The photodynamics of ethylene: A surface-hopping study on structural aspects

Deuterium Isotope Effect on Internal Conversion of Ethylene Studied by Time-Resolved Photoelectron Spectroscopy

The effect of deuterium isotopes on the internal conversion of ethylene is studied by using extreme ultraviolet time-resolved photoelectron spectroscopy. For deuterium-labeled ethylene, the time scale for ultrafast internal conversion is increased by a factor of approximately √2, in agreement with the results of ab initio multiple spawning calculations, indicating the essential role played by hydrogen motion in the conversion process. Following internal conversion, a metastable species with an electron binding energy of ∼9 eV is produced, and it decays with a time constant similar to that for both isotopologues.

Generalized Semiclassical Ehrenfest Method: A Route to Wave Function-Free Photochemistry and Nonadiabatic Dynamics with Only Potential Energies and Gradients

We reconsider recent methods by which direct dynamics calculations of electronically nonadiabatic processes can be carried out while requiring only adiabatic potential energies and their gradients. We show that these methods can be understood in terms of a new generalization of the well-known semiclassical Ehrenfest method. This is convenient because it eliminates the need to evaluate electronic wave functions and their matrix elements along the mixed quantum-classical trajectories. The new approximations and procedures enabling this advance are the curvature-driven approximation to the time-derivative coupling, the generalized semiclassical Ehrenfest method, and a new gradient correction scheme called the time-derivative matrix (TDM) scheme. When spin-orbit coupling is present, one can carry out dynamics calculations in the fully adiabatic basis using potential energies and gradients calculated without spin-orbit coupling plus the spin-orbit coupling matrix elements. Even when spin-orbit coupling is neglected, the method is useful because it allows calculations by electronic structure methods for which nonadiabatic coupling vectors are unavailable. In order to place the new considerations in context, the article starts out with a review of background material on trajectory surface hopping, the semiclassical Ehrenfest scheme, and methods for incorporating decoherence. We consider both internal conversion and intersystem crossing. We also review several examples from our group of successful applications of the curvature-driven approximation.

Quantum Quality with Classical Cost: Ab Initio Nonadiabatic Dynamics Simulations Using the Mapping Approach to Surface Hopping

Nonadiabatic dynamics methods are an essential tool for investigating photochemical processes. In the context of employing first-principles electronic structure techniques, such simulations can be carried out in a practical manner using semiclassical trajectory-based methods or wave packet approaches. While all approaches applicable to first-principles simulations are necessarily approximate, it is commonly thought that wave packet approaches offer inherent advantages over their semiclassical counterparts in terms of accuracy and that this trait simply comes at a higher computational cost. Here we demonstrate that the mapping approach to surface hopping (MASH), a recently introduced trajectory-based nonadiabatic dynamics method, can be efficiently applied in tandem with ab initio electronic structure. Our results even suggest that MASH may provide more accurate results than on-the-fly wave packet techniques, all at a much lower computational cost.

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.

Deciphering Methylation Effects on S2(ππ*) Internal Conversion in the Simplest Linear α,β-Unsaturated Carbonyl

Chemical substituents can influence photodynamics by altering the location of critical points and the topography of the potential energy surfaces (electronic effect) and by selectively modifying the inertia of specific nuclear modes (inertial effects). Using nonadiabatic dynamics simulations, we investigate the impact of methylation on S₂(ππ*) internal conversion in acrolein, the simplest linear α,β-unsaturated carbonyl. Consistent with time constants reported in a previous time-resolved photoelectron spectroscopy study, S₂ → S₁ deactivation occurs on an ultrafast time scale (∼50 fs). However, our simulations do not corroborate the sequential decay model used to fit the experiment. Instead, upon reaching the S₁ state, the wavepacket bifurcates: a portion undergoes ballistic S₁ → S₀ deactivation (∼90 fs) mediated by fast bond-length alternation motion, while the remaining decays on the picosecond time scale. Our analysis reveals that methyl substitution, generally assumed to mainly exert inertial influence, is also manifested in important electronic effects due to its weak electron-donating ability. While methylation at the β C atom gives rise to effects principally of an inertial nature, such as retarding the twisting motion of the terminal -CHCH₃ group and increasing its coupling with pyramidalization, methylation at the α or carbonyl C atom modifies the potential energy surfaces in a way that also contributes to altering the late S₁-decay behavior. Specifically, our results suggest that the observed slowing of the picosecond component upon α-methylation is a consequence of a tighter surface and reduced amplitude along the central pyramidalization, effectively restricting the access to the S₁/S₀-intersection seam. Our work offers new insight into the S₂(ππ*) internal conversion mechanisms in acrolein and its methylated derivatives and highlights site-selective methylation as a tuning knob to manipulate photochemical reactions.

