Add phonon example (#1046)

docs/make.jl

@@ -46,6 +46,7 @@ PAGES = [
     "Response and properties" => [
         "examples/polarizability.jl",
         "examples/forwarddiff.jl",
+        "examples/phonons.jl",
     ],
     "Ecosystem integration" => [
         # This concerns the discussion of interfaces, IO and integration

docs/src/features.md

@@ -28,7 +28,7 @@
     - Density-functional perturbation theory (DFPT)
     - Integration of DFPT with algorithmic differentiation,
       e.g. [Polarizability using automatic differentiation](@ref)
-    - Phonons *(preliminary implementation)*
+    - [Phonon computations](@ref) *(preliminary implementation)*
 
 * Unique features
     - Support for arbitrary floating point types, including `Float32` (single precision)

examples/phonons.jl

@@ -0,0 +1,24 @@
+# # Phonon computations
+#
+# This is a quick sketch how to run a simple phonon calculation using DFTK.
+# First we run an SCF calculation.
+
+using AtomsBuilder
+using DFTK
+using PseudoPotentialData
+
+pseudopotentials = PseudoFamily("cp2k.nc.sr.lda.v0_1.semicore.gth")
+model  = model_DFT(bulk(:Si); pseudopotentials, functionals=LDA())
+basis  = PlaneWaveBasis(model; Ecut=10, kgrid=[4, 4, 4])
+scfres = self_consistent_field(basis, tol=1e-8);
+nothing  # hide
+
+# Next we compute the phonon modes at the q-point `[1/4, 1/4, 1/4]`.
+
+scfres = DFTK.unfold_bz(scfres)
+phret_q0 = @time DFTK.phonon_modes(scfres; q=[0.25, 0.25, 0.25]);
+nothing  # hide
+
+# These are the final phonon frequencies:
+
+phret_q0.frequencies