From the (1B) Spectroscopic State to the Photochemical Product of the Ultrafast Ring-Opening of 1,3-Cyclohexadiene: A Spectral Observation of the Complete Reaction Path

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.

Using a multistate mapping approach to surface hopping to predict the ultrafast electron diffraction signal of gas-phase cyclobutanone

Using the recently developed multistate mapping approach to surface hopping (multistate MASH) method combined with SA(3)-CASSCF(12,12)/aug-cc-pVDZ electronic structure calculations, the gas-phase isotropic ultrafast electron diffraction (UED) of cyclobutanone is predicted and analyzed. After excitation into the n-3s Rydberg state (S2), cyclobutanone can relax through two S2/S1 conical intersections, one characterized by compression of the CO bond and the other by dissociation of the α-CC bond. Subsequent transfer into the ground state (S0) is then achieved via two additional S1/S0 conical intersections that lead to three reaction pathways: α ring-opening, ethene/ketene production, and CO liberation. The isotropic gas-phase UED signal is predicted from the multistate MASH simulations, allowing for a direct comparison to the experimental data. This work, which is a contribution to the cyclobutanone prediction challenge, facilitates the identification of the main photoproducts in the UED signal and thereby emphasizes the importance of dynamics simulations for the interpretation of ultrafast experiments.

Automatic Clustering of Excited-State Trajectories: Application to Photoexcited Dynamics

We introduce automatic clustering as a computationally efficient tool for classifying and interpreting trajectories from simulations of photo-excited dynamics. Trajectories are treated as time-series data, with the features for clustering selected by variance mapping of normalized data. The L2-norm and dynamic time warping are proposed as suitable similarity measures for calculating the distance matrices, and these are clustered using the unsupervised density-based DBSCAN algorithm. The silhouette coefficient and the number of trajectories classified as noise are used as quality measures for the clustering. The ability of clustering to provide rapid overview of large and complex trajectory data sets, and its utility for extracting chemical and physical insight, is demonstrated on trajectories corresponding to the photochemical ring-opening reaction of 1,3-cyclohexadiene, noting that the clustering can be used to generate reduced dimensionality representations in an unbiased manner.

Mapping the photochemistry of cyclopentadiene: from theory to ultrafast X-ray scattering

The photoinduced ring-conversion reaction when cyclopentadiene (CP) is excited at 5.10 eV is simulated using surface-hopping semiclassical trajectories with XMS(3)-CASPT2(4,4)/cc-pVDZ electronic structure theory. In addition, PBE0/def2-SV(P) is employed for ground state propagation of the trajectories. The dynamics is propagated for 10 ps, mapping both the nonadiabatic short-time dynamics (<300 fs) and the increasingly statistical dynamics on the electronic ground state. The short-time dynamics yields a mixture of hot CP and bicyclo[2.1.0]pentene (BP), with the two products reached via different regions of the same conical intersection seam. On the ground state, we observe slow conversion from BP to CP which is modelled by RRKM theory with a transition state determined using PBE0/def2-TZVP. The CP products are furthermore associated with ground state hydrogen shifts and some H-atom dissociation. Finally, the prospects for detailed experimental mapping using novel ultrafast X-ray scattering experiments are discussed and observables for such experiments are predicted. In particular, we assess the possibility of retrieving electronic states and their populations alongside the structural dynamics.

Robust Inversion of Time-Resolved Data via Forward-Optimization in a Trajectory Basis

An inversion method for time-resolved data from ultrafast experiments is introduced, based on forward-optimization in a trajectory basis. The method is applied to experimental data from X-ray scattering of the photochemical ring-opening reaction of 1,3-cyclohexadiene and electron diffraction of the photodissociation of CS₂. In each case, inversion yields a model that reproduces the experimental data, identifies the main dynamic motifs, and agrees with independent experimental observations. Notably, the method explicitly accounts for continuity constraints and is robust even for noisy data.

