Multiple-scattering Paths Research Articles

Quantum localization corrections from the Bethe–Salpeter equation

We investigate coherent matter wave transport in isotropic 3D speckle potentials by using the Bethe–Salpeter equation and the self-consistent theory of localization. This model constitutes an efficient tool to properly evaluate corrections to Boltzmann diffusion by taking into consideration quantum interference terms between the multiple-scattering paths. We calculate analytically and numerically the static current density, the density of states, the dipolar contribution and the reduced diffusion coefficient. Our results reveal that quantum corrections to diffusive transport, known as weak localization may not only lead to shift the above quantities but affect also the position of the mobility edge.

Multiple scattering description of multicenter coherent emission with applications to photoionization and electron scattering in diatomic molecules

In the light of a multiple scattering (MS) description of molecular photodiffraction and photoabsorption processes, we present an investigation of the interplay between initial state coherence and intramolecular scattering, leading to a reinterpretation of the molecular interference in diatomic molecules and in particular of the Cohen-Fano (CF) interference term in photoabsorption. Indeed, the delocalization of the initial state electron over different atoms at positions ${\mathbf{R}}_{n}$ introduces in the language of MS theory as many virtual emitters as there are atoms in the molecule, giving rise to new MS paths as compared to the case of a single emitter. Their emission amplitudes interfere via the usual phase factor ${e}^{i\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathbf{R}}_{n}}$ and in the case of two emitter photoemission describe how the usual picture of the microscopic Young's experiment is modified by the presence of intramolecular scattering. Photoabsorption follows from photoemission by integrating over the emission directions of the photoelectron and characterizes the CF oscillations as the remnants on the energy scale of the photoemission interference patterns introduced by the new paths joining the two centers, exactly like the extended x-ray absorption fine structure signals are the remnants of the closed paths that begin and end at the same atom. In the same context of initial state coherence we also show that the orientationally averaged scattering of electrons off small molecules can give access to CF type of oscillations, although in a more complicated way, due to the lack of site selectivity in comparison with the photoemission process and the absence of a dipole selection rule. It is shown that this type of modulation has the same physical origin as that found in photoabsorption.

MXAN: A new program for ab-initio structural quantitative analysis of XANES experiments

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 summaryProgram Title: MXANCPC Library link to program files:https://doi.org/10.17632/4k9363vcvh.1Licensing provisions: GPLv3Programming language: FORTRAN90External routines/libraries: MKL or OpenBLAS libraryNature 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 [2–4]. 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.

Line-scan imaging of monostatic scattering by a sphere near a flat interface: Identification of direct, indirect, and multiple-scattering paths

Line-scan imaging of monostatic scattering by a sphere near a flat interface: Identification of direct, indirect, and multiple-scattering paths

Antenna–Cavity Hybrids: Matching Polar Opposites for Purcell Enhancements at Any Linewidth

Strong interaction between light and a single quantum emitter is essential to a great number of applications, including single photon sources. Microcavities and plasmonic antennas have been used frequently to enhance these interactions through the Purcell effect. Both can provide large emission enhancements: the cavity typically through long photon lifetimes (high $Q$), and the antenna mostly through strong field enhancement (low mode volume $V$). In this work, we demonstrate that a hybrid system, which combines a cavity and a dipolar antenna, can achieve stronger emission enhancements than the cavity or antenna alone. We show that such systems can be used as a versatile platform to tune the bandwidth of enhancement to any desired value, while simultaneously boosting emission enhancement. Our fully consistent analytical model allows to identify the underlying mechanisms of boosted emission enhancement in hybrid systems, which include radiation damping and constructive interference between multiple-scattering paths. Additionally, we find excellent agreement between strongly boosted enhancement spectra from our analytical model and from finite-element simulations on a realistic cavity-antenna system. Finally, we demonstrate that hybrid systems can simultaneously boost emission enhancement and maintain a near-unity outcoupling efficiency into a single cavity decay channel, such as a waveguide.