Direct structural observation of ultrafast photoisomerization dynamics in sinapate esters

Sinapate esters have been extensively studied for their potential application in 'nature-inspired' photoprotection. There is general consensus that the relaxation mechanism of sinapate esters following photoexcitation with ultraviolet radiation is mediated by geometric isomerization. This has been largely inferred through indirect studies involving transient electronic absorption spectroscopy in conjunction with steady-state spectroscopies. However, to-date, there is no direct experimental evidence tracking the formation of the photoisomer in real-time. Using transient vibrational absorption spectroscopy, we report on the direct structural changes that occur upon photoexcitation, resulting in the photoisomer formation. Our mechanistic analysis predicts that, from the photoprepared ππ* state, internal conversion takes place through a conical intersection (CI) near the geometry of the initial isomer. Our calculations suggest that different CI topographies at relevant points on the seam of intersection may influence the isomerization yield. Altogether, we provide compelling evidence suggesting that a sinapate ester's geometric isomerization can be a more complex dynamical process than originally thought.

Fast Screening of Minimum Energy Crossing Points with Semiempirical Tight-Binding Methods

The investigation of photochemical processes is a highly active field in computational chemistry. One research direction is the automated exploration and identification of minimum energy conical intersection (MECI) geometries. However, due to the immense technical effort required to calculate nonadiabatic potential energy landscapes, the routine application of such computational protocols is severely limited. In this study, we will discuss the prospect of combining adiabatic potential energy surfaces from semiempirical quantum mechanical calculations with specialized confinement potential and metadynamics simulations to identify S₀/T₁ minimum energy crossing point (MECP) geometries. It is shown that MECPs calculated at the GFN2-xTB level can provide suitable approximations to high-level S₀/S₁ab initio conical intersection geometries at a fraction of the computational cost. Reference MECIs of benzene are studied to illustrate the basic concept. An example application of the presented protocol is demonstrated for a set of photoswitch molecules.

Pre-Dewar structure modulates protonated azaindole photodynamics

Recent experimental work revealed that the lifetime of the S₃ state of protonated 7-azaindole is about ten times longer than that of protonated 6-azaindole. We simulated the nonradiative decay pathways of these molecules using trajectory surface hopping dynamics after photoexcitation into S₃ to elucidate the reason for this difference. Both isomers mainly follow a common ππ* relaxation pathway involving multiple state crossings while coming down from S₃ to S₁ in the subpicosecond time scale. However, the simulations reveal that the excited-state topographies are such that while the 6-isomer can easily access the region of nonadiabatic transitions, the internal conversion of the 7-isomer is delayed by a pre-Dewar bond formation with a boat conformation.

Robust ΔSCF calculations with direct energy functional minimization methods and STEP for molecules and materials

The direct energy functional minimization method using the orbital transformation (OT) scheme in the program package CP2K has been employed for Δ self-consistent field (ΔSCF) calculations. The OT method for non-uniform molecular orbitals occupations allows us to apply the ΔSCF method for various kinds of molecules and periodic systems. Vertical excitation energies of heteroaromatic molecules and condensed phase systems, such as solvated ethylene and solvated uracil obeying periodic boundary conditions, are reported using the ΔSCF method. In addition, a Re-phosphate molecule attached to the surface of anatase (TiO₂) has been investigated. Additionally, we have implemented a recently proposed state-targeted energy projection ΔSCF algorithm [K. Carter-Fenk and J. M. Herbert, J. Chem. Theory Comput. 16(8), 5067-5082 (2020)] for diagonalization based SCF in CP2K. It is found that the OT scheme provides a smooth and robust SCF convergence for all investigated excitation energies and (non-)periodic systems.

