Ab initio studies of ultrafast x-ray scattering of the photodissociation of iodine

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.

Photodissociation of aqueous I 3 - observed with liquid-phase ultrafast mega-electron-volt electron diffraction

Developing femtosecond resolution methods for directly observing structural dynamics is critical to understanding complex photochemical reaction mechanisms in solution. We have used two recent developments, ultrafast mega-electron-volt electron sources and vacuum compatible sub-micron thick liquid sheet jets, to enable liquid-phase ultrafast electron diffraction (LUED). We have demonstrated the viability of LUED by investigating the photodissociation of tri-iodide initiated with a 400 nm laser pulse. This has enabled the average speed of the bond expansion to be measured during the first 750 fs of dissociation and the geminate recombination to be directly captured on the picosecond time scale.

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.

On the limits of observing motion in time-resolved X-ray scattering

Limits on the ability of time-resolved X-ray scattering (TRXS) to observe harmonic motion of amplitude, A and frequency, ω₀, about an equilibrium position, R₀, are considered. Experimental results from a TRXS experiment at the LINAC Coherent Light Source are compared to classical and quantum theories that demonstrate a fundamental limitation on the ability to observe the amplitude of motion. These comparisons demonstrate dual limits on the spatial resolution through Q_max and the temporal resolution through ω_max for observing the amplitude of motion. In the limit where ω_max ≈  ω₀, the smallest observable amplitude of motion is A = 2 π/ Q_max. In the limit where ω_max≥2 ω₀, A≤2 π/ Q_max is observable provided there are sufficient statistics. This article is part of the theme issue 'Measurement of ultrafast electronic and structural dynamics with X-rays'.

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.

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.

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.

Self-Referenced Coherent Diffraction X-Ray Movie of Ångstrom- and Femtosecond-Scale Atomic Motion

Time-resolved femtosecond x-ray diffraction patterns from laser-excited molecular iodine are used to create a movie of intramolecular motion with a temporal and spatial resolution of 30 fs and 0.3 Å. This high fidelity is due to interference between the nonstationary excitation and the stationary initial charge distribution. The initial state is used as the local oscillator for heterodyne amplification of the excited charge distribution to retrieve real-space movies of atomic motion on ångstrom and femtosecond scales. This x-ray interference has not been employed to image internal motion in molecules before. Coherent vibrational motion and dispersion, dissociation, and rotational dephasing are all clearly visible in the data, thereby demonstrating the stunning sensitivity of heterodyne methods.

Ab Initio Calculation of Molecular Diffraction

We discuss the application of ab initio X-ray diffraction (AIXRD) to the interpretation of time-resolved and static X-ray diffraction. In our approach, elastic X-ray scattering is calculated directly from the ab initio multiconfigurational wave function via a Fourier transform of the electron density, using the first Born approximation for elastic scattering. Significant gains in efficiency can be obtained by performing the required Fourier transforms analytically, making it possible to combine the calculation of ab initio X-ray diffraction with expensive quantum dynamics simulations. We show that time-resolved X-ray diffraction can detect not only changes in molecular geometry but also changes in the electronic state of a molecule. Calculations for cis-, trans-, and cyclo-butadiene, as well as benzene and 1,3-cyclohexadiene are included.