Theory of polarization-averaged core-level molecular-frame photoelectron angular distributions: II. Extracting the x-ray-induced fragmentation dynamics of carbon monoxide dication from forward and backward intensities

Abstract

Recent developments in high-repetition-rate x-ray free electron lasers (XFELs) such as the European XFEL and the LSCS-II, combined with coincidence measurements using the COLTRIMS-reaction microscope, are now opening a door to realize the long-standing dream of creating molecular movies of photo-induced chemical reactions in gas-phase molecules. In this paper, we propose a new theoretical method to experimentally visualize the dissociation of diatomic molecules via time-resolved polarization-averaged molecular-frame photoelectron angular distribution (PA-MFPAD) measurements using the COLTRIMS-reaction microscope and the two-color XFEL pump–probe set-up. We used first- and second-order scattering theory within the muffin-tin approximation, which is valid for a sufficiently high kinetic energy of photoelectrons, typically above 100 eV, and for long bond lengths. This leads to a simple extended x-ray absorption fine structure (EXAFS)-type formula for the forward and backward scattering peaks in the PA-MFPAD structure. This formula relies only on three semi-empirical parameters obtainable from the time-resolved measurements. It can be used as a ‘bond length ruler’ on experimental results. The accuracy and applicability of the new ruler equation are numerically examined against the PA-MFPADs of CO2+ calculated with full-potential multiple scattering theory as a function of the C–O bond length reported in the preceding work (Ota et al J. Phys. B: At. Mol. Opt.). The bond lengths retrieved from the PA-MFPADs via our EXAFS-like formula coincide within an accuracy of 0.1 Å with the original C–O bond lengths used in the reference ab initio PA-MFPADs. We expect time-resolved PA-MFPADs to become a new attractive tool to make molecular movies visualizing intramolecular reactions.

Trends in angle-resolved molecular photoelectron spectroscopy

“…The interpretation of such PA core-level MFPADs focusing on molecular structure is supported by a full-potential multiple scattering theory for photoelectron energies in the 100 eV range. 354,355 Further comparative studies of 3D MFPADs measured for e.g. O(1s) ionization of methanol with SC calculations, 356 and with earlier results for carbon monoxide MFPADs for similar polarization geometries of the CO central bond, 118 elucidate the influence of both bond lengths and presence of H additional atoms.…”

Investigating charge-up and fragmentation dynamics of oxygen molecules after interaction with strong X-ray free-electron laser pulses

“…This behavior of the backward peak of the PA-MFPAD can be explained already within a simplified theoretical model. 36,37 It employs the single-channel, single-scattering, plane-wave, and muffin-tin approximations. It also includes a superposition of a direct electron wave with momentum k emitted from the left oxygen ion in Fig.…”

“…Using the site T -matrix expansion, 38,39 we obtain the following analytic expression for the polarization-averaged differential probability of the 1s photoionization of the left oxygen atom O l of a fixed-in-space oxygen molecule (see ref. 36 and 37 on details of the derivation):Here, R is the internuclear distance and θ is the electron emission angle with respect to the molecular axis. The first term in eqn (2) represents the direct photoemission from the O l atom and its spherical symmetry owing to the polarization average.…”

High-Energy Molecular-Frame Photoelectron Angular Distributions: A Molecular Bond-Length Ruler

“…So far, concepts proposed for achieving this goal focus on polarization-averaged MFPADs (see, e.g., [17] and references therein), and rely on two prerequisites: Firstly, at sufficiently high photoelectron kinetic energies for which a single-scattering approximation is valid (say, above 70 eV), forward-scattering peaks observable in polarization-averaged MFPADs coincide with the relative location (from the point of view of the emitter atom) of neighboring atoms [18,19]. Secondly, the molecularframe interference pattern caused by the direct and scattered photoelectron waves can be correlated to the distance between the emitter and the scatterers [20,21]. In addition, in case of homo-nuclear molecules, bond lengths information can be obtained exploiting the analogy between Young's double slit principle and MFPADs (see e.g.…”

“…We assume that CP-MFPADs are measured in the polarization plane of the circular light and employ the electric-dipole, single-channel, and single-scattering approximations using a site T -matrix expansion [27,28]. In this case, the CP-MFPAD as a function of photoelectron emission vector, k, is given by the following form [17,21]:…”