Accurate X-ray Absorption Spectra of Dilute Systems: Absolute Measurements and Structural Analysis of Ferrocene and Decamethylferrocene

X-ray absorption fine structure (XAFS) of ferrocene (Fc) and Decamethylferrocene (DmFc) have been determined on an absolute scale using transmission measurements of multiple solutions of differing concentrations (15 mM, 3 mM, pure solvent) at operating temperatures of 10–20 K. Mass attenuation coefficients and photoelectric absorption cross sections are measured and tabulated for both molecules for an extended energy range in excess of 1.5 keV from the Fe K-shell absorption edge. At these temperatures, the minimization of of dynamic disorder has enabled a critical determination of the oscillatory absorption structures created by multiple-scattering paths of the excited photoelectron. These oscillatory structures are highly sensitive to the local conformation environment of the iron absorber in organometallic structures. Crystallographic and scattering studies have reported both structures characterized by staggered cyclopentadienyl rings, in contrast with low temperature crystallography and recent density functional theoretical predictions. Phase changes in the crystallographic space groups are reported for Fc at different temperatures, raising the possibility of alternative conformation states. Robust experimental techniques are described which have allowed the measurement of XAFS spectra of dilute systems by transmission at accuracies ranging from 0.2% to 2%, and observe statistically significant fine structure at photoelectron wavenumbers extending to >12 Å–1. The subtle signatures of the conformations are then investigated via extensive analysis of the XAFS spectra using the full multiple scattering theory as implemented by the FEFF package. Results indicate a near-eclipsed D5h geometry for low-temperature Fc, in contrast with a staggered D5d geometry observed for DmFc. The ability of this experimental approach and data analysis methodology combined with advanced theory to investigate and observe such subtle conformational differences using XAFS is a powerful tool for future challenges and widens the capacity of advanced XAFS to solve a broad range of challenging systems.

Multiangle implementation of atmospheric correction (MAIAC): 1. Radiative transfer basis and look-up tables

[1] This paper describes a radiative transfer basis of the algorithm MAIAC which performs simultaneous retrievals of atmospheric aerosol and bidirectional surface reflectance from the Moderate Resolution Imaging Spectroradiometer (MODIS). The retrievals are based on an accurate semianalytical solution for the top-of-atmosphere reflectance expressed as an explicit function of three parameters of the Ross–Thick Li–Sparse model of surface bidirectional reflectance. This solution depends on certain functions of atmospheric properties and geometry which are precomputed in the look-up table (LUT). This paper further considers correction of the LUT functions for variations of surface pressure/height and of atmospheric water vapor, which is a common task in the operational remote sensing. It introduces a new analytical method for the water vapor correction of the multiple-scattering path radiance. It also summarizes the few basic principles that provide a high efficiency and accuracy of the LUT-based radiative transfer for the aerosol/surface retrievals and optimize the size of LUT. For example, the single-scattering path radiance is calculated analytically for a given surface pressure and atmospheric water vapor. The same is true for the direct surface-reflected radiance, which along with the single-scattering path radiance largely defines the angular dependence of measurements. For these calculations, the aerosol phase functions and kernels of the surface bidirectional reflectance model are precalculated at a high angular resolution. The other radiative transfer functions depend rather smoothly on angles because of multiple scattering and can be calculated at coarser angular resolution to reduce the LUT size. At the same time, this resolution should be high enough to use the nearest neighbor geometry angles to avoid costly three-dimensional interpolation. The pressure correction is implemented via linear interpolation between two LUTs computed for the standard and reduced pressure levels. A linear mixture and a modified linear mixture methods are used to represent different aerosol types in the aerosol/surface retrievals from several base models of the fine and coarse aerosol fractions. In summary, the developed LUT algorithm allows fast high-accuracy simulations of the outgoing radiance with full variability of the atmospheric and surface bidirectional reflectance properties for the aerosol/surface remote sensing.

Wavelet transform EXAFS analysis of mono- and dimolybdate model compounds and a Mo/HZSM-5 dehydroaromatization catalyst

The local structure of molybdate ions in the crystalline materials MgMoO(4) and MgMo(2)O(7) and in Mo/HZSM-5 (2 wt% Mo, Si/Al = 15) was explored by EXAFS at the Mo K-edge, using both Fourier and wavelet transforms. For the two model compounds, curve fitting analysis of the FT-EXAFS reveals the need to include several single- and multiple-scattering paths in order to locate the Mo-Mo paths accurately. Some of these overlapping paths can be identified using WT-EXAFS analysis. Indeed, the positions of WT maxima can be predicted fairly accurately, allowing for qualitative identification of the paths required for curve fitting in samples of unknown structure and providing additional criteria for distinguishing statistically similar curve fits. The application of the WT analysis technique to the heterogeneous catalyst Mo/HZSM-5 clearly shows the presence of dimolybdate ions, although with structures perturbed by their interactions with the zeolite framework.

