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
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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.
In: Physical Review B, Vol. 50, No. 19, 1994, p. 13994-14000.Research output: Contribution to journal › Article
}
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.
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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 -