We present a theoretical study of the polarization-averaged molecular-frame photoelectron angular distributions (PA-MFPADs) emitted from the 1s orbital of oxygen atoms of dissociating dicationic carbon monoxide CO2+. Due to the polarization average, the contribution of the direct wave of the photoelectron, which represents the largest contribution to the MFPADs, is removed, so that the PA-MFPADs clearly show the details of the scattering image of the photoelectron. As a result, it is necessary to employ an accurate theory for the theoretical analysis of the continuum state. In this study, we apply a full-potential multiple scattering theory, where the space is partitioned into Voronoi polyhedra and truncated spheres, to take into account the electron charge density outside the physical atomic spheres. We do not use the spherical harmonic expansion of the cell shape functions to avoid divergence problems. The potentials in the scattering cells are computed using the multiconfigurational second-order perturbation theory restricted active space method to take into account the influence of the core hole in the electron charge density in the final state, so that a realistic relaxation can be achieved. We show that the full-potential treatment plays an important role in the PA-MFPADs at a photoelectron kinetic energy of 100 eV. In contrast, the PA-MFPADs are not sensitive to any type of major excited states in the Auger final state. We also study the dynamics of the CO2+ dissociation. We find that the PA-MFPADs dramatically change their shape as a function of the C–O bond length.

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.

Imaging ultrafast hydrogen migration with few- or sub-femtosecond time resolution is a challenge for ultrafast spectroscopy due to the lightness and small scattering cross section of the moving hydrogen atom....

Gold (Au) clusters with well-defined geometrical structures have attracted substantial attention due to their unique optical and catalytic properties, which are drastically changed by the ligands, compositions, and geometric structures. Here, we investigated the effect of ligand on the electronic state of Au in [Au 9 (PPh 3 ) 8 ] 3+ (Au9) and [Au 25 (SC 2 H 4 Ph) 18 ] − (Au25) by X-ray absorption spectroscopy using high energy resolution fluorescence detection (HERFD) and theoretical calculations. Au L 3 -edge X-ray absorption near-edge structure (XANES) spectra revealed that the white-line intensity of Au9 was comparable to that of Au25, while the white-line peak of Au25 was 3 eV lower than that of Au9. The total area of the white line of Au9 corresponded to that of Au25, which is explained by the natural bond orbital analysis, showing that the occupancy of Au 5d orbitals of Au9 was close to that of Au25. The simulated XANES spectra using finite difference method near-edge structure software resembled the experimental XANES spectra. The projected density of state profiles and molecular orbitals indicated that the unoccupied 5d orbitals of the surface Au in Au9 and of surface and oligomer Au in Au25 interacted with P/S 3s+3p orbitals. The difference in peak locations in Au L 3 -edge XANES between phosphine-and thiolate-protected gold clusters was ascribed to the energy shift of unoccupied Au 5d orbitals, which are modulated by the Au 5d and P/S 3s+3p interaction.

We present a theoretical study on polarization-averaged molecular-frame photoelectron angular distributions (PA-MFPADs) emitted from 1s orbital of oxygen atom of dissociating dicationic carbon monoxide CO 2+ . Due to the polarization-average, contribution of direct wave of photoelectron which has the biggest contribution to MFPADs is removed, so that PA-MFPADs clearly show the detail of scattering image of the photoelectron. As a result, it is necessary to employ well precise theory for the continuum state for the theoretical analysis. In this study, we applied our Full-potential multiple scattering theory, where the space is partitioned by using Voronoi polyhedra and truncated spheres to take into account the electron charge density outside the physical atomic spheres. We did not use spherical harmonic expansion of the cell shape functions to avoid convergence problems. The potentials in scattering cells are prepared employing Multiconfigurational Second-Order Perturbation Theory Restricted Active Space (RASPT2) method in order to take into account the influence of core hole in the electron charge density in the final state to realize realistic relaxation. We showed that the Full-potential treatment plays an important role for the PA-MFPADs at 100 eV of kinetic energy of photoelectron. Instead, the PA-MFPADs are not sensitive to type of major excited state in the Auger final state. We also studied the dynamics of CO 2+ dissociation. We found that the PA-MFPADs dramatically change its shape as a function of C-O bond length.