Adding H2 geometry optimzation example

[gkemlin]

No description provided.

[gkemlin]

I could have added the optimization geometry on H2O, but it takes way too much time even on my computer, so I don't think it might be a good idea to put it in the examples as it will take too long to compute on the cloud.

[antoine-levitt]

Yes, having examples that run quickly is important. What is taking so long here? Is it forces?

[gkemlin]

Yes, that's it: computing forces along with optimization in R^9.

[gkemlin]

The test on Travis to generate doc is failing with the following error (which I don't get on my computer...) :

┌ Error: error when executing notebook based on input file: `~/build/JuliaMolSim/DFTK.jl/examples/geometry_optimization.jl`
└ @ Literate ~/.julia/packages/Literate/5an7K/src/Literate.jl:594

ERROR: LoadError: LoadError: Cannot map the atom at position [-0.6234998046636102, 4.387574846033396e-6, -1.0048786234097246e-5] to another atom of the same element under the symmetry operation (Stilde, τtilde):
([1 0 0; 0 0 -1; 0 1 0], Rational{Int64}[0//1, 1//1, 40903//40904])

Do you know where it might come from ? Maybe we should not use symmetries ?

[antoine-levitt]

Oh that's a fun error. I'm guessing our check uses tolerances different from the one spglib uses?

[mfherbst]

Thanks! A few remarks.

[mfherbst]

Ah yes the issue is that spglib uses a tolerance of 1e-5 to find symmetries, but than we check in DFTK whether these symmetries are correct (with probably a different algorithm). If you add some leg freedom for numerical errors in https://github.com/JuliaMolSim/DFTK.jl/blob/master/src/external/spglib.jl#L90 (like a factor 2 or 5 say) than this error should not show up.