Real-time observation of the Woodward-Hoffmann rule for 1,3-cyclohexadiene by femtosecond soft X-ray transient absorption

The stereochemistry of pericyclic reactions is explained by orbital symmetry conservation, referred to as the Woodward-Hoffmann (WH) rule. Although this rule has been verified using the structures of reactants and products, the temporal evolution of the orbital symmetry during the reaction has not been clarified. Herein, we used femtosecond soft X-ray transient absorption spectroscopy to elucidate the thermal pericyclic reaction of 1,3-cyclohexadiene (CHD) molecules, i.e., their isomerization to 1,3,5-hexatriene. In the present experimental scheme, the ring-opening reaction is driven by the thermal vibrational energy induced by photoexcitation to the Rydberg states at 6.2 eV and subsequent femtosecond relaxation to the ground state of CHD molecules. The direction of the ring opening, which can be conrotatory or disrotatory, was the primary focus, and the WH rule predicts the disrotatory pathway in the thermal process. We observed the shifts in K-edge absorption of the carbon atom from the 1s orbital to vacant molecular orbitals around 285 eV at a delay between 340 and 600 fs. Furthermore, a theoretical investigation predicts that the shifts depend on the molecular structures along the reaction pathways and the observed shifts in induced absorption are attributed to the structural change in the disrotatory pathway. This confirms that the orbital symmetry is dynamically conserved in the ring-opening reaction of CHD molecules as predicted using the WH rule.

Nonadiabatic Dynamics of 1,3-Cyclohexadiene by Curvature-Driven Coherent Switching with Decay of Mixing

The photoinduced ring-opening reaction of 1,3-cyclohexadiene to produce 1,3,5-hexatriene is a classic electrocyclic reaction and is also a prototype for many reactions of biological and synthetic importance. Here, we simulate the ultrafast nonadiabatic dynamics of the reaction in the manifold of the three lowest valence electronic states by using extended multistate complete-active-space second-order perturbation theory (XMS-CASPT2) combined with the curvature-driven coherent switching with decay of mixing (κCSDM) dynamical method. We obtain an excited-state lifetime of 79 fs, and a product quantum yield of 40% from the 500 trajectories initiated in the S₁ excited state. The obtained lifetime and quantum yield values are very close to previously reported experimental and computed values, showing the capability of performing a reasonable nonadiabatic ring-opening dynamics with the κCSDM method that does not require nonadiabatic coupling vectors, time derivatives, or diabatization. In addition, we study the ring-opening reaction by initiating the trajectories in the dark state S₂. We also optimize the S₀/S₁ and S₁/S₂ minimum-energy conical intersections (MECIs) by XMS-CASPT2; for S₁/S₂, we optimized both an inner and an outer local-minimum-energy conical intersections (LMECIs). We provide the potential energy profile along the ring-opening coordinate by joining selected critical points via linear synchronous transit paths. We find the inner S₁/S₂ LMECI to be more crucial than the outer one.

Photochemical Ring-Opening Reaction of 1,3-Cyclohexadiene: Identifying the True Reactive State

The photochemically induced ring-opening isomerization reaction of 1,3-cyclohexadiene to 1,3,5-hexatriene is a textbook example of a pericyclic reaction and has been amply investigated with advanced spectroscopic techniques. The main open question has been the identification of the single reactive state which drives the process. The generally accepted description of the isomerization pathway starts with a valence excitation to the lowest lying bright state, followed by a passage through a conical intersection to the lowest lying doubly excited state, and finally a branching between either the return to the ground state of the cyclic molecule or the actual ring-opening reaction leading to the open-chain isomer. Here, in a joint experimental and computational effort, we demonstrate that the evolution of the excitation-deexcitation process is much more complex than that usually described. In particular, we show that an initially high-lying electronic state smoothly decreasing in energy along the reaction path plays a key role in the ring-opening reaction.

Multichannel photodissociation dynamics in CS2 studied by ultrafast electron diffraction

The structural dynamics of photoexcited gas-phase carbon disulfide (CS₂) molecules are investigated using ultrafast electron diffraction. The dynamics were triggered by excitation of the optically bright ¹B₂(¹Σ_u⁺) state by an ultraviolet femtosecond laser pulse centred at 200 nm. In accordance with previous studies, rapid vibrational motion facilitates a combination of internal conversion and intersystem crossing to lower-lying electronic states. Photodissociation via these electronic manifolds results in the production of CS fragments in the electronic ground state and dissociated singlet and triplet sulphur atoms. The structural dynamics are extracted from the experiment using a trajectory-fitting filtering approach, revealing the main characteristics of the singlet and triplet dissociation pathways. Finally, the effect of the time-resolution on the experimental signal is considered and an outlook to future experiments provided.

