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Modern XAFS (X-ray Absorption Fine Structure) data-analysis is based on accurate multiple-scattering (MS) calculations of the X-ray absorption cross-section. In this paper, we present the inclusion and test of relativistic corrections for the multiple-scattering calculations within the GnXAS suite of programs, which is relevant to the treatment of the XAFS signals when atoms with high atomic number are contained into the system. We present a suitable strategy for introducing relativistic corrections without altering the basic structure of the programs. In particular, this is realized by modifying only the Phagen program calculating the atomic absorption cross sections and scattering t-matrices for the selected cluster. The modification incorporates a pseudo-Schrödinger Equation (SE) replacing the Dirac relativistic form. The phase-shift calculations have been put to a test in two known molecular and crystalline cases: molecular bromine Br2 and crystalline Pb. Calculations in an extended energy range have been shown to be very close to the non-relativistic case for Br2 (Br K-edge) while corrections have been found to exceed 25% for amplitude and phases of the XAFS multiple-scattering signals (Pb L3-edge). Benefits in the structural refinement using relativistic corrections are discussed for crystalline Pb at room temperature.

While the photo-emission process is inherently inelastic, in reality a closer investigation reveals that some coherence effects depending on the single photon and electron self-interference are indeed observable. All hinges on the Feynman’s rule according to which, if the same final state can be reached by different pathways, the probability for its observation is obtained by taking the modulus squared of the sum of the probability amplitudes of the various paths, leading to the mechanism of self-interference. To this purpose we review the two-slit and the usual crystal (Bragg) diffraction experiments, highlighting that in both cases the interference patterns are due to the self-interference of the single incoming photon. Guided by these two examples, we construct the photo-emission equivalent of these experimental set-up in the case of delocalized initial states and discuss their related diffraction patterns using the language of Multiple Scattering (MS) Theory. In the general case this approach shows that coherent emission from atomic sites does not necessarily require their equivalence and new MS processes with different periodicity appear compared to the case of emission from a single localized site. In particular, the cross section for photo-emission from a valence band state factorizes, like in the diffraction counterpart, into an electronic part (photo-emission from a localized atom) and a modulating Bragg factor, where the momentum exchanged with the crystal involves the initial Brillouin Zone, the impinging photon and the final photoelectron wavevectors. Photo-emission from diatomic molecules is a particular case of this general framework. We show that, when the photoelectron is detected, the coherent emission from the two atomic centers realizes the analog of the Young’s two-slit experiment, whereas in the case of photo-absorption the Cohen-Fano interference oscillations observed in the absorption cross section are to be ascribed to new MS paths joining the two sites.

X-ray absorption spectroscopy (XAS) is a powerful method for obtaining electronic and structural information around a well-defined absorbing atom site of different types of matter, from biological systems to condensed materials in almost all possible thermodynamics conditions. The low energy part of the XAS spectrum, from the rising edge up to few hundreds eV, the so called XANES (X-ray absorption near-edge structure) region, is extremely rich of electronic and structural information, like, for example, the oxidation state, overall symmetry, interatomic distances and angles . In this paper we present in details the MXAN method and a new reengineered release of the code proposed in the literature some years ago which allows a complete fit of the XANES energy region in term of well-defined set of structural parameters. This approach is based on the comparison between experimental data and many theoretical calculations performed by varying selected structural parameters starting from a putative structure, i.e. from a well-defined initial geometrical configuration around the absorber. The X-ray photo-absorption cross sections are derived using full multiple-scattering theory, i.e. the scattering path operator is calculated exactly without any series expansion. In this way the analysis can start from the edge without any limitations in the energy range and polarization conditions. Here we present in detail the theoretical background behind the code and new capabilities implemented from theory in this last version of the program as the analysis of XANES data coming from time-dependent spectra. The code is provided with modern technology for rapid deployment of binaries based on Docker runtime so that, without source compiling, its execution reduces to just a command line striking for a full parallel (shared memory) run even using complex construct like memory filesystem in a transparent way to the end-user. Program summary Program Title: MXAN CPC Library link to program files: https://doi.org/10.17632/4k9363vcvh.1 Licensing provisions: GPLv3 Programming language: FORTRAN90 External routines/libraries: MKL or OpenBLAS library Nature of problem: In MXAN (Minuit XANES) program we implemented a fitting procedure based on a full Multiple Scattering (MS) theory [1] able to extract local structural information around the absorbing atom from experimental XANES data. The MXAN method has been successfully used for studying many known and unknown molecular systems, yielding structural geometries and metrics comparable to X-ray diffraction and/or EXAFS results [2] , [3] , [4] . The release of this new code paves the route to new possibilities available now in the latest version of the program, as the analysis of XANES data coming from time-dependent and structural disordered systems. Solution method: MXAN program is based on the comparison between experimental data and iterative theoretical calculations performed by varying selected structural parameters starting from a well-defined initial geometrical configuration around the absorber. The calculation of XANES spectra is performed within the so-called full MS approach, i.e. the inverse of the scattering path operator is computed exactly, avoiding any “a-priori” selection of the relevant MS paths [5] , [6] . The fit procedure is performed in the energy space without the use of any Fourier transform algorithm; polarized spectra can be easily analyzed because the calculation is performed using the full MS approach [1] . The optimization in the space of the parameters is achieved using the CERN-library MINUIT [7] routines minimizing the square residual. Additional comments including restrictions and unusual features: Depending on the molecular system under study and on the operating runtime conditions the program may or may not fit into available host RAM memory. The present release of the code is limited to a single SMP machine by running in parallel using OpenMP and/or the multi-threaded version of MKL or OpenBLAS.