Geometric and path tracing methods for simulating light transport through volumes of water particles

The visual appearance of volumes of water particles, such as clouds, waterfalls, and fog, depends both on microscopic interactions between light rays and individual droplets of water, and also on macroscopic interactions between multiple droplets and paths of light rays. This paper presents a model that builds upon a typical single-scattering volume renderer to correctly account for these effects. To accurately simulate the visual appearance of a surface or a volume of particles in a computer-generated image, the properties of the material or particle must be specified using a Bidirectional Reflectance Distribution Function (BRDF), which describes how light reflects off of a material, and the Bidirectional Transmittance Distribution Function (BTDF), which describes how light refracts into a material. This paper describes an optimized BRDF and BTDF for volumes of water droplets, which takes their geometry into account in order to produce well-known effects, such as rainbows and halos. It also describes how a multiple-scattering path tracing volume integrator can be used to more accurately simulate macroscopic light transport through a volume of water, creating a more "cloudlike" appearance than a single-scattered volume integrator. This paper focuses on replicating the visual appearance of volumes of water particles, and although it makes use of physical models, the techniques presented are not intended to be physically accurate.

Direct determination by low-energy electron diffraction of the atomic structure of surface layers on a known substrate

We develop a technique for the direct determination, by low-energy electron diffraction ~LEED! ,o f the atomic structure of surface layers on a known substrate. The key is the division of multiple-scattering paths into those that scatter solely from the known bulk of the sample and those that include scattering by a surface atom. In a holographic analogy, the sum of the contributions from the former may be identified with a~known! reference wave, and those from the surface with an ~unknown! object wave. The latter may be written as a linear combination of elementary object waves, each of which may be regarded as a renormalized dynamical structure factor of a test two-dimensional ~2D! superlattice of average atoms within a preselected 3D surface slab overlying the bulk crystal. The coefficients of this linear expansion, which may be determined by a maximum entropy algorithm, represent the 3D distribution of atoms within the surface slab. Examples are given of applications of the method for the determination of structures of adsorbates on known substrates from both simulated and experimental LEED data.

Extended X-ray absorption fine-structure (EXAFS) of a complex oxide structure: a full multiple scattering analysis of the Au L 3-edge EXAFS of Au 2O 3

Crystalline Au 2O 3 was obtained by hydrothermal synthesis at 3000 atm and its extended X-ray absorption fine-structure (EXAFS) at the Au L 3-edge was measured at room temperature. A detailed full multiple scattering (MS) analysis using FEFF8 theory shows that only a small number of scattering paths contribute significantly to the EXAFS of Au 2O 3. Because of the complex unit cell (low local symmetry) of the Au 2O 3 structure, contributions of MS paths are almost negligible. The results indicate that FEFF8 theory provides a good reference for the analysis of Au–O phases.

Experimental and theoretical X-ray K-spectra of sulfur of zincblende-based compounds AgGaS 2–CdGa 2S 4–InPS 4

The K-edge X-ray absorption spectrum of sulfur in AgGaS 2, CdGa 2S 4, and InPS 4 was investigated both experimentally and theoretically. The lattices of these compounds can be represented as chalcopyrite with various amounts of defectiveness. The spectra were obtained with an experimental resolution about 0.2 eV. To obtain the theoretical absorption spectrum, the FEFF7 high order multiple scattering code was used. The clusters considered contained 80–87 atoms; up to 624 multiple-scattering paths of the photoelectron were taken into account, with the highest order scattering equal to 6. A very good correspondence between the theoretical and experimental spectra was achieved when the energy dependent exchange energy was calculated according to the Dirac–Hara approximation.

Molecular-dynamics-based investigation of scattering path contributions to the EXAFS spectrum: TheCr3+aqueous solution case

Extended x-ray absorption fine structure spectra were computed based on molecular-dynamics (MD) structural data of a $[\mathrm{Cr}({\mathrm{H}}_{2}\mathrm{O}{)}_{6}{]}^{3+}$ aqueous solution using nonempirical cation-water potentials. An excellent reproduction of the experimental spectrum was achieved. A simple estimation of Debye-Waller factors of the multiple-scattering paths is deduced from MD simulations. The influence of the single-scattering path due to the second hydration shell as compared with the multiple-scattering paths within the first hydration shell allows a reasonable determination of the second hydration shell distance $R(\mathrm{Cr}\ensuremath{-}{\mathrm{O}}_{\mathrm{II}})$ within $0.1$ \AA{}.

