Multiple-scattering theory for space-filling cell potentials

Butler, W. H.; Gonis, A.; Zhang, X.-G.

doi:10.1103/physrevb.45.11527

Cited by 59 publications

(51 citation statements)

References 35 publications

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“…8 Now it is generally accepted that this represents no problem in principle and several realizations of fullpotential KKR codes exist. 5,[9][10][11][12][13][14] Here we use the implementation of Drittler et al, which has been extensively used in impurity calculations. 5,[9][10][11] It consists of a Wigner-Seitz partitioning of the whole space, thus eliminating the interstitial region from the formalism.…”

Section: Introductionmentioning

confidence: 99%

Full-potential KKR calculations for metals and semiconductors

et al. 1999

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We present systematic total energy calculations for metals ͑Al, Fe, Ni, Cu, Rh, Pd, and Ag͒ and semiconductors ͑C, Si, Ge, GaAs, InSb, ZnSe, and CdTe͒, based on the all-electron full-potential ͑FP͒ Korringa-KohnRostoker Green's-function method, using density-functional theory. We show that the calculated lattice parameters and bulk moduli are in excellent agreement with calculated results obtained by other FP methods, in particular, the full-potential linear augmented-plane-wave method. We also investigate the difference between the local-spin-density approximation ͑LSDA͒ and the generalized-gradient approximation ͑GGA͒ of Perdew and Wang ͑PW91͒, and find that the GGA corrects the deficiencies of the LSDA for metals, i.e., the underestimation of equilibrium lattice parameters and the overestimation of bulk moduli. On the other hand, for semiconductors the GGA gives no significant improvement over the LSDA. We also discuss that a perturbative GGA treatment based on FP-LSDA spin densities gives very accurate total energies. Further, we demonstrate that the accuracy of structural properties obtained by FP-LSDA and FP-GGA calculations can also be achieved in the calculations with spherical potentials, provided that the full spin densities are calculated and all Coulomb and exchange integrals over the Wigner-Seitz cell, occurring in the double-counting contributions of the total energy, are correctly evaluated. ͓S0163-1829͑99͒15331-1͔

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Section: Introductionmentioning

confidence: 99%

Full-potential KKR calculations for metals and semiconductors

et al. 1999

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“…We also assume that there exists a finite neighborhood around the origin of each cell lying in the domain of the cell. [12] We then start from the following identity involving surface integrals in…”

Section: Scattering Statesmentioning

confidence: 99%

“…The heart of MST is the introduction of the functions Φ L (r j ; k) which inside cell j are local solutions of the SE with potential v j (r j ) behaving as J L (r j ; k) for r j → 0. They form a complete set of basis functions such that the global scattering wave function can be locally expanded as [12] …”

Section: Scattering Statesmentioning

confidence: 99%

“…Secondly, the generation of the local solutions of the SE with truncated cells in the FP extension of the MST has up to now involved the expansion of the cell shape function in spherical harmonics, which might create convergence problems, as discussed below. 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).…”

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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“…Nonlocality first comes across when considering the Hamiltonian of an electron moving in a potential V with the discrete translational symmetries of an infinite three-dimensional lattice: Its eigenstates are highly nonlocal and extend over the entire system, and the spectrum of eigenenergies, the band structure, lives in reciprocal or k-space. While this band-structure problem cannot be solved analytically, there are nowadays extremely efficient and highly reliable computational tools to solve the single-electron Schrödinger equation for rather general lattice potentials [1][2][3][4].…”

Section: Introductionmentioning

confidence: 99%

Realistic many-body approaches to materials with strong nonlocal correlations

Lechermann

Lichtenstein

Potthoff

2017

Eur. Phys. J. Spec. Top.

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Abstract. Many of the fascinating and unconventional properties of several transition-metal compounds with partially filled d-shells are due to strong electronic correlations. While local correlations are in principle treated exactly within the frame of the dynamical mean-field theory, there are two major and interlinked routes for important further methodical advances: On the one hand, there is a strong need for methods being able to describe material-specific aspects, i.e., methods combining the DMFT with modern band-structure theory, and, on the other hand, nonlocal correlations beyond the mean-field paradigm must be accounted for. Referring to several concrete example systems, we argue why these two routes are worth pursuing and how they can be combined, we describe several related methodical developments and present respective results, and we discuss possible ways to overcome remaining obstacles.

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Multiple-scattering theory for space-filling cell potentials

Cited by 59 publications

References 35 publications

Full-potential KKR calculations for metals and semiconductors

Full-potential KKR calculations for metals and semiconductors

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

Realistic many-body approaches to materials with strong nonlocal correlations

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