Excited Electronic States in Total Isotropic Scattering from Molecules

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.

Ultrafast electron diffraction of photoexcited gas-phase cyclobutanone predicted by ab initio multiple cloning simulations

We present the result of our calculations of ultrafast electron diffraction (UED) for cyclobutanone excited into the S2 electronic state, which is based on the non-adiabatic dynamics simulations with the Ab Initio Multiple Cloning (AIMC) method with the electronic structure calculated at the SA(3)-CASSCF(12,12)/aug-cc-pVDZ level of theory. The key features in the UED pattern were identified, which can be used to distinguish between the reaction pathways observed in the AIMC dynamics, although there is a significant overlap between representative signals due to the structural similarity of the products. The calculated UED pattern can be compared with the experiment.

Extracting the electronic structure signal from X-ray and electron scattering in the gas phase

X-ray and electron scattering from free gas-phase molecules is examined using the independent atom model (IAM) and ab initio electronic structure calculations. The IAM describes the effect of the molecular geometry on the scattering, but does not account for the redistribution of valence electrons due to, for instance, chemical bonding. By examining the total, i.e. energy-integrated, scattering from three molecules, fluoroform (CHF3), 1,3-cyclohexadiene (C6H8) and naphthalene (C10H8), the effect of electron redistribution is found to predominantly reside at small-to-medium values of the momentum transfer (q ≤ 8 Å-1) in the scattering signal, with a maximum percent difference contribution at 2 ≤ q ≤ 3 Å-1. A procedure to determine the molecular geometry from the large-q scattering is demonstrated, making it possible to more clearly identify the deviation of the scattering from the IAM approximation at small and intermediate q and to provide a measure of the effect of valence electronic structure on the scattering signal.

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.

Efficient Computation of Two-Electron Reduced Density Matrices via Selected Configuration Interaction

We create an approach to efficiently calculate two-electron reduced density matrices (2-RDMs) using selected configuration interaction wavefunctions. This is demonstrated using the specific example of Monte Carlo configuration interaction (MCCI). The computation of the 2-RDMs is accelerated by using ideas from fast implementations of full configuration interaction (FCI) and recent advances in implementing the Slater–Condon rules using hardware bitwise operations. This method enables a comparison of MCCI and truncated CI 2-RDMs with FCI values for a range of molecules, which includes stretched bonds and excited states. The accuracy in energies, wavefunctions, and 2-RDMs is seen to exhibit a similar behavior. We find that MCCI can reach sufficient accuracy of the 2-RDM using significantly fewer configurations than truncated CI, particularly for systems with strong multireference character.

Direct Monitoring of Conical Intersection Passage via Electronic Coherences in Twisted X-Ray Diffraction

Quantum coherences in electronic motions play a critical role in determining the pathways and outcomes of virtually all photophysical and photochemical molecular processes. However, the direct observation of electronic coherences in the vicinity of conical intersections remains a formidable challenge. We propose a novel time-resolved twisted x-ray diffraction technique that can directly monitor the electronic coherences created as the molecule passes through a conical intersection. We show that the contribution of electronic populations to this signal is canceled out when using twisted x-ray beams that carry a light orbital angular momentum, providing a direct measurement of transient electronic coherences in gas-phase molecules.

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.

Towards high-resolution X-ray scattering as a probe of electron correlation

We demonstrate that X-ray scattering can be used as a probe of electron–electron correlation.

Determination of excited state molecular structures from time-resolved gas-phase X-ray scattering

We present a comprehensive investigation of a recently introduced method to determine transient structures of molecules in excited electronic states with sub-ångstrom resolution from time-resolved gas-phase scattering signals. The method, which is examined using time-resolved X-ray scattering data measured on the molecule N-methylmorpholine (NMM) at the Linac Coherent Light Source (LCLS), compares the experimentally measured scattering patterns against the simulated patterns corresponding to a large pool of molecular structures to determine the full set of structural parameters. In addition, we examine the influence of vibrational state distributions and find the effect negligible within the current experimental detection limits, despite that the molecules have a comparatively high internal vibrational energy. The excited state structures determined using three structure pools generated using three different computational methods are in good agreement, demonstrating that the procedure is largely independent of the computational chemistry method employed as long as the pool is sufficiently expansive in the vicinity of the sought structure and dense enough to yield good matches to the experimental patterns.

Mapping static core-holes and ring-currents with X-ray scattering

Measuring the attosecond movement of electrons in molecules is challenging due to the high temporal and spatial resolutions required. X-ray scattering-based methods are promising, but many questions remain concerning the sensitivity of the scattering signals to changes in density, as well as the means of reconstructing the dynamics from these signals. In this paper, we present simulations of stationary core-holes and electron dynamics following inner-shell ionization of the oxazole molecule. Using a combination of time-dependent density functional theory simulations along with X-ray scattering theory, we demonstrate that the sudden core-hole ionization produces a significant change in the X-ray scattering response and how the electron currents across the molecule should manifest as measurable modulations to the time dependent X-ray scattering signal. This suggests that X-ray scattering is a viable probe for measuring electronic processes at time scales faster than nuclear motion.

Strong-field induced fragmentation and isomerization of toluene probed by ultrafast femtosecond electron diffraction and mass spectrometry

We investigate the fragmentation and isomerization of toluene molecules induced by strong-field ionization with a femtosecond near-infrared laser pulse. Momentum-resolved coincidence time-of-flight ion mass spectrometry is used to determine the relative yield of different ionic products and fragmentation channels as a function of laser intensity. Ultrafast electron diffraction is used to capture the structure of the ions formed on a picosecond time scale by comparing the diffraction signal with theoretical predictions. Through the combination of the two measurements and theory, we are able to determine the main fragmentation channels and to distinguish between ions with identical mass but different structures. In addition, our diffraction measurements show that the independent atom model, which is widely used to analyze electron diffraction patterns, is not a good approximation for diffraction from ions. We show that the diffraction data is in very good agreement with ab initio scattering calculations.

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.