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.

The Ring-Closing Reaction of Cyclopentadiene Probed with Ultrafast X-ray Scattering.

The dynamics of cyclopentadiene (CP) following optical excitation at 243 nm was investigated by time-resolved pump-probe X-ray scattering using 16.2 keV X-rays at the Linac Coherent Light Source (LCLS). We present the first ultrafast structural evidence that the reaction leads directly to the formation of bicyclo[2.1.0]pentene (BP), a strained molecule with three- and four-membered rings. The bicyclic compound decays via a thermal backreaction to the vibrationally hot CP with a time constant of 21 ± 3 ps. A minor channel leads to ring-opened structures on a subpicosecond time scale.

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.

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.

Valence shell electronically excited states of norbornadiene and quadricyclane.

The absolute photoabsorption cross sections of norbornadiene (NBD) and quadricyclane (QC), two isomers with chemical formula C7H8 that are attracting much interest for solar energy storage applications, have been measured from threshold up to 10.8 eV using the Fourier transform spectrometer at the SOLEIL synchrotron radiation facility. The absorption spectrum of NBD exhibits some sharp structure associated with transitions into Rydberg states, superimposed on several broad bands attributable to valence excitations. Sharp structure, although less pronounced, also appears in the absorption spectrum of QC. Assignments have been proposed for some of the absorption bands using calculated vertical transition energies and oscillator strengths for the electronically excited states of NBD and QC. Natural transition orbitals indicate that some of the electronically excited states in NBD have a mixed Rydberg/valence character, whereas the first ten excited singlet states in QC are all predominantly Rydberg in the vertical region. In NBD, a comparison between the vibrational structure observed in the experimental 11B1-11A1 (3sa1 ← 5b1) band and that predicted by Franck-Condon and Herzberg-Teller modeling has necessitated a revision of the band origin and of the vibrational assignments proposed previously. Similar comparisons have encouraged a revision of the adiabatic first ionization energy of NBD. Simulations of the vibrational structure due to excitation from the 5b2 orbital in QC into 3p and 3d Rydberg states have allowed tentative assignments to be proposed for the complex structure observed in the absorption bands between ∼5.4 and 7.0 eV.

Ultrafast X-ray scattering offers a structural view of excited-state charge transfer.

Intramolecular charge transfer and the associated changes in molecular structure in N,N'-dimethylpiperazine are tracked using femtosecond gas-phase X-ray scattering. The molecules are optically excited to the 3p state at 200 nm. Following rapid relaxation to the 3s state, distinct charge-localized and charge-delocalized species related by charge transfer are observed. The experiment determines the molecular structure of the two species, with the redistribution of electron density accounted for by a scattering correction factor. The initially dominant charge-localized state has a weakened carbon-carbon bond and reorients one methyl group compared with the ground state. Subsequent charge transfer to the charge-delocalized state elongates the carbon-carbon bond further, creating an extended 1.634 Å bond, and also reorients the second methyl group. At the same time, the bond lengths between the nitrogen and the ring-carbon atoms contract from an average of 1.505 to 1.465 Å. The experiment determines the overall charge transfer time constant for approaching the equilibrium between charge-localized and charge-delocalized species to 3.0 ps.

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.

The contribution of Compton ionization to ultrafast x-ray scattering.

We investigate the role of Compton ionization in ultrafast non-resonant x-ray scattering using a molecular model system, which includes the ionization continuum via an orthonormalized plane wave ansatz. Elastic and inelastic components of the scattering signal, as well as coherent-mixed scattering that arises from electron dynamics, are calculated. By virtue of a near-quantitative distinction between scattering related to electronic transitions into bound and continuum states, we demonstrate how Compton ionization contributes to the coherent-mixed component. Analogous to inelastic scattering, the contribution to the coherent-mixed signal is significant and particularly manifests at intermediate and high-momentum transfers. Strikingly, for molecules with inversion symmetry, the exclusion of bound or continuum transitions may lead to the prediction of spurious coherent-mixed signals. We conclude that qualitative and quantitative accuracies of predicted scattering signals on detectors without energy resolution require that elements of the two-electron density operator are used. This approach inherently accounts for all accessible electronic transitions, including ionization.

Excited-state van der Waals potential energy surfaces for the NO A2Σ+ + CO2X1Σg+ collision complex.

Excited state van der Waals (vdW) potential energy surfaces (PESs) of the NO A2Σ+ + CO2X1Σg+ system are thoroughly investigated using coupled cluster theory and complete active space perturbation theory to second order (CASPT2). First, it is shown that pair natural orbital coupled cluster singles and doubles with perturbative triples yields comparable accuracy compared to CCSD(T) for molecular properties and vdW-minima at a fraction of computational cost of the latter. Using this method in conjunction with highly diffuse basis sets and counterpoise correction for basis set superposition error, the PESs for different intermolecular orientations are investigated. These show numerous vdW-wells, interconnected for all geometries except one, with a maximum depth of up to 830 cm-1; considerably deeper than those on the ground state surface. Multi-reference effects are investigated with CASPT2 calculations. The long-range vdW-surfaces support recent experimental observations relating to rotational energy transfer due the anisotropy in the potentials.

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

X-ray scattering cross sections are calculated using a range of increasingly correlated methods: Hartree-Fock (HF), complete active space self-consistent field (CASSCF), Monte Carlo configuration interaction (MCCI), and full configuration interaction (FCI). Even for the seemingly straightforward case of ground state Ne, the accuracy of the total scattering is significantly better with a more correlated wavefunction. Scanning the bond distance in ground state CO shows that the total scattering signal tracks the multireference character. We examine the convergence of the elastic, inelastic, and total scattering of O3. Overall, the inelastic and total components are found to be the most sensitive to the strength of correlation. Our results suggest that highly accurate measurement of X-ray scattering could provide a sensitive probe of pair-wise correlation between electrons.