Sleeping Beauties in Chemistry. Oosterhoff, Havinga and Schlatmann: Four Years Before "The Woodward-Hoffmann Rules"†

Several forerunners to the Woodward-Hoffmann rules appear in the chemical literature in the early 1960s. While these precedents refer to orbital symmetry and explain either electrocyclic reactions (Luitzen Oosterhoff, cited by Egbert Havinga and Jos Schlatmann in Tetrahedron in 1961) or some cycloaddition reactions (Kenichi Fukui, in a book chapter published in 1964), they did not attract any attention and did not serve to initiate any research prior to the publication of the five Woodward and Hoffmann communications in 1965. Even Woodward and Hoffmann were unaware of these precedents (though Hoffmann knew of Fukui's frontier orbital theory) until after they had completed the relevant portions of their work. The Oosterhoff-Havinga-Schlatmann story will be told in this paper; the Fukui story will be told in the next paper in this series on the history of the development of the Woodward-Hoffmann rules. Explanations for these precedents not being productive in solving the no-mechanism problem are discussed.

On Electron Pair Rearrangements in Photochemical Reactions: 1,3-Cyclohexadiene Ring Opening

1,3-Cyclohexadiene ring opening has been studied within the bonding evolution theory (BET) framework. We have focused on describing for the first time the electron pair rearrangements leading to the cis-1,3,5-hexatriene (HT) product from CHD. The nature of bonding in this process begins with the weakening of the double bonds in the Franck-Condon region. Along the 1¹B surface, the C-C sigma bond weakens. Meanwhile, its density redistributes toward the whole CHD ring, mainly over double bonds. Breaking of this bond occurs on the 2¹A surface due to the symmetrical splitting of pair density from this region. This density redistributes toward the reaction center once the pericyclic minimum is reached. The formation of the double bonds that characterize HT occurs gradually in the ground state. However, near the 2¹A/1¹A intersection, these bonds are partially established.

Ultraviolet Excitation Dynamics of Nitrobenzenes

Time-resolved photoelectron imaging was used to investigate nonadiabatic processes operating in the excited electronic states of nitrobenzene and three methyl-substituted derivatives: 3,5-, 2,6-, and 2,4-dimethylnitrobenzene. The primary goal was evaluating the dynamical impact of the torsional angle between the NO₂ group and the benzene ring plane-something previously implicated in mediating the propensity for branching into different photodissociation pathways (NO vs NO₂ elimination). Targeted, photoinitiated release of NO radicals is of interest for clinical medicine applications, and there is a need to establish basic structure-dynamics-function principles in systematically varied model systems following photoexcitation. Within our 200 ps experimental detection window, we observed no significant differences in the excited-state lifetimes exhibited by all species under study using a 267 nm pump and ionization with an intense 400 nm probe. In agreement with previous theoretical predictions, this suggests that the initial energy redistribution dynamics within the singlet and triplet manifolds are driven by motions localized predominantly on the NO₂ group. Our findings also imply that both NO and NO₂ elimination occur from a vibrationally hot ground state on extended (nanosecond) timescales, and any variations in NO vs NO₂ branching upon site-selective methylation are due to steric effects influencing isomerization prior to dissociation.

