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.

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.

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.

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.

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.

Excited Electronic States in Total Isotropic Scattering from Molecules.

Ultrafast X-ray scattering experiments are routinely analyzed in terms of the isotropic scattering component. Here, we present an analytical method for calculating total isotropic scattering for ground and excited electronic states directly from ab initio two-electron densities. The method is generalized to calculate the isotropic elastic, inelastic, and coherent mixed scattering. The presented computational results focus on the potential for differentiating between electronic states and the decomposition of the total scattering in terms of elastic and inelastic scattering. For the specific example of the umbrella motion in the first excited state of ammonia, we show that the redistribution of electron density along this coordinate leaves a comparably constant fingerprint in the total scattering that is similar in magnitude to the effect of changes in molecular geometry.

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.

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.

Ab Initio Calculation of Total X-ray Scattering from Molecules.

We present a method to calculate total X-ray scattering cross sections directly from ab initio electronic wave functions in atoms and molecules. The approach can be used in conjunction with multiconfigurational wave functions and exploits analytical integrals of Gaussian-type functions over the scattering operator, which leads to accurate and efficient calculations. The results are validated by comparison to experimental results and previous theory for the molecules H2 and CO2. Importantly, we find that the inelastic component of the total scattering varies strongly with molecular geometry. The method is appropriate for use in conjunction with quantum molecular dynamics simulations for the analysis of new ultrafast X-ray scattering experiments and to interpret accurate gas-phase scattering experiments.

Ab initio calculation of inelastic scattering.

Nonresonant inelastic electron and X-ray scattering cross sections for bound-to-bound transitions in atoms and molecules are calculated directly from ab initio electronic wavefunctions. The approach exploits analytical integrals of Gaussian-type functions over the scattering operator, which leads to accurate and efficient calculations. The results are validated by comparison to analytical cross sections in H and He+, and by comparison to experimental results and previous theory for closed-shell He and Ne atoms, open-shell C and Na atoms, and the N2 molecule, with both inner-shell and valence electronic transitions considered. The method is appropriate for use in conjunction with quantum molecular dynamics simulations and for the analysis of new ultrafast X-ray scattering experiments.

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. Instead of the standard independent atom model (IAM) method, the X-ray scattering is calculated directly from ab initio wavefunctions. The role of molecular symmetry and Friedel's law is examined, with the molecules BF3, C5H5-, NF3, and 1,3-cyclohexadiene used as specific examples. The contributions to the elastic X-ray scattering from the electronic, vibrational, and rotational portions of the molecular wavefunction are examined in CS2. In particular, it is observed that the rotational states give rise to distinct signatures in the scattering signal.

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 X1Σg+ and first-excited EF1Σg+ 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.