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(1Σu+) 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.

Transient vibration and product formation of photoexcited CS2 measured by time-resolved x-ray scattering.

We have observed details of the internal motion and dissociation channels in photoexcited carbon disulfide (CS2) using time-resolved x-ray scattering (TRXS). Photoexcitation of gas-phase CS2 with a 200 nm laser pulse launches oscillatory bending and stretching motion, leading to dissociation of atomic sulfur in under a picosecond. During the first 300 fs following excitation, we observe significant changes in the vibrational frequency as well as some dissociation of the C-S bond, leading to atomic sulfur in the both 1D and 3P states. Beyond 1400 fs, the dissociation is consistent with primarily 3P atomic sulfur dissociation. This channel-resolved measurement of the dissociation time is based on our analysis of the time-windowed dissociation radial velocity distribution, which is measured using the temporal Fourier transform of the TRXS data aided by a Hough transform that extracts the slopes of linear features in an image. The relative strength of the two dissociation channels reflects both their branching ratio and differences in the spread of their dissociation times. Measuring the time-resolved dissociation radial velocity distribution aids the resolution of discrepancies between models for dissociation proposed by prior photoelectron spectroscopy work.

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.

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.

Electronic Coherence in Ultrafast X-Ray Scattering from Molecular Wave Packets.

Simulations of nonresonant ultrafast x-ray scattering from a molecular wave packet in H_{2} are used to examine and classify the components that contribute to the total scattering signal. The elastic component, which can be used to determine the structural dynamics of the molecule, is also found to carry a strong signature of an adiabatic electron transfer that occurs in the simulated molecule. The inelastic component, frequently assumed to be constant, is found to change with the geometry of the molecule. Finally, a coherent mixed component due to interferences between different inelastic transitions is identified and shown to provide a direct probe of transient electronic coherences.

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. We present an in-depth comparison of two simulations of photodissociation in the CS2 molecule following excitation to the 11B2 state. The simulations account for nonadiabatic and spin-orbit coupling, and are performed using the SHARC surface-hopping approach combined with state-averaged SA8-CASSCF(8,6)/SVP and SA8-CASSCF(10,8)/SVP ab initio calculations, with additional reference calculations at the MRCI(14,10)/aug-cc-pvTZ level. The relative performance and veracity of the simulations can be assessed by inspection of the potential energy curves along specific coordinates. The simulations demonstrate direct competition between internal conversion and intersystem crossing, with strong correlation between molecular geometry, electronic state density, and dynamics.

Photodissociation dynamics of CH3I probed via multiphoton ionisation photoelectron spectroscopy.

The dissociation dynamics of CH3I is investigated on the red (269 nm) and blue (255 nm) side of the absorption maximum of the A-band. Using a multiphoton ionisation probe in a time-resolved photoelectron imaging experiment we observe very different dynamics at the two wavelengths, with significant differences in the measured lifetime and dynamic structure. The differences are explained in terms of changes in excitation cross-sections of the accessible 3Q0 and 1Q1 states and the subsequent dynamics upon each of them. The measurements support the existing literature on the rapid dissociation dynamics on the red side of the absorption maximum at 269 nm which is dominated by the dynamics along the 3Q0 state. At 255 nm we observe similar dynamics along the 3Q0 state but also a significant contribution from the 1Q1 state. The dynamics along the 1Q1 potential show a more complex structure in the photoelectron spectrum and a significantly increased lifetime, indicative of a more complex reaction pathway.

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.

Theory of ultrafast x-ray scattering by molecules in the gas phase.

We recast existing theory of ultrafast time-resolved x-ray scattering by molecules in the gas phase into a unified and coherent framework based on first-order time-dependent perturbation theory and quantum electrodynamics. The effect of the detection window is analyzed in detail and the contributions to the total scattering signal are discussed. This includes the coherent mixed component caused by interference between scattering amplitudes from different electronic states. A new, detailed, and fully converged simulation of ultrafast total x-ray scattering by excited H2 molecules illustrates the theory and demonstrates that the inelastic component can contribute strongly to the total difference scattering signal, i.e., on the same order of magnitude as the elastic component.

Scattering off molecules far from equilibrium.

Pump-probe gas phase X-ray scattering experiments, enabled by the development of X-ray free electron lasers, have advanced to reveal scattering patterns of molecules far from their equilibrium geometry. While dynamic displacements reflecting the motion of wavepackets can probe deeply into the reaction dynamics, in many systems, the thermal excitation embedded in the molecules upon optical excitation and energy randomization can create systems that encompass structures far from the ground state geometry. For polyatomic molecular systems, large amplitude vibrational motions are associated with anharmonicity and shifts of interatomic distances, making analytical solutions using traditional harmonic approximations inapplicable. More generally, the interatomic distances in a polyatomic molecule are not independent and the traditional equations commonly used to interpret the data may give unphysical results. Here, we introduce a novel method based on molecular dynamic trajectories and illustrate it on two examples of hot, vibrating molecules at thermal equilibrium. When excited at 200 nm, 1,3-cyclohexadiene (CHD) relaxes on a subpicosecond time scale back to the reactant molecule, the dominant pathway, and to various forms of 1,3,5-hexatriene (HT). With internal energies of about 6 eV, the energy thermalizes quickly, leading to structure distributions that deviate significantly from their vibrationless equilibrium. The experimental and theoretical results are in excellent agreement and reveal that a significant contribution to the scattering signal arises from transition state structures near the inversion barrier of CHD. In HT, our analysis clarifies that previous inconsistent structural parameters determined by electron diffraction were artifacts that might have resulted from the use of inapplicable analytical equations.