The contribution of Compton ionization to ultrafast x-ray scattering

Abstract

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.

Ultrafast x-ray scattering and electronic coherence at avoided crossings: complete isotropic signals

“…The isotropic two-electron scattering matrix elements defined in equation ( 4) are calculated from ab-initio electronic wavefunctions, obtained by SA-CASSCF(6,23)/aug-cc-pVTZ, using methods and codes developed in our group [49,[103][104][105][106]. Given the formal equivalence of equations ( 2) and (10) with an untruncated sum over f, these scattering matrix elements implicitly account for all inelastic transitions from the two states populated by the pump pulse to all energetically accessible final states, bound and continuum [46]. To limit the computational effort, which scales exponentially with the size of the wavefunction, the scattering matrix elements are calculated at a lower level of electronic structure theory than the potential energy curves and NACMEs used for the dynamics.…”

“…While equations ( 10) and (2), as well as equations ( 9) and ( 13), are formally equivalent, it is important to note that equation (10) involves an infinite sum over all final states. This sum also includes the continuum of singly ionised states and is not guaranteed to converge when only the energetically lowest-lying electronic states are considered [46]. A truncation of equation (10) can therefore lead to incomplete or, in the case of CMS, even spurious results.…”

“…Here, we extend their effort by carrying out a quantitative calculation of this process, accounting for the contributions of all electronic transitions to the inelastic and coherent mixed components of the scattering signal. Since recent work has indicated that unpopulated electronic states can make a significant contribution to the CMS signal, [46] it is pertinent to account for all final states, which is done in the current study by calculating the energyintegrated total and CMS signals from two-electron rather than one-electron (transition) densities. Moreover, we simulate the isotropic scattering signals that would be measured in an actual experiment.…”

Trendbericht Theoretische Chemie 2023 (3/3): Dynamik beobachten – explizite Beschreibung der Pulseigenschaften

“…Dieser kann unterschiedlich groß sein. 5) Desweiteren wurden Quantum State Holography, 13) zeitaufgelöste Röntgenstreuung, die neben der zeitlichen Information auch Aussagen über die räumliche Verteilung der Elektronen erlaubt, 14) High-harmonic generation, 15) sowie der Auger-Meitner-Prozess mit einem zirkularpolarisierten Streakinglaser 16) unter Berücksichtigung der Pulse untersucht.…”

Kurz notiert: Emitter, Isolator und Diode

“…Dieser kann unterschiedlich groß sein. 5) Desweiteren wurden Quantum State Holography, 13) zeitaufgelöste Röntgenstreuung, die neben der zeitlichen Information auch Aussagen über die räumliche Verteilung der Elektronen erlaubt, 14) High-harmonic generation, 15) sowie der Auger-Meitner-Prozess mit einem zirkularpolarisierten Streakinglaser 16) unter Berücksichtigung der Pulse untersucht. Emitter, Isolator und Diode…”