Theory on polarization-averaged core-level molecular-frame photoelectron angular distributions: I. A Full-potential method and its application to dissociating carbon monoxide dication

Abstract

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.

Theory on 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

“…In equation 3, T is the transition operator (or scattering T matrix) and G is the KKR structure factor which is the matrix form expanded in scattering sites and angular momentum [22,23]. More details are reported in the preceding paper [1] of this series papers. Figure 1 depicts PA-MFPADs calculated with changing the C-O bond length R using our Full-potential multiple scattering method mentioned above, where the electron charge density was calculated at the RASPT2/ANO-RCC-VQZP level of theory as implemented in MOLCAS 8.2 [24] for a major excited state 1σ −1 5σ −2 (i.e.…”

“…Thus, it is worth considering their ratio here. Figure 2 depicts the intensity ratio of forward-and backward-intensity peaks of oxygen 1s PA-MFPADs of CO 2+ as a function of the C-O bond length R from 1.1283 Å (equilibrium bond length in ground state) to 2.1283 Å, obtained by the full-multiple scattering calculations using Full-potential method [1]. We can clearly see the EXAFS oscillation in the ratio.…”

“…The details of the theory is found in the preceding paper of Ref. [1]. Then, we derive analytical expressions for the ratio of backward-intensity to forward-intensity in Section 2.3 as a function of C-O bond length based on single-scattering and the Plane Wave approximation within the Muffin-tin approximation.…”

“…This formula acts as an experimentally applicable "bond length ruler" by adjusting only three semi-empirical parameters from the time-resolved measurements. The accuracy and applicability of a new ruler equation are numerically examined against the PA-MFPADs of CO 2+ calculated by Full-potential multiple scattering theory as a function of the C-O bond length reported in the preceding work [1]. The bond lengths retrieved from the PA-MFPADs via the EXAFS formula well reproduce the original C-O bond lengths used in the reference ab-initio PA-MFPADs with accuracy of 0.1 Å.…”

“…We derive analytical EXAFS-type expressions for the backward-forward scattering peaks within the first and second order scattering theories with the Muffin-tin approximation. Employing the Full-potential multiple scattering PA-MFPADs data reported in a preceding paper [1], we introduce parametrization formula for describing the EXAFS-like oscillation in the ratios of the forward-backward intensities, with three semi-empirical parameters, which take account of the effects from Fullpotential multiple scattering to PA-MFPADs and thus may be used for extraction of the bond length from the experimental PA-MFPADs, which varies as a function of pump-probe delay.…”