitations and perspectives of each approach.

The fluorescence of a mercury probe based on osthol

The ability of osthol (OST) to recognize mercury ions in aqueous solution was studied using fluorescence, UV–vis spectrophotometry, mass spectrometry, and ¹H NMR spectroscopy, and the recognition mechanism is discussed. The results showed that OST and Hg²⁺ can form a complex with a stoichiometric ratio of 1:1. The binding constant was 1.552 × 10⁵ L∙mol⁻¹, having a highly efficient and specific selectivity for Hg²⁺. The fluorescence intensity of OST showed a good linear correlation with the Hg²⁺ concentration (6.0 × 10⁻⁵ to 24.0 × 10⁻⁵ mol∙L⁻¹, R² = 0.9954), and the detection limit of the probe was 5.04 × 10⁻⁸ mol∙L⁻¹, which can be used for the determination of Hg²⁺ traces.

Fluorescence Quantum Yields in Complex Environments from QM-MM TDDFT Simulations: The Case of Indole in Different Solvents

Fluorescence is commonly exploited to probe microscopic properties. An important example is tryptophan in protein environments, where variations in fluorescence quantum yield, and in absorption and emission maxima, are used as indicators of changes in the environment. Modeling the fluorescence quantum yield requires the determination of both radiative and nonradiative decay constants, both on the potential energy surface of the excited fluorophore. Furthermore, the inclusion of complex environments implies their accurate representation as well as extensive configurational sampling. In this work, we present and test various methodologies based on time-dependent density functional theory (TDDFT) and quantum mechanics/molecular mechanics (QM/MM) dynamics that take all of these requirements into account to provide a quantitative prediction of the effect of the environment on the fluorescence quantum yield of indole, a tryptophan fluorophore. This investigation paves the way for applications to the realistic spectroscopic characterization of the local protein environment of tryptophan from computer simulations.

SSAIMS-Stochastic-Selection Ab Initio Multiple Spawning for Efficient Nonadiabatic Molecular Dynamics

Ab initio multiple spawning provides a powerful and accurate way of describing the excited-state dynamics of molecular systems, whose strength resides in the proper description of coherence effects during nonadiabatic processes thanks to the coupling of trajectory basis functions. However, the simultaneous propagation of a large number of trajectory basis functions can be numerically inconvenient. We propose here an elegant and simple solution to this issue, which consists of (i) detecting uncoupled groups of coupled trajectory basis functions and (ii) selecting stochastically one of these groups to continue the ab initio multiple spawning dynamics. We show that this procedure can reproduce the results of full ab initio multiple spawning dynamics in cases where the uncoupled groups of trajectory basis functions stay uncoupled throughout the dynamics (which is often the case in high-dimensional problems). We present and discuss the aforementioned idea in detail and provide simple numerical applications on indole, ethylene, and protonated formaldimine, highlighting the potential of stochastic-selection ab initio multiple spawning.

A high-throughput computational approach to UV-Vis spectra in protein mutants

In this work we present a high-throughput approach to the computation of absorption UV-Vis spectra tailored to mutagenesis studies. The scheme makes use of a single molecular dynamics trajectory of a reference (non-mutated) species. The shifts in absorption energy caused by a residue mutation are evaluated by building an effective potential of the environment and computing a correction term based on perturbation theory. The sampling is only performed in the phase space of the initial protein. We analyze the robustness of the method by comparing different approximations for the effective potential, the sampling of mutant residue geometries and observing the impact in the prediction of both bathocromic and hypsochromic shifts. As a test subject, we consider a red fluorescent protein variant with potential biotechnological applications.

Excited state dynamics of aniline homoclusters

We have investigated the relaxation, following excitation in the 290-235 nm region, of neutral aniline homoclusters (An)n formed in a supersonic expansion by femtosecond time resolved ionization. The applied method permits isolation of the dynamics of the dimer from that originated in bigger species of the generated distribution. Interestingly, and differently from the monomer and (An)n≥3 clusters, the dimer does not present a N-H dissociative 1πσ* channel. This fact can be explained in terms of the symmetric structure adopted, in which each molecule establishes two N-Hπ interactions, destabilizing the H dissociation channel. The observations permit relating the photophysics to the interactions established by the aniline units and confirming previous observations and theoretical predictions on the structure of aniline aggregates.

