Phonon example

[mfherbst]

Following up on #1039 I just wanted to test phonons on silicon. q = 0 I manage but I don't manage to do other q points (e.g. [0.25, 0.25, 0.25]). Here is what I did:

using DFTK

a = 10.26  # Silicon lattice constant in Bohr
lattice = a / 2 * [[0 1 1.];
                   [1 0 1.];
                   [1 1 0.]]
Si = ElementPsp(:Si, load_psp("hgh/lda/Si-q4"))
atoms     = [Si, Si]
positions = [ones(3)/8, -ones(3)/8]

model = model_DFT(lattice, atoms, positions; functionals=LDA())
basis = PlaneWaveBasis(model; Ecut=15, kgrid=[4, 4, 4])
scfres = self_consistent_field(basis, tol=1e-8)

phret_q0 = DFTK.phonon_modes(scfres; q=[0.25, 0.25, 0.25])
@show phret_q0.frequencies