Ultrafast excited state dynamics of provitamin D3 and analogs in solution and in lipid bilayers

The photochemical ring-opening reaction of 7-dehydrocholesterol (DHC, provitamin D₃) is responsible for the light-initiated formation of vitamin D₃ in mammalian skin membranes. Visible transient absorption spectroscopy was used to explore the excited state dynamics of DHC and two analogs: ergosterol (provitamin D₂) and DHC acetate free in solution and confined to lipid bilayers chosen to model the biological cell membrane. In solution, the excited state dynamics of the three compounds are nearly identical. However, when confined to lipid bilayers, the heterogeneity of the lipid membrane and packing forces imposed on the molecule by the lipid alter the excited state dynamics of these compounds. When confined to lipid bilayers in liposomes formed using DPPC, two solvation environments are identified. The excited state dynamics for DHC and analogs in fluid-like regions of the liposome membrane undergo internal conversion and ring-opening on 1 ps-2 ps time scales, similar to those observed in isotropic solution. In contrast, the excited state lifetime of a subpopulation in regions of lower fluidity is 7 ps-12 ps. The long decay component is unique to these liposomes and results from the structural properties of the lipid bilayer. Additional measurements in liposomes prepared with lipids having slightly longer or shorter alkane tails support this conclusion. In the lipid environments studied, the longest lifetimes are observed for DHC. The unsaturated sterol tail of ergosterol and the acetate group of DHC acetate disrupt the packing around the molecule and permit faster internal conversion and relaxation back to the ground state.

Excited state dynamics of cis,cis-1,3-cyclooctadiene: UV pump VUV probe time-resolved photoelectron spectroscopy

We present UV pump, vacuum ultraviolet probe time-resolved photoelectron spectroscopy measurements of the excited state dynamics of cis,cis-1,3-cyclooctadiene. A 4.75 eV deep UV pump pulse launches a vibrational wave packet on the first electronically excited state, and the ensuing dynamics are probed via ionization using a 7.92 eV probe pulse. The experimental results indicate that the wave packet undergoes rapid internal conversion to the ground state in under 100 fs. Comparing the measurements with electronic structure and trajectory surface hopping calculations, we are able to interpret the features in the measured photoelectron spectra in terms of ionization to several states of the molecular cation.

Structural or population dynamics: what is revealed by the time-resolved photoelectron spectroscopy of 1,3-cyclohexadiene? A study with an ensemble density functional theory method

Time-resolved photoelectron spectra during the photochemical ring-opening reaction of 1,3-cyclohexadiene (CHD) are modeled by an ensemble density functional theory (eDFT) method. The computational methodology employed in this work is capable of correctly describing the multi-reference effects arising in the ground and excited electronic states of molecules, which is important for the correct description of the ring-opening reaction of CHD. The geometries of molecular species along the non-adiabatic molecular dynamics (NAMD) trajectories reported in a previous study of the CHD photochemical ring-opening were used in this work to calculate the ionization energies and the respective Dyson orbitals for all possible ionization channels. The obtained theoretical time-resolved spectra display decay characteristics in a reasonable agreement with the experimental observations; i.e., the decay (and rise) of the most mechanistically significant signals occurs on the timescale of 100-150 fs. This is very different from the excited state population decay characteristics (τ_S1 = 234 ± 8 fs) obtained in the previous NAMD study. The difference between the population decay and the decay of the photoelectron signal intensity is traced back to the geometric transformation that the molecule undergoes during the photoreaction. This demonstrates the importance of including the geometric information in interpretation of the experimental observations.

Ultrafast x-ray and electron scattering of free molecules: A comparative evaluation

Resolving gas phase molecular motions with simultaneous spatial and temporal resolution is rapidly coming within the reach of x-ray Free Electron Lasers (XFELs) and Mega-electron-Volt (MeV) electron beams. These two methods enable scattering experiments that have yielded fascinating new results, and while both are important methods for determining transient molecular structures in photochemical reactions, it is important to understand their relative merits. In the present study, we evaluate the respective scattering cross sections of the two methods and simulate their ability to determine excited state molecular structures in light of currently existing XFEL and MeV source parameters. Using the example of optically excited N-methyl morpholine and simulating the scattering patterns with shot noise, we find that the currently achievable signals are superior with x-ray scattering for equal samples and on a per-shot basis and that x-ray scattering requires fewer detected signal counts for an equal fidelity structure determination. Importantly, within the independent atom model, excellent structure determinations can be achieved for scattering vectors only to about 5 Å-1, leaving larger scattering vector ranges for investigating vibrational motions and wavepackets. Electron scattering has a comparatively higher sensitivity toward hydrogen atoms, which may point to applications where electron scattering is inherently the preferred choice, provided that excellent signals can be achieved at large scattering angles that are currently difficult to access.

