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

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 » calculated, both as a test of our method and to study the relativistic effects.« less
Authors:
 [1] ;  [2] ; ORCiD logo [3] ; ORCiD logo [4]
  1. Carnegie Mellon Univ., Pittsburgh, PA (United States). Dept. of Physics
  2. Carnegie Mellon Univ., Pittsburgh, PA (United States). Pittsburgh Supercomputing Center
  3. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Center for Computational Sciences
  4. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Materials Science & Technology Division
Publication Date:
Grant/Contract Number:
AC05-00OR22725; OCI-1053575
Type:
Accepted Manuscript
Journal Name:
Computer Physics Communications
Additional Journal Information:
Journal Volume: 224; Journal Issue: C; Journal ID: ISSN 0010-4655
Publisher:
Elsevier
Research Org:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22); National Science Foundation (NSF)
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; Multiple scattering theory; Full-potential; Dirac equation; KKR method; Green function; Pole-searching
OSTI Identifier:
1430624

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., Web. doi:10.1016/j.cpc.2017.10.011.
Liu, Xianglin, Wang, Yang, Eisenbach, Markus, & Stocks, George Malcolm. Fully-relativistic full-potential multiple scattering theory: A pathology-free scheme. United States. doi:10.1016/j.cpc.2017.10.011.
Liu, Xianglin, Wang, Yang, Eisenbach, Markus, and Stocks, George Malcolm. 2017. "Fully-relativistic full-potential multiple scattering theory: A pathology-free scheme". United States. doi:10.1016/j.cpc.2017.10.011. https://www.osti.gov/servlets/purl/1430624.
@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 = {2017},
month = {10}
}