Fully-relativistic full-potential multiple scattering theory: A pathology-free scheme

Liu, Xianglin; Wang, Yang; Eisenbach, Markus; Stocks, George Malcolm

doi:10.1016/j.cpc.2017.10.011

Title: Fully-relativistic full-potential multiple scattering theory: A pathology-free scheme

Full Record
Other Related Research

Abstract

The Green function plays an essential role in the Korringa–Kohn–Rostoker(KKR) multiple scattering method. In practice, it is constructed from the regular and irregular solutions of the local Kohn–Sham equation and robust methods exist for spherical potentials. However, when applied to a non-spherical potential, numerical errors from the irregular solutions give rise to pathological behaviors of the charge density at small radius. Here we present a full-potential implementation of the fully-relativistic KKR method to perform ab initio self-consistent calculation by directly solving the Dirac differential equations using the generalized variable phase (sine and cosine matrices) formalism Liu et al. (2016). The pathology around the origin is completely eliminated by carrying out the energy integration of the single-site Green function along the real axis. Here, by using an efficient pole-searching technique to identify the zeros of the well-behaved Jost matrices, we demonstrated that this scheme is numerically stable and computationally efficient, with speed comparable to the conventional contour energy integration method, while free of the pathology problem of the charge density. As an application, this method is utilized to investigate the crystal structures of polonium and their bulk properties, which is challenging for a conventional real-energy scheme. The noble metals are alsomore »« less

Authors:

Liu, Xianglin ^[1]; Wang, Yang ^[2];

^[3];

^[4]

Carnegie Mellon Univ., Pittsburgh, PA (United States). Dept. of Physics
Carnegie Mellon Univ., Pittsburgh, PA (United States). Pittsburgh Supercomputing Center
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Center for Computational Sciences
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Materials Science & Technology Division

Publication Date:: Sat Oct 28 00:00:00 EDT 2017

Research Org.:: Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)

Sponsoring Org.:: USDOE Office of Science (SC), Basic Energy Sciences (BES); National Science Foundation (NSF)

OSTI Identifier:: 1430624

Alternate Identifier(s):: OSTI ID: 1576842

Grant/Contract Number:: AC05-00OR22725; OCI-1053575

Resource Type:: Accepted Manuscript

Journal Name:: Computer Physics Communications

Additional Journal Information:: Journal Volume: 224; Journal Issue: C; Journal ID: ISSN 0010-4655

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 36 MATERIALS SCIENCE; Multiple scattering theory; Full-potential; Dirac equation; KKR method; Green function; Pole-searching

Citation Formats


                    Liu, Xianglin, Wang, Yang, Eisenbach, Markus, and Stocks, George Malcolm. Fully-relativistic full-potential multiple scattering theory: A pathology-free scheme.  United States: N. p., 2017. 
Web.  doi:10.1016/j.cpc.2017.10.011.

Copy to clipboard


                    Liu, Xianglin, Wang, Yang, Eisenbach, Markus, & Stocks, George Malcolm. Fully-relativistic full-potential multiple scattering theory: A pathology-free scheme.  United States.  https://doi.org/10.1016/j.cpc.2017.10.011

Copy to clipboard


                    Liu, Xianglin, Wang, Yang, Eisenbach, Markus, and Stocks, George Malcolm. Sat .  
"Fully-relativistic full-potential multiple scattering theory: A pathology-free scheme".  United States.  https://doi.org/10.1016/j.cpc.2017.10.011.  https://www.osti.gov/servlets/purl/1430624.

Copy to clipboard


                    
@article{osti_1430624,

  title        = {Fully-relativistic full-potential multiple scattering theory: A pathology-free scheme},

  author       = {Liu, Xianglin and Wang, Yang and Eisenbach, Markus and Stocks, George Malcolm},

  abstractNote = {The Green function plays an essential role in the Korringa–Kohn–Rostoker(KKR) multiple scattering method. In practice, it is constructed from the regular and irregular solutions of the local Kohn–Sham equation and robust methods exist for spherical potentials. However, when applied to a non-spherical potential, numerical errors from the irregular solutions give rise to pathological behaviors of the charge density at small radius. Here we present a full-potential implementation of the fully-relativistic KKR method to perform ab initio self-consistent calculation by directly solving the Dirac differential equations using the generalized variable phase (sine and cosine matrices) formalism Liu et al. (2016). The pathology around the origin is completely eliminated by carrying out the energy integration of the single-site Green function along the real axis. Here, by using an efficient pole-searching technique to identify the zeros of the well-behaved Jost matrices, we demonstrated that this scheme is numerically stable and computationally efficient, with speed comparable to the conventional contour energy integration method, while free of the pathology problem of the charge density. As an application, this method is utilized to investigate the crystal structures of polonium and their bulk properties, which is challenging for a conventional real-energy scheme. The noble metals are also calculated, both as a test of our method and to study the relativistic effects.},

  doi          = {10.1016/j.cpc.2017.10.011},

  journal      = {Computer Physics Communications},

  number       = C,

  volume       = 224,

  place        = {United States},

  year         = {Sat Oct 28 00:00:00 EDT 2017},

  month        = {Sat Oct 28 00:00:00 EDT 2017}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (Publisher)