Multiple scattering of electrons in solids and molecules: A cluster-model approach

A method for the simulation of electron scattering and diffraction in solids and molecules within the cluster approach is presented with explicit applications to photoelectron diffraction, electron scattering in molecules, and low-energy electron diffraction. No approximations are made beyond the muffin-tin model, and, in particular, an exact representation of the free-electron Green function is used. All multiple-scattering paths are accounted for up to an order of scattering that ensures convergence. The method relies upon a convenient separation of the free-electron Green function in rotation matrices and translations along the z axis, which greatly reduces the computation time and storage demand. The evaluation of the multiple-scattering expansion is implemented using the fully convergent recursion method, which permits one to perform an iterative refinement of the final-state wave function, as expressed in the basis set of spherical harmonics attached to each atom of the cluster. Examples are offered in which the direct multiple-scattering expansion and the more elaborated simultaneous relaxation method fail to converge, whereas the recursion method leads to convergence. The computation time needed by the resulting computer program of electron diffraction in atomic clusters to determine the self-consistently scattered wave function is proportional to ${N}^{2}{(l}_{\mathrm{max}}{+1)}^{3},$ where N is the number of atoms in the cluster and ${l}_{\mathrm{max}}$ is the maximum angular momentum for which the scattering phase shifts take non-negligible values. Within this method it is possible to establish that in practical cases $N>1000$ might be needed for a convergence of the cluster size, although the angular averaging inherent in many experiments may reduce this. The recursion method was also modified to reduce the effort in computing angular distributions of photoelectrons and low-energy diffracted electrons, which now require negligible time for each angle of emission once the wave function has been determined for a given electron energy. Angle and energy distributions of core-level photoemission, elastic scattering of electrons from a free molecule, and low-energy electron diffraction in large-unit-cell surfaces are calculated.

Importance of multiple-scattering phenomena in XAS structural determinations of [Ni(CN)4]2- in condensed phases.

A quantitative analysis of the XAS spectra of the tetracyanonickelate complex [Ni(CN)4]2- has been carried out. The simultaneous study of the EXAFS and XANES regions yielded complementary information regarding the geometric and electronic structures of the complex. XANES spectra were modeled by applying recently developed self-consistent, full multiple-scattering algorithms in the FEFF8 code (version 8 x 34). XANES spectra for clusters of different sizes (from 9 to 125 atoms) were computed and compared with experimental spectra. This region of the spectra was proportional to a broadened Ni p-density of states diagram above the Fermi level. Although the main features of the XANES spectra were reasonably reproduced by computations, the weak dependence of the theoretical spectra on cluster size contrasts with the close similarity between the experimental spectra of the solid and solution systems. Because of the special geometry of the complex, calculations with polarized light parallel and perpendicular to the molecular plane were carried out, yielding a reasonable reproduction of the experimental data from another report for cluster sizes equal to or higher than 45 atoms. The highly symmetric square planar structure of the complex was found to be responsible for the unusual amplitude of the multiple-scattering (MS) contributions to the EXAFS spectra. Spectra in this region were fitted using the FEFFIT EXAFS analysis program, taking into account only the MS paths that simultaneously have both a high amplitude, as calculated with the ab initio code FEFF, and a small Debye-Waller factor, as estimated by the independent-vibration approximation model. Fitting results yielded very similar structures for the Ni2+ complex in the solid state and in solution, though the larger Debye-Waller factors found for the solid suggest higher static disorder in this state.

X-ray natural circular dichroism and chiral-EXAFS in gyrotropic crystals

X-ray natural circular dichroism (XNCD) has been recently detected in the XANES region for uniaxial and biaxial gyrotropic crystals. Chiral-EXAFS (chi-EXAFS) spectra are reported for the first time over a wider energy range and are analysed in terms of multiple-scattering paths of relevant symmetry. For such heavily absorbing single crystals as lithium iodate, paratellurite or potassium titanyl phosphate, the differential absorption between left-handed and right-handed circularly polarized X-ray photons cannot be measured in transmission but gyrotropy effects can still be detected in fluorescence excitation spectra. Whereas XNCD and fluorescence-detected X-ray natural circular dichroism spectra are strictly identical for uniaxial crystals, it has been established that this was true only to the first order for biaxial crystals such as potassium titanyl phosphate.

X-ray-absorption fine structure determination of pressure-induced bond-angle changes inReO3

We report here on a Marquardt-type method to fit the x-ray absorption fine structure (XAFS) of ${\mathrm{ReO}}_{3}.$ We find that, when the ambient-pressure structure of ${\mathrm{ReO}}_{3}$ is used as a starting point, the pressure dependence of the angle of the Re-O-Re bond in ${\mathrm{ReO}}_{3}$ is fairly straightforwardly and robustly determined using FEFF curved-wave, multiple-scattering programs and is accurate to about \ifmmode\pm\else\textpm\fi{}1.5\ifmmode^\circ\else\textdegree\fi{} or better. We present an argument that XAFS and scattering experiments fundamentally differ in what they measure in the case of nearly linear atomic bridges. Focussed multiple-scattering paths involving the Re-O-Re bridge make a contribution to the XAFS spectrum that is sensitive to the rms deviation of oxygen from the [100]-type directions. Fits to simulated spectra back up our contention that for XAFS experiments the effective position of the oxygen atom is its rms displacement whether the average displacement is zero or not.

