Basis sets-Gaussian orbital versus plane waves

Basis sets-Gaussian orbital versus plane waves 

As described earlier, electronic states of atoms are dispersed in energy bands when condensed into a crystalline solid phase. The descriptive model chosen allows a qualitative understanding of the origins of bands, but neglects many details such as the effects of atomic periodicity and crystal symmetry. Quantitative treatment of an allowed electronic state in a solid ( /) is based on Bloch s theorem which states that /(r) = e M(r) where r is a location in the unit cell, k is the wave vector, and (r) renresents a periodic electrostatic potential (see Ashcroft and Mermin 1976). The term 

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