Basis Sets and Boundary Conditions

For practical implementations it is necessary to represent the molecular electronic wave functions as a linear combination of some convenient set of basis functions. In principle any choice of basis set is permissible although the basis set must span any electronic configuration of the molecule. This implies that the basis must form a complete set. 

Bloch s theorem states that in a periodic solid each electronic wave function can be expressed as the product of a wave-like component (with wave vector k) and a cell-periodic component/ (r)  

The KS equation (Eq. 23) when expressed in terms of a plane-wave basis set takes a very simple form  

There are several advantages associated with the plane wave approach. For example  

The minimisation problem can be distributed over the nodes of a parallel computer, thereby allowing the method to be applied to very large molecules. 

---