Fewest switches surface hopping with Baeck-An couplings

In the Baeck-An (BA) approximation, first-order nonadiabatic coupling vectors are given in terms of adiabatic energy gaps and the second derivative of the gaps with respect to the coupling coordinate. In this paper, a time-dependent (TD) BA approximation is derived, where the couplings are computed from the energy gaps and their second time-derivatives. TD-BA couplings can be directly used in fewest switches surface hopping, enabling nonadiabatic dynamics with any electronic structure methods able to provide excitation energies and energy gradients. Test results of surface hopping with TD-BA couplings for ethylene and fulvene show that the TD-BA approximation delivers a qualitatively correct picture of the dynamics and a semiquantitative agreement with reference data computed with exact couplings. Nevertheless, TD-BA does not perform well in situations conjugating strong couplings and small velocities. Considered the uncertainties in the method, TD-BA couplings could be a competitive approach for inexpensive, exploratory dynamics with a small trajectories ensemble. We also assessed the potential use of TD-BA couplings for surface hopping dynamics with time-dependent density functional theory (TDDFT), but the results are not encouraging due to singlet instabilities near the crossing seam with the ground state.

Fewest switches surface hopping with Baeck-An couplings

In the Baeck-An (BA) approximation, first-order nonadiabatic coupling vectors are given in terms of adiabatic energy gaps and the second derivative of the gaps with respect to the coupling coordinate. In this paper, a time-dependent (TD) BA approximation is derived, where the couplings are computed from the energy gaps and their second time-derivatives. TD-BA couplings can be directly used in fewest switches surface hopping, enabling nonadiabatic dynamics with any electronic structure methods able to provide excitation energies and energy gradients. Test results of surface hopping with TD-BA couplings for ethylene and fulvene show that the TD-BA approximation delivers a qualitatively correct picture of the dynamics and a semiquantitative agreement with reference data computed with exact couplings. Nevertheless, TD-BA does not perform well in situations conjugating strong couplings and small velocities. Considered the uncertainties in the method, TD-BA couplings could be a competitive approach for inexpensive, exploratory dynamics with a small trajectories ensemble. We also assessed the potential use of TD-BA couplings for surface hopping dynamics with time-dependent density functional theory (TDDFT), but the results are not encouraging due to singlet instabilities near the crossing seam with the ground state.

Machine Learning for Electronically Excited States of Molecules

Electronically excited states of molecules are at the heart of photochemistry, photophysics, as well as photobiology and also play a role in material science. Their theoretical description requires highly accurate quantum chemical calculations, which are computationally expensive. In this review, we focus on not only how machine learning is employed to speed up such excited-state simulations but also how this branch of artificial intelligence can be used to advance this exciting research field in all its aspects. Discussed applications of machine learning for excited states include excited-state dynamics simulations, static calculations of absorption spectra, as well as many others. In order to put these studies into context, we discuss the promises and pitfalls of the involved machine learning techniques. Since the latter are mostly based on quantum chemistry calculations, we also provide a short introduction into excited-state electronic structure methods and approaches for nonadiabatic dynamics simulations and describe tricks and problems when using them in machine learning for excited states of molecules.

