Relax requirement that tricilinic angles must be all acute or all obtuse

[kbarros]

Hi @thchr, thank you for the very nice package. I'm working to integrate it with our Sunny software for magnetic simulations.

There is a check here that triclinic angles must be all-acute or all-obtuse:

Brillouin.jl/src/bravais-branches.jl

Lines 129 to 147 in 7defcdc

	elseif bt == "aP"
	# SeeK-path only provides paths for all-acute or all-obtuse reciprocal aP cells
	# (more precisely, SeeK-path will transform to this setting automatically) so check:
	# get reciprocal basis inter-angles angles
	Gs = (Rs[2]×Rs[3], Rs[3]×Rs[1], Rs[1]×Rs[2]) # NB: "scale" prefactor omitted here
	aᴳ, bᴳ, cᴳ = basisnorms(Gs)
	cosαᴳ = dot(Gs[2], Gs[3]) / (bᴳ * cᴳ)
	cosβᴳ = dot(Gs[1], Gs[3]) / (aᴳ * cᴳ)
	cosγᴳ = dot(Gs[1], Gs[2]) / (aᴳ * bᴳ)
	# detect whether all-obtuse or all-acute reciprocal basis
	if cosαᴳ ≤ 0 && cosβᴳ ≤ 0 && cosγᴳ ≤ 0 # all-obtuse
	return :aP2
	elseif cosαᴳ ≥ 0 && cosβᴳ ≥ 0 && cosγᴳ ≥ 0 # all-acute
	return :aP3
	else
	_throw_triclinic_angles(Rs)
	end

You commented that SeeK-path automatically transforms to this setting. Is this something that Brillouin.jl might also automate? Otherwise, is there a suggestion for how to implement this in one's own code?

[thchr]

Yeah, transforming to this is something I've wanted to implement for a while but haven't yet. I think the main steps are the following: 1. transform to Niggli-reduced cell and 2. transform from Niggli-reduced cell to a standard/conventional cell. I recently added a method to do step 1 (Niggli-reduced cell in Bravais.jl), but haven't gotten around to doing step 2. I think it's probably described in ITA how to do it. Would love to add it to Bravais.jl one day; with that, it'd would be trivial to do this automatically in Brillouin.jl as well.

In the meanwhile, it should be possible to do this via Spglib.jl: see https://thchr.github.io/Brillouin.jl/stable/kpaths/#Treating-unit-cells-in-non-standard-settings.

[kbarros]

Ah, this helps a lot. We already depend on Spglib, but I didn't realize it could standardize the triclinic lattice like this. Thanks!