Multiple Scattering in Solids

Gonis, A.; Butler, W. H.

doi:10.1007/978-1-4612-1290-4

Cited by 90 publications

(120 citation statements)

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“…The expansion of the shape function and the cell potential in spherical harmonics leads to a high number of spherical components in the coupled radial equations that becomes progressively cumbersome to handle and time consuming with increasing energy and in absence of symmetry. This feature might also be at the origin of another problem related with the saturation of "internal" sums in the MSE [13], as discussed later in this paper. Moreover no critical discussion is devoted in their work to the l-convergence problems of MST or the use of square matrices in the theory.…”

Section: Introductionmentioning

confidence: 76%

“…Thirdly, the FP extension of MST has generated a lot of controversies that have gone on for more than thirty years [12]. Some of the problems have found a solution and we refer the reader to the book of Gonis and Butler [13] for a comprehensive review of the state of the art in this field (in particular see their chapter 6). However, questions like the l-convergence of the theory or the use of square matrices are still matter of debate and some rigorous answer should be given to them.…”

Section: Introductionmentioning

confidence: 99%

“…In the words of Ref. [13], "the feeling that one should calculate the "near-field-corrections" (NFC), coupled with the need to solve a fairly complicated system of coupled differential equation to determine the local (cell) solutions (based on the phase function method) has contributed greatly to the slow development of a FP method based on MST". It was only after it was realized that NFC are not necessary and a new method to generate local solutions was found that progress became faster, at least in the calculation of the electronic structure of solids.…”

Section: Introductionmentioning

confidence: 99%

“…Section 3 provides a new derivation of the FP-MST that allows us to work with square matrices for the phase functions S LL and E LL and for the cell T LL matrix with only one truncation parameter, contrary to the present accepted view. [13] Due to their importance in the theory, various equivalent forms for the Green's function are presented in this scheme. This latter is extended to the calculation of bound states of polyatomic molecules and tested against the known eigenvalues of the hydrogen molecular ion.…”

Section: Introductionmentioning

confidence: 99%

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Full-potential multiple scattering theory with space-filling cells for bound and continuum states

Hatada¹,

Hayakawa²,

Benfatto³

et al. 2010

J. Phys.: Condens. Matter

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Abstract. We present a rigorous derivation of a real space Full-Potential MultipleScattering-Theory (FP-MST) that is free from the drawbacks that up to now have impaired its development (in particular the need to expand cell shape functions in spherical harmonics and rectangular matrices), valid both for continuum and bound states, under conditions for space-partitioning that are not excessively restrictive and easily implemented. In this connection we give a new scheme to generate local basis functions for the truncated potential cells that is simple, fast, efficient, valid for any shape of the cell and reduces to the minimum the number of spherical harmonics in the expansion of the scattering wave function. The method also avoids the need for saturating 'internal sums' due to the re-expansion of the spherical Hankel functions around another point in space (usually another cell center). Thus this approach, provides a straightforward extension of MST in the Muffin-Tin (MT) approximation, with only one truncation parameter given by the classical relation l max = kR b , where k is the electron wave vector (either in the excited or ground state of the system under consideration) and R b the radius of the bounding sphere of the scattering cell. Moreover, the scattering path operator of the theory can be found in terms of an absolutely convergent procedure in the l max → ∞ limit. Consequently, this feature provides a firm ground to the use of FP-MST as a viable method for electronic structure calculations and makes possible the computation of x-ray spectroscopies, notably photo-electron diffraction, absorption and anomalous scattering among others, with the ease and versatility of the corresponding MT theory. Some numerical applications of the theory are presented, both for continuum and bound states.

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Section: Introductionmentioning

confidence: 76%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Full-potential multiple scattering theory with space-filling cells for bound and continuum states

Hatada¹,

Hayakawa²,

Benfatto³

et al. 2010

J. Phys.: Condens. Matter

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“…There have been many attempts to extend the MS theory to the FP level [10][11][12][13][14][15]. Here we give a brief summary of our FPMS method developed previously by some of us [7].…”

Section: Theory a Fpms Methodsmentioning

confidence: 99%

X-ray absorption spectra of graphene and graphene oxide by full-potential multiple scattering calculations with self-consistent charge density

Krüger

Natoli

et al. 2015

Phys. Rev. B

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X-ray absorption near edge structure (XANES) of graphene, graphene oxide and diamond are studied by the recently developed real-space full potential multiple scattering (FPMS) theory with space-filling cells. It is shown how accurate potentials for FPMS can be generated from self-consistent charge densities obtained with other schemes, especially the projector augmented wave method. Compared to standard multiple scattering calculations in the muffin-tin approximation, FPMS gives much better agreement with experiment. The effects of various structural modifications on the graphene spectra are well reproduced. (1) Stacking of graphene layers increases the peak intensity in the higher energy region. (2) The spectrum of the C atom located at the edge of graphene sheet shows a prominent pre-edge structure. (3) Adsorption of oxygen gives rise to the so-called interlayer-state peak. Moreover, O K-edge spectra of graphene oxide are calculated for three types of bonding, C-OH, C-O-C and C-O, and the proportions of these bondings at 800 • C are deduced by fitting them to the experimental spectrum.

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Single Electron Inelastic Scattering

2018

Electron Beam‐Specimen Interactions and Simulation Methods in Microscopy

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Multiple Scattering in Solids

Cited by 90 publications

References 0 publications

Full-potential multiple scattering theory with space-filling cells for bound and continuum states

Full-potential multiple scattering theory with space-filling cells for bound and continuum states

X-ray absorption spectra of graphene and graphene oxide by full-potential multiple scattering calculations with self-consistent charge density

Single Electron Inelastic Scattering

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