Machine Learning for Electronically Excited States of Molecules

Electronically excited states of molecules are at the heart of photochemistry, photophysics, as well as photobiology and also play a role in material science. Their theoretical description requires highly accurate quantum chemical calculations, which are computationally expensive. In this review, we focus on not only how machine learning is employed to speed up such excited-state simulations but also how this branch of artificial intelligence can be used to advance this exciting research field in all its aspects. Discussed applications of machine learning for excited states include excited-state dynamics simulations, static calculations of absorption spectra, as well as many others. In order to put these studies into context, we discuss the promises and pitfalls of the involved machine learning techniques. Since the latter are mostly based on quantum chemistry calculations, we also provide a short introduction into excited-state electronic structure methods and approaches for nonadiabatic dynamics simulations and describe tricks and problems when using them in machine learning for excited states of molecules.

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

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

Mechanistic Aspects of the Photophysics of UVA Filters Based on Meldrum Derivatives

Skin photoprotection against UVA radiation is crucial, but it is hindered by the sparsity of approved commercial UVA filters. Sinapoyl malate (SM) derivatives are promising candidates for a new class of UVA filters. They have been previously identified as an efficient photoprotective sunscreen in plants due to their fast nonradiative energy dissipation. Combining experimental and computational results, in our previous letter (J. Phys. Chem. Lett. 2021, 12, 337-344) we showed that coumaryl Meldrum (CMe) and sinapoyl Meldrum (SMe) are outstanding candidates for UVA filters in sunscreen formulations. Here, we deliver a comprehensive computational characterization of the excited-state dynamics of these molecules. Using reaction pathways and excited-state dynamics simulations, we could elucidate the photodeactivation mechanism of these molecules. Upon photoexcitation, they follow a two-step logistic decay. First, an ultrafast and efficient relaxation stabilizes the excited state alongside a 90° twisting around the allylic double bond, giving rise to a minimum with a twisted intramolecular excited-state (TICT) character. From this minimum, internal conversion to the ground state occurs after overcoming a 0.2 eV barrier. Minor differences in the nonradiative decay and fluorescence of CMe and SMe are associated with an additional minimum present only in the latter.

Velocity Adjustment in Surface Hopping: Ethylene as a Case Study of the Maximum Error Caused by Direction Choice

The most common surface hopping dynamics algorithms require velocity adjustment after hopping to ensure total-energy conservation. Based on the semiclassical analysis, this adjustment must be made parallel to the nonadiabatic coupling vector's direction. Nevertheless, this direction is not always known, and the common practice has been to adjust the velocity in either the linear momentum or velocity directions. This paper benchmarks surface hopping dynamics of photoexcited ethylene with velocity adjustment in several directions, including those of the nonadiabatic coupling vector, the momentum, and the energy gradient difference. It is shown that differences in time constants and structural evolution fall within the statistical uncertainty of the method considering up to 500 trajectories in each dynamics set, rendering the three approaches statistically equivalent. For larger ensembles beyond 1000 trajectories, significant differences between the results arise, limiting the validity of adjustment in alternative directions. Other possible adjustment directions (velocity, single-state gradients, angular momentum) are evaluated as well. Given the small size of ethylene, the results reported in this paper should be considered an upper limit for the error caused by the choice of the velocity-adjustment direction on surface hopping dynamics.

Photochemistry of Amylene Double Bond in Clusters on Free Argon Nanoparticles

We have investigated reactivity of double bond in 2-methyl-2-butene (also trimethylethylene or amylene) in the excited and ionized states. In a combined experimental and theoretical study, we focused on both the intermolecular and intramolecular reactions. In a molecular beam experiment, we have sequentially picked up several amylene molecules on the surface of argon nanoparticles Ar_M, M̅ ≈ 90, acting as a cold support. Ionization with 70 eV electrons yields mass spectra strongly dominated by amylene cluster ions Am(Am)_n⁺. Interestingly, upon multiphoton ionization with 193 nm (6.4 eV) photons, a new strong fragment series appears in the spectra, nominally corresponding to an addition of two carbon atoms, i.e., (Am)_nC₂⁺. This difference between electron and photoionization suggests a reaction in an excited state of amylene with a neighboring amylene molecule. We used techniques of nonadiabatic molecular dynamics to study the reactivity of amylene molecules both in the excited and in ionized states. Possible reaction pathways are proposed, substantiating the observed differences between the electron ionization and photoionization mass spectra.