Observation of the molecular response to light upon photoexcitation

When a molecule interacts with light, its electrons can absorb energy from the electromagnetic field by rapidly rearranging their positions. This constitutes the first step of photochemical and photophysical processes that include primary events in human vision and photosynthesis. Here, we report the direct measurement of the initial redistribution of electron density when the molecule 1,3-cyclohexadiene (CHD) is optically excited. Our experiments exploit the intense, ultrashort hard x-ray pulses of the Linac Coherent Light Source (LCLS) to map the change in electron density using ultrafast x-ray scattering. The nature of the excited electronic state is identified with excellent spatial resolution and in good agreement with theoretical predictions. The excited state electron density distributions are thus amenable to direct experimental observation.

Photoabsorption is a fundamental process that leads to changes in the electron density in matter. Here, the authors show a direct measurement of the distribution of electron density when a cyclohexadine molecule is excited by pulsed UV radiation and probed by a time delayed X-ray pulse generated at LCLS.

The valence and Rydberg states of dienes

MC-PDFT can give the most accurate excitation energies for both valence and Rydberg states of 1,4-cyclohexadiene and 1,3-cyclohexadiene when the active space includes Rydberg orbitals.

Ab Initio Fragment Method for Calculating Molecular X-ray Diffraction

A fragment-based approach for the prediction of elastic X-ray scattering is presented. The total diffraction pattern is assembled from anisotropic form factors calculated for individual molecular fragments, optionally including corrections for pairwise interactions between fragments. The approach is evaluated against full ab initio scattering calculations in the peptide diphenylalanine, and the optimal selection of fragments is examined in the ethanol molecule. The approach is found to improve significantly on the independent atom model while remaining conceptually simple and computationally efficient. It is expected to be particularly useful for macromolecules with repeated subunits, such as peptides, proteins, DNA, or RNA and other polymers, where it is straightforward to define appropriate fragments.

Correspondence between electronic structure calculations and simulations: nonadiabatic dynamics in CS2

The choice of ab initio electronic structure method is an important factor in determining the fidelity of nonadiabatic dynamics simulations.

Imaging the ring opening reaction of 1,3-cyclohexadiene with MeV ultrafast electron diffraction

We resolve the structural dynamics of the ultrafast photoinduced ring opening reaction of 1,3-cyclohexadiene in space and time employing megaelectronvolt gas phase ultrafast electron diffraction. We, furthermore, observe coherent large amplitude motions of the photoproduct.

Photoinduced C–H bond fission in prototypical organic molecules and radicals

We survey and assess current knowledge regarding the primary photochemistry of hydrocarbon molecules and radicals.

Ultrafast X-ray Transient Absorption Spectroscopy of Gas-Phase Photochemical Reactions: A New Universal Probe of Photoinduced Molecular Dynamics

