4 Computational Details

4.1 Symmetry Properties of the Integrals

There are symmetries additional to the spatial symmetry that can be used to reduce the number of integrals to be computed and stored. For example, in the overlap matrix S(k), Eq. (6), the χp(r)χqμ(r)si192_e integrals are invariant with respect to any integer shift of the origin for r, so that

Spq(k)=μ=exp2πiμkχprχqrμzˆ=μ=exp2πiμkχpr+μzˆχqr.

si193_e

By setting μμsi194_e and taking into account ...

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