Two-center Slater-Koster integrals

Physical Review B - Condensed Matter and Materials Physics

Volumn 58, Issue 8, 1998, Pages 4293-4303

  McMahan, A ^a  

^a LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33645116103     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.58.4293     Document Type: Article

References (14)

1. J. C. Slater and G. F. Koster, Phys. Rev. 94, 1498 (1954).
2. L. Colombo, in Annual Reviews of Computational Physics IV, edited by D. Stauffer (World Scientific, Singapore, 1996), p. 147.
3. D. A. Papaconstantopoulos, Handbook of the Band Structure of Elemental Solids (Plenum, New York, 1986).
4. W. A. Harrison, Electronic Structure and the Properties of Solids (Dover, New York, 1989), p. 481.
5. K. Lendi, Phys. Rev. B 9, 2433 (1974).
6. Phys. Rev. BK. Lendi10, 1768 (1974). Takegahara, Aoki, and Yanase (Ref. 7) note that the coefficient of (Formula presented) in (Formula presented) should be (Formula presented). The coefficient of (Formula presented) in (Formula presented) should also be (Formula presented).
7. R. R. Sharma, Phys. Rev. B 19, 2813 (1979).
8. K. Takegahara, Y. Aoki, and A. Yanase, J. Phys. C 13, 583 (1980).
9. R. R. Sharma, Phys. Rev. B 21, 2647 (1980).
10. J. Kollár and B. Ujfalussy, J. Comput. Phys. 110, 187 (1994). The exponent of (Formula presented) in Eq. (7) should be (Formula presented), as may be seen by comparison to Eq. (21) of Ref. 6, where Sharma’s (Formula presented) is Kollár and Ujfalussy’s (Formula presented). The last equation in Eq. (13) should also have a different sign, (Formula presented) although (Formula presented) and (Formula presented) are correct as shown or implied. Note that the relation between (Formula presented) and (Formula presented) is the same as between (Formula presented) and (Formula presented), where the bar or its absence indicates use of the real, (Formula presented) or original, (Formula presented) spherical harmonics, respectively. This follows, since (Formula presented) [Eq. (12)] and, for the non-negative (Formula presented) case of interest, (Formula presented) [below Eq. (9)], have formally identical two center expansions.
11. A. K. McMahan and J. E. Klepeis, Phys. Rev. B 56, 12 250 (1997).
12. A. K. McMahan and J. E. Klepeis, in Tight-Binding Approach to Computational Materials Science, edited by P. E. A. Turchi, A. Gonis, and L. Colombo (Materials Research Society, Warrendale, PA, 1998), p. 199.
13. S. Wolfram, Mathematica (Addison-Wesley, Reading, MA, 1988).
14. J. C. Duthie and D. G. Pettifor, Phys. Rev. Lett. 38, 564 (1977).