Time-resolved spectroscopic investigations of light-induced chemical reactions with universal detection capitalize recently on single-photon molecular probing using laser pulses in the extreme ultraviolet or X-ray regimes. Direct and simultaneous mappings of the time-evolving populations of ground-state reactants, Franck-Condon (FC) and transition state regions, excited-state intermediates and conical intersections (CI), and photoproducts in photochemical reactions utilize probe pulses that are broadband and energy-tunable. The limits on temporal resolution are set by the transit- or dwell-time of the photoexcited molecules at specific locations on the potential energy surface, typically ranging from a few femtoseconds to several hundred picoseconds. Femtosecond high-harmonic generation (HHG) meets the stringent demands for a universal spectroscopic probe of large regions of the intramolecular phase-space in unimolecular photochemical reactions. Extreme-ultraviolet and soft X-ray pulses generated in this manner with few-femtosecond or sub-femtosecond durations have enormous bandwidths, allowing the probing of many elements simultaneously through excitation or ionization of core-electrons, creating molecular movies that shed light on entire photochemical pathways. At free electron lasers (FELs), powerful investigations are also possible, recognizing their higher flux and tunability but more limited bandwidths. Femtosecond time-resolved X-ray transient absorption spectroscopy, in particular, is a valuable universal probe of reaction pathways that maps changes via the fingerprint core-to-valence resonances. The particular power of this method over valence-ionization probes lies in its unmatched element and chemical-site specificities. The elements carbon, nitrogen, and oxygen constitute the fundamental building blocks of life; photochemical reactions involving these elements are ubiquitous, diverse, and manifold. However, table-top HHG sources in the "water-window" region (280-550 eV), which encompasses the 1s-absorption edges of carbon (284 eV), nitrogen (410 eV), and oxygen (543 eV), are far from abundant or trivial. Recent breakthroughs in the laboratory have embraced this region by using long driving-wavelength optical parametric amplifiers coupled with differentially pumped high-pressure gas source cells. This has opened avenues to study a host of photochemical reactions in organic molecules using femtosecond time-resolved transient absorption at the carbon K-edge. In this Account, we summarize recent efforts to deploy a table-top carbon K-edge source to obtain crucial chemical insights into ultrafast, ultraviolet-induced chemical reactions involving ring-opening, nonadiabatic excited-state relaxation, bond dissociation and radical formation. The X-ray probe provides a direct spectroscopic viewport into the electronic characters and configurations of the valence electronic states through spectroscopic core-level transitions into the frontier molecular orbitals of the photoexcited molecules, laying fertile ground for the real-time mapping of the evolving valence electronic structure. The profound detail and mechanistic insights emerging from the pioneering experiments at the carbon K-edge are outlined here. Comparisons of the experimental methodology with other techniques employed to study similar reactions are drawn, where applicable and relevant. We show that femtosecond time-resolved X-ray transient absorption spectroscopy blazes a new trail in the study of nonadiabatic molecular dynamics. Despite table-top implementations being largely in their infancy, future chemical applications of the technique will set the stage for widely applicable, universal probes of photoinduced molecular dynamics with unprecedented temporal resolution.

Time-resolved high-harmonic spectroscopy of ultrafast photoisomerization dynamics

We report the first time-resolved high-harmonic spectroscopy (TR-HHS) study of a chemical bond rearrangement. We investigate the transient change of the high-harmonic signal from 1,3-cyclohexadiene (CHD), which undergoes ring-opening and isomerizes to 1,3,5-hexatriene (HT) upon photoexcitation. We associated the harmonic yield variation with the changes in the molecule's electronic state and vibrational frequencies, which are caused by isomerization. This showed us that the electronic excited state of CHD created through two-photon absorption of 3.1 eV photons relaxes almost completely within 100 fs to the electronic ground state of CHD with vibrational excitation. Subsequently, the molecule isomerizes to HT (i.e., ring-opening occurs, around 400 fs after the excitation). The present results demonstrate that TR-HHS, which can track both electronic and nuclear dynamics, is a powerful tool for studying ultrafast photochemical reactions.

The ring-opening channel and the influence of Rydberg states on the excited state dynamics of furan and its derivatives

One important relaxation pathway for photo-excited five-membered heterocyclic organic molecules is ring-opening via a dissociative πσ^* state. In this study, we investigate the influence of this pathway in furan and several hydrogenated and methylated derivatives by combining time-resolved photoelectron spectroscopy with time-dependent density functional theory and coupled cluster calculations. We find strong experimental evidence that the ring-opening channel is the major relaxation channel in furan, 2,3-dihydrofuran, and 2-methylfuran (2-MF). In 2,5-dimethylfuran (25-DMF), however, we observe that the molecules relax either via a π3s Rydberg state or through a direct return to the ground state by undergoing ring-puckering motions. From the supporting calculations, for 2-MF and 25-DMF, we predict that there is strong mixing between the πσ^* state and the π3s Rydberg state along the ring opening pathway. However, in 25-DMF, no crossing between the πσ^*/π3s state and the initially excited ππ^* state can be found along the ring opening coordinate, effectively blocking this channel.