The statistical molecular fragmentation model compared to experimental plasma induced hydrocarbon decays

We compare the predictions of our recently developed statistical molecular fragmentation model with experimental results from plasma induced decay of propene and other small hydrocarbons.

A molecular perspective on Tully models for nonadiabatic dynamics

We present a series of standardized molecular tests for nonadiabatic dynamics, reminiscent of the one-dimensional Tully models proposed in 1990.

Quasi-Diabatic Scheme for Nonadiabatic On-the-Fly Simulations

We use the quasi-diabatic (QD) propagation scheme to perform on-the-fly nonadiabatic simulations of the photodynamics of ethylene. The QD scheme enables a seamless interface between accurate diabatic-based quantum dynamics approaches and adiabatic electronic structure calculations, explicitly avoiding any efforts to construct global diabatic states or reformulate the diabatic dynamics approach to the adiabatic representation. Using the partial linearized path-integral approach and the symmetrical quasi-classical approach as the diabatic dynamics methods, the QD propagation scheme enables direct nonadiabatic simulation with complete active space self-consistent field on-the-fly electronic structure calculations. The population dynamics obtained from both approaches are in a close agreement with the quantum wavepacket-based method and outperform the widely used trajectory surface-hopping approach. Further analysis of the ethylene photodeactivation pathways demonstrates the correct predictions of competing processes of nonradiative relaxation mechanism through various conical intersections. This work provides the foundation of using accurate diabatic dynamics approaches and on-the-fly adiabatic electronic structure information to perform ab initio nonadiabatic simulation.

Coherence in nonradiative transitions: internal conversion in Rydberg-excited N-methyl and N-ethyl morpholine

The survival of coherent wavepacket motion during internal conversions is observed in relatively large molecules, N-methyl morpholine and N-ethyl morpholine, where standard models imply fast decoherence in a statistical limit.

Early events in the photochemistry of 5-diazo Meldrum's acid: formation of a product manifold in C–N bound and pre-dissociated intersection seam regions

Photolysis of 5-diazo Meldrum's acid yields three different primary products in a sub-ps scale. High-level computations show that this is due to the presence of an extended seam of intersection associated to different reaction paths.

Photochemistry and photophysics at extended seams of conical intersection

The role of extended seams of conical intersection in excited-state mechanisms is reviewed. Seams are crossings of the potential energy surface in many dimensions where the decay from the excited to the ground state can occur, and the extended seam is composed of different segments lying along a reaction coordinate. Every segment is associated with a different primary photoproduct, which gives rise to competing pathways. This idea is first illustrated for fulvene and ethylene, and then it is used to explain more complex cases such as the dependence of the isomerisation of retinal chromophore isomers on the protein environment, the dependence of the efficiency of the azobenzene photochemical switch on the wavelength of irradiation and the direction of the isomerisation, and the coexistence of different mechanisms in the photo-induced Wolff rearrangement of diazonaphthoquinone. The role of extended seams in the photophysics of the DNA nucleobases and the relationship between two-state seams and three-state crossings is also discussed. As an outlook, the design of optical control strategies based on the passage of the excited molecule through the seam is considered, and it is shown how the excited-state lifetime of fulvene can be modulated by shaping the energy of the seam.

Spin-flip reactions of Zr + C2H6 researched by relativistic density functional theory

Density functional theory (DFT) with relativistic corrections of zero-order regular approximation (ZORA) has been applied to explore the reaction mechanisms of ethane dehydrogenation by Zr atom with triplet and singlet spin-states. Among the complicated minimum energy reaction path, the available states involves three transition states (TS), and four stationary states (1) to (4) and one intersystem crossing with spin-flip (marked by -->): (3) Zr + C 2 H 6 → (3) Zr-CH 3 -CH 3 ((3)1) → (3)TS 1/2 → (3) ZrH-CH 2 -CH 3 ((3)2) → (3) TS 2/3 --> (1) ZrH2-CH2 = CH2 ((1) 3) → (1) TS 3/4 → (1) ZrH 3 -CH = CH 2 ((1)4). The minimum energy crossing point is determined with the help of the DFT fractional-occupation-number (FON) approach. The spin inversion leads the reaction pathway transferring from the triplet potential energy surface (PES) to the singlet's accompanying with the activation of the second C-H bond. The overall reaction is calculated to be exothermic by about 231 kJ mol(-1). Frequency and NBO analysis are also applied to confirm with the experimental observed data.