Multistate hybrid time-dependent density functional theory with surface hopping accurately captures ultrafast thymine photodeactivation

We report an efficient analytical implementation of first-order nonadiabatic derivative couplings between arbitrary Born–Oppenheimer states in the hybrid time-dependent density functional theory (TDDFT) framework using atom-centered basis functions.

Structure of the aqueous electron

A cavity or excluded-volume structure best explains the experimental properties of the aqueous or “hydrated” electron.

Ultrafast photochemistry of free-base porphyrin: a theoretical investigation of B → Q internal conversion mediated by dark states

We examine the mechanism of ultrafast internal conversion between the B band (Soret band) and the Q band in porphine (H2P), the prototypical free-base porphyrin, using electronic structure studies and on-the-fly surface-hopping nonadiabatic dynamics. Our study highlights the crucial role of dark states within the N band which are found to mediate B/Q state transfer, necessitating a treatment beyond Gouterman's classic four-orbital model. The sequential B → N → Q pathway dominates largely over the direct B → Q pathway which is found to be energetically unfavorable. Potential energy surface cuts and conical intersections between excited states are determined by TDDFT and validated by CASSCF/CASPT2 and XMCQDPT2 calculations. Both the static analysis and on-the-fly surface-hopping calculations suggest a pathway which involves minor structural deformations via in-plane vibrations. The B → N conversion is a barrierless adiabatic process occurring within ∼20 fs, while the subsequent N → Q conversion occurs via a conical intersection within ∼100 fs, in agreement with time-resolved experiments for porphine and related free base porphyrins. Furthermore, evidence for both sequential and direct transfer to the Qx and Qy states is obtained.

Nuclear Ensemble Approach with Importance Sampling

We show that the importance sampling technique can effectively augment the range of problems where the nuclear ensemble approach can be applied. A sampling probability distribution function initially determines the collection of initial conditions for which calculations are performed, as usual. Then, results for a distinct target distribution are computed by introducing compensating importance sampling weights for each sampled point. This mapping between the two probability distributions can be performed whenever they are both explicitly constructed. Perhaps most notably, this procedure allows for the computation of temperature dependent observables. As a test case, we investigated the UV absorption spectra of phenol, which has been shown to have a marked temperature dependence. Application of the proposed technique to a range that covers 500 K provides results that converge to those obtained with conventional sampling. We further show that an overall improved rate of convergence is obtained when sampling is performed at intermediate temperatures. The comparison between calculated and the available measured cross sections is very satisfactory, as the main features of the spectra are correctly reproduced. As a second test case, one of Tully's classical models was revisited, and we show that the computation of dynamical observables also profits from the importance sampling technique. In summary, the strategy developed here can be employed to assess the role of temperature for any property calculated within the nuclear ensemble method, with the same computational cost as doing so for a single temperature.

Quantum stochastic trajectories: the Smoluchowski-Bohm equation

Molecular systems are quantum systems, but the complete characterization of molecular motions within a fully quantum framework might appear to be an unfeasible task because it would require that the actual nuclear positions are established at any time. One would like to use a quantum molecular trajectory that defines the instantaneous nuclear positions and satisfies the predictions of quantum mechanics in terms of its statistical properties. Even though it can be proven that the single Bohm trajectory provides a representation of the quantum molecular trajectory, this solves the issue only on a theoretical ground: exact solutions of the Schrödinger-Bohm dynamical system are extremely computationally demanding. Therefore, we derive a stochastic equation of Smoluchowski type from the Schrödinger-Bohm dynamics, through projection operator techniques, in order to characterize the molecular motions of open quantum systems. The main quantum features of the motions emerge from the equilibrium distribution, i.e., the wave function's squared modulus integrated on the environment degrees of freedom. Furthermore, we verify the accuracy of the stochastic equation by comparing its predictions with those of the deterministic dynamics for a model system of six interacting harmonic oscillators. The indisputable advantage of this full quantum mechanical approach is that of representing the molecular dynamics, which controls important phenomena like vibrational relaxation, conformational transitions and activated processes, in a self consistent way and at the low computational cost of solving simple stochastic equations.

Mechanism of ultrafast non-reactive deactivation of the retinal chromophore in non-polar solvents

Counterion sensitive photodynamics of the retinal chromophore in solution.

