Sometimes site symmetry can't be inferred

[kbarros]

In this example,

a = b = 4.05012  # angstroms
c = 6.75214
lat_vecs = lattice_vectors(a, b, c, 90, 90, 120)
Crystal(lat_vecs, [[0,0,0]], 164; types=["Fe"])

Sunny builds the correct crystal, but cannot infer the site symmetry. The output is:

Crystal
HM symbol 'P -3 m 1' (164)
Lattice params a=4.05, b=4.05, c=6.752, α=90°, β=90°, γ=120°
Cell volume 95.92
Type 'Fe':
   1. [0, 0, 0]

However, if we also include the iodine atoms, then

Crystal(lat_vecs, [[0,0,0], [1/3, 2/3, 1/4]], 164; types=["Fe", "I"])

correctly outputs:

Crystal
HM symbol 'P -3 m 1' (164)
Lattice params a=4.05, b=4.05, c=6.752, α=90°, β=90°, γ=120°
Cell volume 95.92
Type 'Fe', Wyckoff 1a (point group '-3m.'):
   1. [0, 0, 0]
Type 'I', Wyckoff 2d (point group '3m.'):
   2. [0.3333, 0.6667, 0.25]
   3. [0.6667, 0.3333, 0.75]

which indicates the point group of -3m. for Fe.

The latter works by asking Spglib to infer all symmetry information about the crystal cell. From what I can tell, Spglib has no functionality to report point group symmetry information for a position and a given Hall number. See, e.g., spglib/spglib#135.

[kbarros]

Another caution is that the Spglib documentation states this:

[Site symmetry symbols] are valid for the standard settings. For different settings and choices belonging to the same space group type, the same set of the symbols is returned.

Source. It's not clear to me whether this means that the returned symbols could be invalid for non-standard settings?

[kbarros]

The same problem arose in a surprising way for Na4Ir3O8 (the iridium are arranged in a hyperkagome here)

a = 8.981
latvecs = lattice_vectors(a, a, a, 90, 90, 90)

x = 0.141
p = [0.125, x, x+1/4]
cryst = Crystal(latvecs, [p], 213) # Wyckoff 12d, point group ..2
@assert !isnothing(cryst.sitesyms)

x = 0
p = [0.125, x, x+1/4]
cryst = Crystal(latvecs, [p], 213) # Site symmetry is the same, but can't be inferred
@assert isnothing(cryst.sitesyms)

In the special case of x = 0, it appears that spglib needs more crystallographic information to infer the spacegroup symmetry 213, and our "hack" breaks.

[kavanase]

Just noting I mentioned the symmetry/Wyckoff analysis functions in doped which could possibly be used for this goal in spglib/spglib#135

[kbarros]

This looks great, thanks for sharing! I wonder if the logic could be ported into Sunny/Julia without too much trouble.

[kbarros]

If the chemical cell is known to be "conventional" for the given space group (in the sense of the Bilbao server), then it is possible to look up the data from tables, e.g., as available from the wyckoffs function of Crystalline.jl: https://thchr.github.io/Crystalline.jl/dev/api/#Crystalline.wyckoffs-Union{Tuple{Integer},%20Tuple{D},%20Tuple{Integer,%20Val{D}}}%20where%20D