Nonlinear dimensionality reduction for nonadiabatic dynamics: the influence of conical intersection topography on population transfer rates

Conical intersections play a critical role in the nonadiabatic relaxation of excited electronic states. However, there are an infinite number of these intersections and it is difficult to predict which are actually relevant. Furthermore, traditional descriptors such as intrinsic reaction coordinates and steepest descent paths often fail to adequately characterize excited state reactions due to their highly nonequilibrium nature. To address these deficiencies in the characterization of excited state mechanisms, we apply a nonlinear dimensionality reduction scheme (diffusion mapping) to generate reaction coordinates directly from ab initio multiple spawning dynamics calculations. As illustrated with various examples of photoisomerization dynamics, excited state reaction pathways can be derived directly from simulation data without any a priori specification of relevant coordinates. Furthermore, diffusion maps also reveal the influence of intersection topography on the efficiency of electronic population transfer, providing further evidence that peaked intersections promote nonadiabatic transitions more effectively than sloped intersections. Our results demonstrate the usefulness of nonlinear dimensionality reduction techniques as powerful tools for elucidating reaction mechanisms beyond the statistical description of processes on ground state potential energy surfaces.

Wave Packet Dynamics at an Extended Seam of Conical Intersection: Mechanism of the Light-Induced Wolff Rearrangement

Quantum dynamics calculations on a model surface based on CASPT2//CASSCF calculations are carried out to probe the traversal of a wave packet through an extended seam of conical intersection during the light-induced Wolff rearrangement of diazonaphtoquinone. The reaction is applied in the fabrication of integrated circuits. It consists of nitrogen elimination and ring rearrangement to yield a ketene. After excitation, the wave packet relaxes and reaches the extended seam. A fraction of the wave packet decays to the ground state at a region of the seam connected to a carbene intermediate, while the remaining part decays at a region leading to the ketene. The passage of the wave packet through the extended seam explains the competition between concerted ketene formation and a stepwise mechanism involving a carbene. The two primary photoproducts are formed in the first 100 fs of the simulation, in agreement with recent ultrafast spectroscopy measurements.

Ultrafast internal conversion in ethylene. I. The excited state lifetime

Using a combined theoretical and experimental approach, we investigate the non-adiabatic dynamics of the prototypical ethylene (C(2)H(4)) molecule upon π → π∗ excitation. In this first part of a two part series, we focus on the lifetime of the excited electronic state. The femtosecond time-resolved photoelectron spectrum (TRPES) of ethylene is simulated based on our recent molecular dynamics simulation using the ab initio multiple spawning method with multi-state second order perturbation theory [H. Tao, B. G. Levine, and T. J. Martinez, J. Phys. Chem. A 113, 13656 (2009)]. We find excellent agreement between the TRPES calculation and the photoion signal observed in a pump-probe experiment using femtosecond vacuum ultraviolet (hν = 7.7 eV) pulses for both pump and probe. These results explain the apparent discrepancy over the excited state lifetime between theory and experiment that has existed for ten years, with experiments [e.g., P. Farmanara, V. Stert, and W. Radloff, Chem. Phys. Lett. 288, 518 (1998) and K. Kosma, S. A. Trushin, W. Fuss, and W. E. Schmid, J. Phys. Chem. A 112, 7514 (2008)] reporting much shorter lifetimes than predicted by theory. Investigation of the TRPES indicates that the fast decay of the photoion yield originates from both energetic and electronic factors, with the energetic factor playing a larger role in shaping the signal.