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

## Abstract

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 and Butler, Phys. Rev. B 46, 7433]. We present a numerically ecient and accurate augmented-KKR Green's function formalism that solves the KKR equations by exact matrix inversion [R ^{3} process with rank N(l _{tr} + 1) ^{2}] and includes higher-L contributions via linear algebra [R ^{2} process with rank N(l _{max} +1) ^{2}]. Augmented-KKR approach yields properly normalized wave-functions, numerically cheaper basis-set convergence, and a total charge density and electron count that agrees with Lloyd's formula. We apply our formalism to fcc Cu, bcc Fe and L1 _{0} CoPt, andmore »

- Authors:

- Indian Inst. of Technology (IIT), Mumbai (India). Dept. of Physics
- Ames Lab., Ames, IA (United States). Division of Materials Science & Engineering
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Ames Lab., Ames, IA (United States). Division of Materials Science & Engineering; Iowa State Univ., Ames, IA (United States). Dept. of Materials Science & Engineering

- Publication Date:

- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Ames Laboratory (AMES), Ames, IA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

- OSTI Identifier:
- 1286786

- Alternate Identifier(s):
- OSTI ID: 1180863

- Grant/Contract Number:
- AC05-00OR22725; FG02-03ER46026; AC02- 07CH11358; 13IRCCSG020; AC02-07CH11358

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physical Review. B, Condensed Matter and Materials Physics

- Additional Journal Information:
- Journal Volume: 90; Journal Issue: 20; Journal ID: ISSN 1098-0121

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 36 MATERIALS SCIENCE; Korringa-Kohn-Rostoker (KKR) Green's function; multiple-scattering

### Citation Formats

```
Alam, Aftab, Khan, Suffian N., Smirnov, A. V., Nicholson, D. M., and Johnson, Duane D. Green's function multiple-scattering theory with a truncated basis set: An augmented-KKR formalism. United States: N. p., 2014.
Web. doi:10.1103/PhysRevB.90.205102.
```

```
Alam, Aftab, Khan, Suffian N., Smirnov, A. V., Nicholson, D. M., & Johnson, Duane D. Green's function multiple-scattering theory with a truncated basis set: An augmented-KKR formalism. United States. doi:10.1103/PhysRevB.90.205102.
```

```
Alam, Aftab, Khan, Suffian N., Smirnov, A. V., Nicholson, D. M., and Johnson, Duane D. Tue .
"Green's function multiple-scattering theory with a truncated basis set: An augmented-KKR formalism". United States. doi:10.1103/PhysRevB.90.205102. https://www.osti.gov/servlets/purl/1286786.
```

```
@article{osti_1286786,
```

title = {Green's function multiple-scattering theory with a truncated basis set: An augmented-KKR formalism},

author = {Alam, Aftab and Khan, Suffian N. and Smirnov, A. V. and Nicholson, D. M. and Johnson, Duane D.},

abstractNote = {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 Lmax = (l,m)max, while scattering matrices, which determine spectral properties, are truncated at Ltr = (l,m)tr where phase shifts δl>ltr are negligible. Historically, Lmax is set equal to Ltr, which is correct for large enough Lmax but not computationally expedient; a better procedure retains higher-order (free-electron and single-site) contributions for Lmax > Ltr with δl>ltr set to zero [Zhang and Butler, Phys. Rev. B 46, 7433]. We present a numerically ecient and accurate augmented-KKR Green's function formalism that solves the KKR equations by exact matrix inversion [R3 process with rank N(ltr + 1)2] and includes higher-L contributions via linear algebra [R2 process with rank N(lmax +1)2]. Augmented-KKR approach yields properly normalized wave-functions, numerically cheaper basis-set convergence, and a total charge density and electron count that agrees with Lloyd's formula. We apply our formalism to fcc Cu, bcc Fe and L10 CoPt, and present the numerical results for accuracy and for the convergence of the total energies, Fermi energies, and magnetic moments versus Lmax for a given Ltr.},

doi = {10.1103/PhysRevB.90.205102},

journal = {Physical Review. B, Condensed Matter and Materials Physics},

number = 20,

volume = 90,

place = {United States},

year = {2014},

month = {11}

}

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Works referenced in this record:

##
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- Monkhorst, Hendrik J.; Pack, James D.
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