We investigate the ground state and low-energy spin-orbital excitations of a single iron(II) phthalocyanine molecule in isolation and on an oxidized Cu(110) surface. Considering the subspace spanned by the three lowest spin-triplet states of 3A2g and 3Eg symmetry, we diagonalize the Hamiltonian made of the anisotropic spin-orbit interaction and the ligand field splitting Δ, defined as the energy difference between 3Eg and 3A2g. We find that the ground state switches from a 3Eg-like state with large orbital moment and out-of-plane easy axis for Δ−60 meV. The analysis of the first excited states in the two regimes explains the zero-field splitting data reported for β-FePc as well as for FePc molecules adsorbed on an oxidized Cu(110) surface [N. Tsukahara et al., Phys. Rev. Lett. 102, 167203 (2009)]. Importantly, the calculated magnetic susceptibility obtained with the ab initio value Δ=93 meV compares remarkably well with the experimental data of β-FePc in the whole available temperature range of 1–300 K., This work has been partially supported by the Spanish MAT2017-83468-R project, Aragonese E-12 17R RASMIA (co-funded by Fondo Social Europeo), and of the European Union FEDER (ES). We also acknowledge funding by the European Union COST MP1306 EUSPEC project and by the Japan Society for the Promotion of Science (JSPS), Grant KAKENHI JP 16K05393.

We determine the magnetic ground state of the FePc molecule on Au-supported thin films based on the observed values of orbital anisotropy and spectroscopic x-ray magnetic circular dichroism (XMCD) measurements at the Fe $K$ and $L$ edges. Starting from ab initio molecular orbital multiplet calculations for the isolated molecule, we diagonalize the spin-orbit interaction in the subspace spanned by the three lowest spin triplet states of ${}^{3}{A}_{2g}$ and ${}^{3}{E}_{g}$ symmetry in the presence of a saturating magnetic field at a polar angle $\ensuremath{\theta}$ with respect to the normal to the plane of the film, plus an external perturbation representing the effect of the molecules in the stack on the FePc molecule under consideration. We find that the orbital moment of the ground state strongly depends on the magnetic field direction in agreement with the sum rule analysis of the ${L}_{23}$-edge XMCD data. We calculate integrals over the XMCD spectra at the Fe $K$ and ${L}_{23}$ edges as used in the sum rules and explicitly show that they agree with the expectation values of the orbital moment and effective spin moment of the ground state. On the basis of this analysis, we can rule out alternative candidates proposed in the literature.

We determine the magnetic ground state of the FePc molecule on Au-supported thin films based on the observed values of orbital anisotropy and spectroscopic x-ray magnetic circular dichroism (XMCD) measurements at the Fe K and L edges. Starting from ab initio molecular orbital multiplet calculations for the isolated molecule, we diagonalize the spin-orbit interaction in the subspace spanned by the three lowest spin triplet states of 3A2g and 3Eg symmetry in the presence of a saturating magnetic field at a polar angle θ with respect to the normal to the plane of the film, plus an external perturbation representing the effect of the molecules in the stack on the FePc molecule under consideration. We find that the orbital moment of the ground state strongly depends on the magnetic field direction in agreement with the sum rule analysis of the L23-edge XMCD data. We calculate integrals over the XMCD spectra at the Fe K and L23 edges as used in the sum rules and explicitly show that they agree with the expectation values of the orbital moment and effective spin moment of the ground state. On the basis of this analysis, we can rule out alternative candidates proposed in the literature., J.B. and F.B. acknowledge the financial support of the Spanish MINEICO MAT2017-83468-R project, Aragonese E-12 17R RASMIA (co-funded by Fondo Social Europeo), and of the European Union FEDER (ES). We acknowledge support by the European Union COST MP1306 EUSPEC project.