Fullyrelativistic fullpotential multiple scattering theory: A pathologyfree 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 nonspherical potential, numerical errors from the irregular solutions give rise to pathological behaviors of the charge density at small radius. Here we present a fullpotential implementation of the fullyrelativistic KKR method to perform ab initio selfconsistent 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 singlesite Green function along the real axis. Here, by using an efficient polesearching technique to identify the zeros of the wellbehaved 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 realenergy scheme. The noble metals are alsomore »
 Authors:

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 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:
 Grant/Contract Number:
 AC0500OR22725; OCI1053575
 Type:
 Accepted Manuscript
 Journal Name:
 Computer Physics Communications
 Additional Journal Information:
 Journal Volume: 224; Journal Issue: C; Journal ID: ISSN 00104655
 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) (SC22); National Science Foundation (NSF)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 36 MATERIALS SCIENCE; Multiple scattering theory; Fullpotential; Dirac equation; KKR method; Green function; Polesearching
 OSTI Identifier:
 1430624
Liu, Xianglin, Wang, Yang, Eisenbach, Markus, and Stocks, George Malcolm. Fullyrelativistic fullpotential multiple scattering theory: A pathologyfree scheme. United States: N. p.,
Web. doi:10.1016/j.cpc.2017.10.011.
Liu, Xianglin, Wang, Yang, Eisenbach, Markus, & Stocks, George Malcolm. Fullyrelativistic fullpotential multiple scattering theory: A pathologyfree scheme. United States. doi:10.1016/j.cpc.2017.10.011.
Liu, Xianglin, Wang, Yang, Eisenbach, Markus, and Stocks, George Malcolm. 2017.
"Fullyrelativistic fullpotential multiple scattering theory: A pathologyfree scheme". United States.
doi:10.1016/j.cpc.2017.10.011. https://www.osti.gov/servlets/purl/1430624.
@article{osti_1430624,
title = {Fullyrelativistic fullpotential multiple scattering theory: A pathologyfree 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 nonspherical potential, numerical errors from the irregular solutions give rise to pathological behaviors of the charge density at small radius. Here we present a fullpotential implementation of the fullyrelativistic KKR method to perform ab initio selfconsistent 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 singlesite Green function along the real axis. Here, by using an efficient polesearching technique to identify the zeros of the wellbehaved 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 realenergy 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}
}