Page 148 - Strategies and Applications in Quantum Chemistry From Molecular Astrophysics to Molecular Engineer

QUASICRYSTALS AND MOMENTUM SPACE 133
Substituting (III. 19) in (III. 18) and using the special properties of (III. 14) we can then
write the Fourier component of the density as

A more condensed expression is obtained using (III. 14) and (III.17b):

Here is the Fourier component of the square of the absolute value of the Bloch
orbital which can be written as a product of a plane wave and a function
having the periodicity of the lattice:

Using (III. 16) we can also write this Fourier component in terms of the momentum space
orbitals as

If the density is invariant under the space group operation {R|m} we have with (III.4) and
(III.17b),