Structural dynamics of photochemical reactions probed by time-resolved photoelectron spectroscopy using high harmonic pulses

Femtosecond ring-opening dynamics of 1,3-cyclohexadiene (CHD) in gas phase upon two-photon excitation at 400 nm (=3.1 eV) was investigated by time-resolved photoelectron spectroscopy using 42 nm (=29.5 eV) high harmonic photons probing the dynamics of the lower-lying occupied molecular orbitals (MOs), which are the fingerprints of the molecular structure. After 500 fs, the photoelectron intensity of the MO constituting the C[double bond, length as m-dash]C sigma bond (σ_{C[double bond, length as m-dash]C}) of CHD was enhanced, while that of the MO forming the C-C sigma bond (σ_CC) of CHD was decreased. The changes in the photoelectron spectra suggest that the ring of CHD opens to form a 1,3,5-hexatriene (HT) after 500 fs. The dynamics of the σ_{C[double bond, length as m-dash]C} and σ_CC bands between 200 and 500 fs reflects the ring deformation to a conical intersection between the 2¹A and 1¹A potential energy surfaces prior to the ring-opening reaction.

Effects of probe energy and competing pathways on time-resolved photoelectron spectroscopy: the ring-opening of 1,3-cyclohexadiene

Photoelectron spectra for the ring-opening dynamics of 1,3-cyclohexadiene are studied using a model based on quantum molecular dynamics and the Dyson orbital approach.

Exploring the Dynamics of the Photoinduced Ring-Opening of Heterocyclic Molecules

Excited states formed by electron promotion to an antibonding σ* orbital are now recognized as key to understanding the photofragmentation dynamics of a broad range of heteroatom containing small molecules: alcohols, thiols, amines, and many of their aromatic analogues. Such excited states may be populated by direct photoexcitation, or indirectly by nonadiabatic transfer of population from some other optically excited state (e.g., a ππ* state). This Perspective explores the extent to which the fast-growing literature pertaining to such (n/π)σ*-state mediated bond fissions can inform and enhance our mechanistic understanding of photoinduced ring-opening in heterocyclic molecules.

Molecular Photofragmentation Dynamics in the Gas and Condensed Phases

Exciting a molecule with an ultraviolet photon often leads to bond fission, but the final outcome of the bond cleavage is typically both molecule and phase dependent. The photodissociation of an isolated gas-phase molecule can be viewed as a closed system: Energy and momentum are conserved, and the fragmentation is irreversible. The same is not true in a solution-phase photodissociation process. Solvent interactions may dissipate some of the photoexcitation energy prior to bond fission and will dissipate any excess energy partitioned into the dissociation products. Products that have no analog in the corresponding gas-phase study may arise by, for example, geminate recombination. Here, we illustrate the extent to which dynamical insights from gas-phase studies can inform our understanding of the corresponding solution-phase photochemistry and how, in the specific case of photoinduced ring-opening reactions, solution-phase studies can in some cases reveal dynamical insights more clearly than the corresponding gas-phase study.

Femtosecond x-ray spectroscopy of an electrocyclic ring-opening reaction

The ultrafast light-activated electrocyclic ring-opening reaction of 1,3-cyclohexadiene is a fundamental prototype of photochemical pericyclic reactions. Generally, these reactions are thought to proceed through an intermediate excited-state minimum (the so-called pericyclic minimum), which leads to isomerization via nonadiabatic relaxation to the ground state of the photoproduct. Here, we used femtosecond (fs) soft x-ray spectroscopy near the carbon K-edge (~284 electron volts) on a tabletop apparatus to directly reveal the valence electronic structure of this transient intermediate state. The core-to-valence spectroscopic signature of the pericyclic minimum observed in the experiment was characterized, in combination with time-dependent density functional theory calculations, to reveal overlap and mixing of the frontier valence orbital energy levels. We show that this transient valence electronic structure arises within 60 ± 20 fs after ultraviolet photoexcitation and decays with a time constant of 110 ± 60 fs.

Ab initio calculation of inelastic scattering

We calculate nonresonant inelastic electron and X-ray scattering cross sections for bound-to-bound transitions in atoms and molecules from ab initio electronic wavefunctions.

Imaging rotations and vibrations in polyatomic molecules with X-ray scattering

An approach for calculating elastic X-ray scattering from polyatomic molecules in specific electronic, vibrational, and rotational states is presented, and is used to consider the characterization of specific states in polyatomic molecules using elastic X-ray scattering.

