Abstract
The relativistic augmented plane wave (RAPW) method1 had been used extensively to perform energy band calculations for the heavier (higher atomic number) materials. Except for the use of the relativistic formalism, it is precisely the same method as the non-relativistic APW method2 which has done so well in the region of lower atomic numbers. Both are energy-variational based techniques3,4 using basis functions constructed by joining atomic-like functions near the nuclei onto plane waves in the outer regions. However, a new feature of an additional spin variable arises in the RAPW method because the spin-orbit coupling term has been included. This makes the RAPW method considerably more time consuming to apply because it doubles the size of the basis set in addition to making the matrix elements slightly more complicated.
Supported by the Air Force Office of Scientific Research.
On leave from FOA, Stockholm.
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References
T. Loucks, Augmented Plane Wave Method, W. A. Benjamin, New York (1967).
J. C. Slater, Phys. Rev. 51, 846 (1937).
R. S. Leigh, Proc. Phys. Soc. (London) 69, 388 (1956); H. Schlosser and P. M. Marcus, Int. J. of Quantum Chem. 1, 567, 42, (1968)
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D. Koelling, “The relativistic APW Method and its Convergence in ℓ”, Quarterly Progress Report of the Solid State and Molecular Theory Group, MIT (unpublished) 68, 36 (1968). Also see ref. 6.
Some of the details are given in the refs. 6–7 and the use of the spherical harmonic sum rule is obvious. The rewriting of the spin-orbit term to actually look like a spin-orbit term by G.A.) will be presented in the forthcoming paper.
N. Parada, “Localized Defects in PbTe via a \(\overrightarrow K \cdot \overrightarrow \pi\) — APW Energy Band Calculation”, Tech. Rep. No. 8 of the Materials Theory Group, MIT (1968).
Our SRAPW tests indicate that there is still a bug in the construction of the RAPW matrix elements leading to small (.02 Ryd.) errors. Thus we can only discuss those features which are unaffected by these errors.
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© 1971 Plenum Press, New York
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Arbman, G., Koelling, D. (1971). An RAPW Expanded Basis Set. In: Marcus, P.M., Janak, J.F., Williams, A.R. (eds) Computational Methods in Band Theory. The IBM Research Symposia Series. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-1890-3_4
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DOI: https://doi.org/10.1007/978-1-4684-1890-3_4
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