Femtosecond Excited State Dynamics of Size Selected Neutral Molecular Clusters

The work describes a novel experimental approach to track the relaxation dynamics of an electronically excited distribution of neutral molecular clusters formed in a supersonic expansion, by pump-probe femtosecond ionization. The introduced method overcomes fragmentation issues and makes possible to retrieve the dynamical signature of a particular cluster from each mass channel, by associating it to an IR transition of the targeted structure. We have applied the technique to study the nonadiabatic relaxation of pyrrole homoclusters. The results obtained exciting at 243 nm, near the origin of the bare pyrrole electronic absorption, allow us to identify the dynamical signature of the dimer (Py)2, which exhibits a distinctive lifetime of τ1 ∼ 270 fs, considerably longer than the decays recorded for the monomer and bigger size clusters (Py)n>2. A possible relationship between the measured lifetime and the clusters geometries is tentatively discussed.

Photoexcitation and relaxation kinetics of molecular systems in solution: towards a complete in silico model

A theoretical–computational method is proposed for modelling the complete kinetics – from photo-excitation to relaxation – of a chromophore in solution.

Photo-induced reactions from efficient molecular dynamics with electronic transitions using the FIREBALL local-orbital density functional theory formalism

The computational simulation of photo-induced processes in large molecular systems is a very challenging problem. Firstly, to properly simulate photo-induced reactions the potential energy surfaces corresponding to excited states must be appropriately accessed; secondly, understanding the mechanisms of these processes requires the exploration of complex configurational spaces and the localization of conical intersections; finally, photo-induced reactions are probability events, that require the simulation of hundreds of trajectories to obtain the statistical information for the analysis of the reaction profiles. Here, we present a detailed description of our implementation of a molecular dynamics with electronic transitions algorithm within the local-orbital density functional theory code FIREBALL, suitable for the computational study of these problems. As an example of the application of this approach, we also report results on the [2 + 2] cycloaddition of ethylene with maleic anhydride and on the [2 + 2] photo-induced polymerization reaction of two C60 molecules. We identify different deactivation channels of the initial electron excitation, depending on the time of the electronic transition from LUMO to HOMO, and the character of the HOMO after the transition.

The CHARMM-TURBOMOLE interface for efficient and accurate QM/MM molecular dynamics, free energies, and excited state properties

The quantum mechanical (QM)/molecular mechanical (MM) interface between Chemistry at HARvard Molecular Mechanics (CHARMM) and TURBOMOLE is described. CHARMM provides an extensive set of simulation algorithms, like molecular dynamics (MD) and free energy perturbation, and support for mature nonpolarizable and Drude polarizable force fields. TURBOMOLE provides fast QM calculations using density functional theory or wave function methods and excited state properties. CHARMM-TURBOMOLE is well-suited for extended QM/MM MD simulations using first principles methods with large (triple-ζ) basis sets. We demonstrate these capabilities with a QM/MM simulation of Mg(2+) (aq), where the MM outer sphere water molecules are represented using the SWM4-NDP Drude polarizable force field and the ion and inner coordination sphere are represented using QM PBE, PBE0, and MP2 methods. The relative solvation free energies of Mg(2+) and Zn(2+) were calculated using thermodynamic integration. We also demonstrate the features for excited state properties. We calculate the time-averaged solution absorption spectrum of indole, the emission spectrum of the indole 1La excited state, and the electronic circular dichroism spectrum of an oxacepham.

Photodissociation dynamics of propargylene, HCCCH

We report a joint theoretical and experimental study on the photodissociation of the C₃H₂ isomer propargylene, HCCCH, combining velocity map imaging with nonadiabatic surface hopping calculations.

Dynamical steps that bridge piecewise adiabatic shapes in the exact time-dependent potential energy surface

We study the exact time-dependent potential energy surface (TDPES) in the presence of strong nonadiabatic coupling between the electronic and nuclear motion. The concept of the TDPES emerges from the exact factorization of the full electron-nuclear wave function [A. Abedi, N. T. Maitra, and E. K. U. Gross, Phys. Rev. Lett. 105, 123002 (2010)]. Employing a one-dimensional model system, we show that the TDPES exhibits a dynamical step that bridges between piecewise adiabatic shapes. We analytically investigate the position of the steps and the nature of the switching between the adiabatic pieces of the TDPES.