International
Tables for
Crystallography
Volume D
Physical properties of crystals
Edited by A. Authier

© International Union of Crystallography 2006
International Tables for Crystallography (2006). Vol. D. ch. 2.2, p. 299

Section 2.2.9.2. The choice of basis sets and wavefunctions

K. Schwarza*

a Institut für Materialchemie, Technische Universität Wien, Getreidemarkt 9/165-TC, A-1060 Vienna, Austria
Correspondence e-mail: kschwarz@theochem.tuwein.ac.at

2.2.9.2. The choice of basis sets and wavefunctions

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Most calculations of the electronic structure in solids (Pisani, 1996[link]; Singh, 1994[link]; Altmann, 1994[link]) use a linear combination of basis functions in one form or another but differ in the basis sets. Some use a linear combination of atomic orbitals (LCAO) where the AOs are given as Gaussian- or Slater-type orbitals (GTOs or STOs); others use plane-wave (PW) basis sets with or without augmentations; and still others make use of muffin-tin orbitals (MTOs) as in LMTO (linear combination of MTOs; Skriver, 1984[link]) or ASW (augmented spherical wave; Williams et al., 1979[link]). In the former cases, the basis functions are given in analytic form, but in the latter the radial wavefunctions are obtained numerically by integrating the radial Schrödinger equation (Singh, 1994[link]) (see Section 2.2.11[link]).

Closely related to the choice of basis sets is the explicit form of the wavefunctions, which can be well represented by them, whether they are nodeless pseudo-wavefunctions or all-electron wavefunctions including the complete radial nodal structure and a proper description close to the nucleus.

References

First citation Altmann, S. L. (1994). Band theory of solids: An introduction from the view of symmetry. Oxford: Clarendon Press.Google Scholar
 First citation Pisani, C. (1996). Quantum-mechanical ab-initio calculation of properties of crystalline materials. Lecture notes in chemistry, 67, 1–327. Berlin, Heidelberg, New York: Springer-Verlag.Google Scholar
 First citation Singh, D. J. (1994). Plane waves, pseudopotentials and the LAPW method. Boston, Dordrecht, London: Kluwer Academic Publishers.Google Scholar
 First citation Skriver, H. L. (1984). The LMTO method. Springer series in solid-state sciences, Vol. 41. Berlin, Heidelberg, New York, Tokyo: Springer.Google Scholar
 First citation Williams, A. R., Kübler, J. & Gelatt, C. D. Jr (1979). Cohesive properties of metallic compounds: Augmented-spherical-wave calculations. Phys. Rev. B, 19, 6094–6118.Google Scholar








































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