References 167
(a) Show that the normalisation condition (6.47) can be rewritten as
〈Rl|H−E|R ̇l〉=1.
(b) Use this result, together with the fact thatRlis an eigenfunction ofHinside the
muffin tin with eigenvalueE, and partial differentiation, to deriveEq. (6.50).References
[1] N. W. Ashcroft and N. D. Mermin,Solid State Physics. New York, Holt, Reinhart and Winston,
1976.
[2] C. Kittel,Introduction to Solid State Physics, 6th edn. New York, John Wiley, 1973.
[3] R. M. Martin,Electronic Structure. Cambridge, Cambridge University Press, 2004.
[4] J. M. Thijssen and J. E. Inglesfield, ‘Embedding muffin tins into a finite difference grid,’
Europhys. Lett., 27 (1994), 65–70.
[5] S. Baroni and P. Giannozzi, ‘Towards very large-scale electronic structure calculations,’
Europhys. Lett., 17 (1992), 547–52.
[6] L.-W. Wang and A. Zunger, ‘Electronic-structure pseudopotential calculations of large
(approximate-to-1000 atoms) Si quantum dots,’J. Phys. Chem., 98 (1994), 2158–65.
[7] T. L. Beck, ‘Real-space mesh techniques in density-functional theory,’Rev. Mod. Phys., 72
(2000), 1041–80.
[8] S. Reich, J. Maultzsch, C. Thomsen, and P. Ordéjon, ‘Tight-binding description of graphene,’
Phys. Rev. B, 66 (2002), 035412.
[9] J. C. Slater and G. F. Koster, ‘Simplified LCAO method for the periodic potential problem,’Phys.
Rev., 94 (1954), 1498–524.
[10] V. Heine, ‘The pseudopotential concept,’ inSolid State Physics(F. Seitz and D. Turnbull, eds.),
vol. 24. New York, Academic Press, 1970, p. 1.
[11] J. C. Slater, ‘Wave functions in a periodic potential,’Phys. Rev., 51 (1937), 846–51.
[12] J. C. Slater, ‘An augmented plane wave method for the periodic potential problem,’Phys. Rev.,
92 (1953), 603–8.
[13] A. Messiah,Quantum Mechanics, vols. 1 and 2. Amsterdam, North-Holland, 1961.
[14] L. F. Mattheis, J. H. Wood, and A. C. Switendick, ‘A procedure for calculating electronic energy
bands using symmetrised augmented planes,’ inMethods in Computational Physics, vol. 8.
New York, Academic Press, 1968, pp. 63–147.
[15] T. Loucks,Augmented Plane Wave Method. New York, Benjamin, 1967.
[16] J. Callaway,Quantum Theory of the Solid State. 2nd edn. San Diego, Academic Press, 1991.
[17] O. K. Andersen, ‘Linear methods in band theory,’Phys. Rev. B, 12 (1975), 3060–83.
[18] D. D. Koelling and G. O. Arbman, ‘Use of the energy derivative of the radial solution in an
augmented plane wave method: application to copper,’J. Phys. F, 5 (1975), 2041–54.
[19] N. W. Ashcroft and D. C. Lang, ‘Compressibility and binding energy of the simple metals,’Phys.
Rev., 155 (1967), 682–4.
[20] D. Brust, ‘The pseudopotential method and the single-particle electronic excitation spectra of
crystals,’Methods in Computational Physics, vol. 8. pp. 33–61, New York, Academic Press,
1968, pp. 33–61.
[21] W. E. Pickett, ‘Pseudopotential methods in condensed matter applications,’Comp. Phys. Rep.,
9 (1989), 115–97.
[22] J. R. Chelikowsky and M. L. Cohen, ‘Electronic structure of silicon,’Phys. Rev. B, 10 (1974),
5095–107.
[23] G. B. Bachelet, D. R. Hamann, and M. Schlüter, ‘Pseudopotentials that work,’Phys. Rev. B, 26
(1982), 4199–288.