Accepted Manuscript (DOE)

Publisher's Version of Record

https://doi.org/10.1016/j.cpc.2017.10.011

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 3 works

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

Similar Records in DOE PAGES and OSTI.GOV collections:

Green's function multiple-scattering theory with a truncated basis set: An augmented-KKR formalism

Journal Article Alam, Aftab ; Khan, Suffian N. ; Smirnov, A. V. ; ... - Physical Review. B, Condensed Matter and Materials Physics

Korringa-Kohn-Rostoker (KKR) Green's function, multiple-scattering theory is an ecient sitecentered, electronic-structure technique for addressing an assembly of N scatterers. Wave-functions are expanded in a spherical-wave basis on each scattering center and indexed up to a maximum orbital and azimuthal number L_max = (l,m)_max, while scattering matrices, which determine spectral properties, are truncated at L_tr = (l,m)_tr where phase shifts δl>l_tr are negligible. Historically, L_max is set equal to L_tr, which is correct for large enough L_max but not computationally expedient; a better procedure retains higher-order (free-electron and single-site) contributions for L_max > L_tr with δl>l_tr set to zero [Zhang andmore »« less
Cited by 9
https://doi.org/10.1103/PhysRevB.90.205102

Full Text Available
Full-potential KKR within the removed-sphere method: A practical and accurate solution to the Poisson equation

Journal Article Ning, Zhenhua ; Smirnov, A. V. ; Shelton, Jr., William A. ; ... - Physical Review. B

Here an efficient and accurate generalization of the removed-sphere method (RSM) to solve the Poisson equation for total charge density in a solid with space-filling convex Voronoi polyhedra (VPs) and any symmetry is presented. The generalized RSM avoids the use of multipoles and VP shape functions for cellular integrals, which have associated ill-convergent large, double-internal L sums in spherical-harmonic expansions, so that fast convergence in single-L sums is reached. Our RSM adopts full Ewald formulation to work for all configurations or when symmetry breaking occurs, such as for atomic displacements or elastic constant calculations. The structure-dependent coefficients A_L that definemore »« less
https://doi.org/10.1103/physrevb.106.235114

Full Text Available
Electronic structure of FeTiSb using relativistic and scalar-relativistic approaches

Journal Article Sahariya, Jagrati ; Mund, H. S., E-mail: hmoond@gmail.com - AIP Conference Proceedings

Electronic and magnetic properties of FeTiSb have been reported. The calculations are performed using spin polarized relativistic Korringa-Kohn-Rostoker scheme based on Green’s function method. Within SPR-KKR a fully relativistic and scalar-relativistic approaches have been used to investigate electronic structure of FeTiSb. Energy bands, total and partial density of states, atom specific magnetic moment along with total moment of FeTiSb alloys are presented.
https://doi.org/10.1063/1.4946643
Thermodynamic, Kinetic, and Physical Properties of Nb-U (Niobium-Uranium)

Technical Report Turchi, Patrice E. A.

Based on an improved coupling between ab initio energetics output, phenomenological thermodynamics based on the CALPHAD (CALculation of Phase Diagrams) approach, and the use of the Thermo-Calc software, together with experimental data (whenever available), a thermodynamic assessment of the Nb-U alloy system was carried out. We made use of the full array of modern electronic-structure techniques based on density functional theory, including ab initio fully relativistic full-potential linear-muffin orbital method (FR-FP-LMTO), methods, the Scalar Relativistic Korringa-Kohn-Rostoker Atomic-Sphere Approximation (SR-KKR-ASA), and the fully relativistic or scalar relativistic Exact muffin-orbital (SR- or FR-EMTO) method, both based on the Green function formalism thatmore »« less
https://doi.org/10.2172/1459121

Full Text Available
Local-environment fluctuations and densities of states in substitutionally disordered alloys

Journal Article Gonis, A ; Stocks, G M ; Butler, W H ; ... - Phys. Rev. B: Condens. Matter; (United States)

We report calculations of densities of states (DOS) associated with specific atomic configurations of compact clusters in substitutionally disordered alloys describable by a Hamiltonian with nonoverlapping muffin-tin potentials. The method of calculation consists in evaluating the Green function associated with a cluster of atoms embedded in a translationally invariant effective medium such as the one determined in the Korringa-Kohn-Rostoker, coherent-potential-approximation (KKR-CPA) method. This method yields well-defined, analytic, and physically meaningful results and takes proper account of the crystal structure of the lattice. Numerical results are reported for near-neighbor clusters in both one-dimensional model muffin-tin alloys, as well as in realisticmore »« less
https://doi.org/10.1103/PhysRevB.29.555

Similar Records