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. 301

Section 2.2.11.1. LCAO (linear combination of atomic orbitals)

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

2.2.11.1. LCAO (linear combination of atomic orbitals)

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For the description of crystalline wavefunctions (Bloch functions), one often starts with a simple concept of placing atomic orbitals (AOs) at each site in a crystal denoted by [|m\rangle], from which one forms Bloch sums in order to have proper translational symmetry: [\chi_{{\bf k}}({\bf r})=\textstyle\sum\limits_{m}\exp({i{\bf kT}_{{m}}})|m{\rangle}.\eqno(2.2.11.1)]Then Bloch functions can be constructed by taking a linear combination of such Bloch sums, where the linear-combination coefficients are determined by the variational principle in which a secular equation must be solved. The LCAO can be used in combination with both the Hartree–Fock method and DFT.








































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