### Abstract

The search for electronic energy bands in full-potential Korringa-Kohn-Rostoker (KKR) band theory requires the evaluation of the scattering matrices at many different energies for a certain number of wave vectors. We develop Chebyshev-function approximations for the scattering matrices, which can save a factor of 2 to 3 in computing time for the case of silicon. Moreover, the Chebyshev coefficients of the scattering matrices can be used in a polynomial expansion of the KKR secular matrix, which transforms the search for the energy bands to an eigenvalue problem. In a test calculation for silicon it turns out that if one wants to reproduce energy bands to within 1 mRy one needs to include cubic terms in the polynomial expansions. Calculations with polynomial coefficients from a Chebyshev series expansion are found to give more precise energy eigenvalues than calculations where the polynomial coefficients were obtained from a Taylor series expansion without using any additional computing time.

Original language | English |
---|---|

Pages (from-to) | 13994-14000 |

Number of pages | 7 |

Journal | Physical Review B |

Volume | 50 |

Issue number | 19 |

DOIs | |

Publication status | Published - 1994 |

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### ASJC Scopus subject areas

- Condensed Matter Physics

### Cite this

*Physical Review B*,

*50*(19), 13994-14000. https://doi.org/10.1103/PhysRevB.50.13994

**Chebyshev expansions for the scattering matrices in full-potential Korringa-Kohn-Rostoker band-structure calculations.** / Bei Der Kellen, S.; Oh, Yoonsik; Badralexe, E.; Freeman, Arthur J.

Research output: Contribution to journal › Article

*Physical Review B*, vol. 50, no. 19, pp. 13994-14000. https://doi.org/10.1103/PhysRevB.50.13994

}

TY - JOUR

T1 - Chebyshev expansions for the scattering matrices in full-potential Korringa-Kohn-Rostoker band-structure calculations

AU - Bei Der Kellen, S.

AU - Oh, Yoonsik

AU - Badralexe, E.

AU - Freeman, Arthur J

PY - 1994

Y1 - 1994

N2 - The search for electronic energy bands in full-potential Korringa-Kohn-Rostoker (KKR) band theory requires the evaluation of the scattering matrices at many different energies for a certain number of wave vectors. We develop Chebyshev-function approximations for the scattering matrices, which can save a factor of 2 to 3 in computing time for the case of silicon. Moreover, the Chebyshev coefficients of the scattering matrices can be used in a polynomial expansion of the KKR secular matrix, which transforms the search for the energy bands to an eigenvalue problem. In a test calculation for silicon it turns out that if one wants to reproduce energy bands to within 1 mRy one needs to include cubic terms in the polynomial expansions. Calculations with polynomial coefficients from a Chebyshev series expansion are found to give more precise energy eigenvalues than calculations where the polynomial coefficients were obtained from a Taylor series expansion without using any additional computing time.

AB - The search for electronic energy bands in full-potential Korringa-Kohn-Rostoker (KKR) band theory requires the evaluation of the scattering matrices at many different energies for a certain number of wave vectors. We develop Chebyshev-function approximations for the scattering matrices, which can save a factor of 2 to 3 in computing time for the case of silicon. Moreover, the Chebyshev coefficients of the scattering matrices can be used in a polynomial expansion of the KKR secular matrix, which transforms the search for the energy bands to an eigenvalue problem. In a test calculation for silicon it turns out that if one wants to reproduce energy bands to within 1 mRy one needs to include cubic terms in the polynomial expansions. Calculations with polynomial coefficients from a Chebyshev series expansion are found to give more precise energy eigenvalues than calculations where the polynomial coefficients were obtained from a Taylor series expansion without using any additional computing time.

UR - http://www.scopus.com/inward/record.url?scp=26144445324&partnerID=8YFLogxK

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U2 - 10.1103/PhysRevB.50.13994

DO - 10.1103/PhysRevB.50.13994

M3 - Article

VL - 50

SP - 13994

EP - 14000

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 1098-0121

IS - 19

ER -