Highlights from Faraday Discussion 193: Ultrafast Imaging of Photochemical Dynamics, Edinburgh, 2016

On August 31st 2016, 116 delegates from 16 countries gathered at the handsome and historic premises of the Royal Society of Edinburgh.

Elastic X-ray scattering from state-selected molecules

The characterization of electronic, vibrational, and rotational states using elastic (coherent) X-ray scattering is considered. The scattering is calculated directly from complete active space self-consistent field level ab initio wavefunctions for H₂ molecules in the ground-state X¹Σ_g⁺ and first-excited EF¹Σ_g⁺ electronic states. The calculated scattering is compared to recent experimental measurements [Y.-W. Liu et al., Phys. Rev. A 89, 014502 (2014)], and the influence of vibrational and rotational states on the observed signal is examined. The scaling of the scattering calculations with basis set is quantified, and it is found that energy convergence of the ab initio calculations is a good indicator of the quality of the scattering calculations.

Resonant multiphoton ionisation probe of the photodissociation dynamics of ammonia

The dissociation dynamics of the Ã-state of ammonia have been studied using a resonant multiphoton ionisation probe in a photoelectron spectroscopy experiment. The use of a resonant intermediate in the multiphoton ionisation process changes the ionisation propensity, allowing access to different ion states when compared with equivalent single photon ionisation experiments. Ionisation through the E' ¹A₁' Rydberg intermediate means we maintain overlap with the ion state for an extended period, allowing us to monitor the excited state population for several hundred femtoseconds. The vibrational states in the photoelectron spectrum show two distinct timescales, 200 fs and 320 fs, that we assign to the non-adiabatic and adiabatic dissociation processes respectively. The different timescales derive from differences in the wavepacket trajectories for the two dissociation pathways that resonantly excite different vibrational states in the intermediate Rydberg state. The timescales are similar to those obtained from time resolved ion kinetic energy release measurements, suggesting we can measure the different trajectories taken out to the region of conical intersection.

Extreme population inversion in the fragments formed by UV photoinduced S-H bond fission in 2-thiophenethiol

H atom loss following near ultraviolet photoexcitation of gas phase 2-thiophenethiol molecules has been studied experimentally, by photofragment translational spectroscopy (PTS) methods, and computationally, by ab initio electronic structure calculations. The long wavelength (277.5 ≥ λ(phot) ≥ 240 nm) PTS data are consistent with S-H bond fission after population of the first (1)πσ* state. The partner thiophenethiyl (R) radicals are formed predominantly in their first excited Ã(2)A' state, but assignment of a weak signal attributable to H + R(X˜(2)A'') products allows determination of the S-H bond strength, D0 = 27,800 ± 100 cm(-1) and the Ã-X˜ state splitting in the thiophenethiyl radical (ΔE = 3580 ± 100 cm(-1)). The deduced population inversion between the à and X˜ states of the radical reflects the non-planar ground state geometry (wherein the S-H bond is directed near orthogonal to the ring plane) which, post-photoexcitation, is unable to planarise sufficiently prior to bond fission. This dictates that the dissociating molecules follow the adiabatic fragmentation pathway to electronically excited radical products. π* ← π absorption dominates at shorter excitation wavelengths. Coupling to the same (1)πσ* potential energy surface (PES) remains the dominant dissociation route, but a minor yield of H atoms attributable to a rival fragmentation pathway is identified. These products are deduced to arise via unimolecular decay following internal conversion to the ground (S0) state PES via a conical intersection accessed by intra-ring C-S bond extension. The measured translational energy disposal shows a more striking change once λ(phot) ≤ 220 nm. Once again, however, the dominant decay pathway is deduced to be S-H bond fission following coupling to the (1)πσ* PES but, in this case, many of the evolving molecules are deduced to have sufficiently near-planar geometries to allow passage through the conical intersection at extended S-H bond lengths and dissociation to ground (X˜) state radical products. The present data provide no definitive evidence that complete ring opening can compete with fast S-H bond fission following near UV photoexcitation of 2-thiophenethiol.