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Title: Implementation and validation of fully relativistic GW calculations: Spin–orbit coupling in molecules, nanocrystals, and solids

Abstract

We present an implementation of G 0W 0 calculations including spin–orbit coupling (SOC) enabling investigations of large systems, with thousands of electrons, and we discuss results for molecules, solids, and nanocrystals. Using a newly developed set of molecules with heavy elements (called GW-SOC81), we find that, when based upon hybrid density functional calculations, fully relativistic (FR) and scalar-relativistic (SR) G 0W 0 calculations of vertical ionization potentials both yield excellent performance compared to experiment, with errors below 1.9%. We demonstrate that while SR calculations have higher random errors, FR calculations systematically underestimate the VIP by 0.1 to 0.2 eV. We further verify that SOC effects may be well approximated at the FR density functional level and then added to SR G 0W 0 results for a broad class of systems. We also address the use of different root-finding algorithms for the G 0W 0 quasiparticle equation and the significant influence of including d electrons in the valence partition of the pseudopotential for G 0W 0 calculations. Lastly, we present statistical analyses of our data, highlighting the importance of separating definitive improvements from those that may occur by chance due to a limited number of samples. We suggest the statistical analysesmore » used here will be useful in the assessment of the accuracy of a large variety of electronic structure methods« less

Authors:
 [1];  [2];  [3];  [2]
  1. The Univ. of Chicago, Chicago, IL (United States)
  2. The Univ. of Chicago, Chicago, IL (United States); Argonne National Lab. (ANL), Argonne, IL (United States)
  3. National Institute for Materials Science, Tsukuba (Japan)
Publication Date:
Research Org.:
Argonne National Lab. (ANL), Argonne, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
OSTI Identifier:
1262100
Grant/Contract Number:
AC02-06CH11357; 5J-30161-0010A
Resource Type:
Journal Article: Published Article
Journal Name:
Journal of Chemical Theory and Computation
Additional Journal Information:
Journal Volume: 12; Journal Issue: 8; Journal ID: ISSN 1549-9618
Publisher:
American Chemical Society
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; 36 MATERIALS SCIENCE

Citation Formats

Scherpelz, Peter, Govoni, Marco, Hamada, Ikutaro, and Galli, Giulia. Implementation and validation of fully relativistic GW calculations: Spin–orbit coupling in molecules, nanocrystals, and solids. United States: N. p., 2016. Web. doi:10.1021/acs.jctc.6b00114.
Scherpelz, Peter, Govoni, Marco, Hamada, Ikutaro, & Galli, Giulia. Implementation and validation of fully relativistic GW calculations: Spin–orbit coupling in molecules, nanocrystals, and solids. United States. doi:10.1021/acs.jctc.6b00114.
Scherpelz, Peter, Govoni, Marco, Hamada, Ikutaro, and Galli, Giulia. 2016. "Implementation and validation of fully relativistic GW calculations: Spin–orbit coupling in molecules, nanocrystals, and solids". United States. doi:10.1021/acs.jctc.6b00114.
@article{osti_1262100,
title = {Implementation and validation of fully relativistic GW calculations: Spin–orbit coupling in molecules, nanocrystals, and solids},
author = {Scherpelz, Peter and Govoni, Marco and Hamada, Ikutaro and Galli, Giulia},
abstractNote = {We present an implementation of G0W0 calculations including spin–orbit coupling (SOC) enabling investigations of large systems, with thousands of electrons, and we discuss results for molecules, solids, and nanocrystals. Using a newly developed set of molecules with heavy elements (called GW-SOC81), we find that, when based upon hybrid density functional calculations, fully relativistic (FR) and scalar-relativistic (SR) G0W0 calculations of vertical ionization potentials both yield excellent performance compared to experiment, with errors below 1.9%. We demonstrate that while SR calculations have higher random errors, FR calculations systematically underestimate the VIP by 0.1 to 0.2 eV. We further verify that SOC effects may be well approximated at the FR density functional level and then added to SR G0W0 results for a broad class of systems. We also address the use of different root-finding algorithms for the G0W0 quasiparticle equation and the significant influence of including d electrons in the valence partition of the pseudopotential for G0W0 calculations. Lastly, we present statistical analyses of our data, highlighting the importance of separating definitive improvements from those that may occur by chance due to a limited number of samples. We suggest the statistical analyses used here will be useful in the assessment of the accuracy of a large variety of electronic structure methods},
doi = {10.1021/acs.jctc.6b00114},
journal = {Journal of Chemical Theory and Computation},
number = 8,
volume = 12,
place = {United States},
year = 2016,
month = 6
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1021/acs.jctc.6b00114

Citation Metrics:
Cited by: 5works
Citation information provided by
Web of Science

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  • We present an implementation of G 0W 0 calculations including spin–orbit coupling (SOC) enabling investigations of large systems, with thousands of electrons, and we discuss results for molecules, solids, and nanocrystals. Using a newly developed set of molecules with heavy elements (called GW-SOC81), we find that, when based upon hybrid density functional calculations, fully relativistic (FR) and scalar-relativistic (SR) G 0W 0 calculations of vertical ionization potentials both yield excellent performance compared to experiment, with errors below 1.9%. We demonstrate that while SR calculations have higher random errors, FR calculations systematically underestimate the VIP by 0.1 to 0.2 eV. Wemore » further verify that SOC effects may be well approximated at the FR density functional level and then added to SR G 0W 0 results for a broad class of systems. We also address the use of different root-finding algorithms for the G 0W 0 quasiparticle equation and the significant influence of including d electrons in the valence partition of the pseudopotential for G 0W 0 calculations. Lastly, we present statistical analyses of our data, highlighting the importance of separating definitive improvements from those that may occur by chance due to a limited number of samples. We suggest the statistical analyses used here will be useful in the assessment of the accuracy of a large variety of electronic structure methods« less
  • We describe the implementation of total angular momentum dependent pseudopotentials in a plane wave formulation of density functional theory. Our approach thus goes beyond the scalar-relativistic approximation usually made in ab initio pseudopotential calculations and explicitly includes spin-orbit coupling. We outline the necessary extensions and compare the results to available all-electron calculations and experimental data.
  • The effect of spin-orbit interaction on the structure of the ground state in the conduction band of spherical silicon nanocrystals is theoretically studied using the envelope-function approximation and the k {center_dot} p method. It is shown that the arising weak spin-orbit coupling of the conduction- and valence bands leads to specific asymmetric hybridization of the s- and p-type envelope functions with opposite spin orientations caused by the anisotropy of spin mixing in the silicon conduction band. As a result, the wave functions of the ground-state transform which is accompanied by an insignificant decrease in its energy. In this case, themore » spin-mixing parameter in nanocrystals depends strongly on their size due to the quantum-confinement effect.« less
  • The role of spin-orbit interaction has been exploited to construct an emergent gauge theory in solids. It has been shown that the charge and spin currents in such a solid form a SU(2) Multiplication-Sign U(1) gauge theory. The lack of gauge symmetry in the SU(2) sector and as a consequence, the non-conservation of spin is spelled out. The phenomenon of spin motive force and spin Hall effect is discussed. The importance of such force in the mesoscopic transport as well as Aharonov-Casher effect is outlined. It is shown that the spin currents in such a theory become the source ofmore » electric field.« less