Multiple-Scattering EXAFS Analysis of Tetraalkylammonium Manganese Oxide Colloids

X-ray absorption spectroscopy at the Mn K edge was employed to elucidate the structure of colloidal tetraalkylammonium (TAA) manganese oxides in sols and gels obtained by different preparation and heat treatment procedures. Two series of colloidal TAA MnOx prepared with tetrapropylammonium (TPA) and tetraethylammonium (TEA) cations were studied. Several manganese oxides, birnessite, and feitknechtite were also measured and served as model compounds for structural refinements. Near edge structure (XANES) analysis revealed different average valences of the colloidal systems. As synthesized and heat-treated, TAA colloids exhibited an average valence of 3.6−3.7, whereas gelled TAA colloids showed a lower average valence of ∼3.5. Extended absorption fine structure (EXAFS) analysis was carried out to distances of ∼6.0 A around the central Mn atom using theoretical backscattering phases and amplitudes calculated from the ab initio FEFF code. All multiple-scattering (MS) paths with a weight of 2% and more with re...

Rapid single- and multiple-scattering EXAFS Debye-Waller factor calculations on active sites of metalloproteins.

This paper describes recent results using our approach to calculating self-consistently single (SS) and multiple-scattering (MS) DebyeWaller factors (DWF) on active sites of metalloproteins. The calculation of MS DWF, together with the Feff7 program allows us to simulate ab-initio EXAFS spectra for a given temperature systems with no adjustable parameters. In our latest report (Dimakis N., and Bunker G., 1998) we calculate, using density functional and semiempirical approaches, the SS and MS DWF for small molecules and compared them to Raman, infrared and EXAFS spectra. In this report calculation of DWFs is done for tetrahedral Zn imidazole, a complex containing thirty two atoms that is similar in certain respects to active sites of many metalloproteins. Ab-initio calculation, although it is a more accurate and reliable scheme, it is not at present practical on desktop computers; computation times are weeks. Therefore as an alternative we have tried the semiempirical MNDO Hamiltonian, which is at least three orders of magnitude faster than ab-initio, and can be expected to be of reasonable accuracy because it is parameterized for organic compounds. Our approaches take advantage of commercially available molecular orbital programs. We have written additional programs which, using normal mode calculations, calculate the MS paths, and transparently interface with Fef-f'/to produce the EXAFS spectra. Results are in very good agreement with experimental data tested.

Convergence and reliability of the Rehr-Albers formalism in multiple-scattering calculations of photoelectron diffraction

The Rehr-Albers (RA) separable Green's-function formalism, which is based on an expansion series, has been successful in speeding up multiple-scattering cluster calculations for photoelectron diffraction simulations, particularly in its second-order version. The performance of this formalism is explored here in terms of computational speed, convergence over orders of multiple scattering, over orders of approximation, and over cluster size, by comparison with exact cluster-based formalisms. It is found that the second-order RA approximation [characterized by $(6\ifmmode\times\else\texttimes\fi{}6)$ scattering matrices] is adequate for many situations, particularly if the initial state from which photoemission occurs is of s or p type. For the most general and quantitative applications, higher-order versions of RA may become necessary for d initial states [third-order, i.e., $(10\ifmmode\times\else\texttimes\fi{}10)$ matrices] and f initial states [fourth-order, i.e., $(15\ifmmode\times\else\texttimes\fi{}15)$ matrices]. However, the required RA order decreases as an electron wave proceeds along a multiple-scattering path, and this can be exploited, together with the selective and automated cutoff of weakly contributing matrix elements and paths, to yield computer time savings of at least an order of magnitude with no significant loss of accuracy. Cluster sizes of up to approximately 100 atoms should be sufficient for most problems that require about 5% accuracy in diffracted intensities. Excellent sensitivity to structure is seen in comparisons of second-order theory with variable geometry to exact theory as a fictitious ``experiment.'' Our implementation of the Rehr-Albers formalism thus represents a versatile, quantitative, and efficient method for the accurate simulation of photoelectron diffraction.