GTP gives incorrect subgroups for Oh


I am using GTPack v1.3 on Mathematica 12.1, and obtained an error when I tried to run the CrystalFieldSplitting routine going from Oh to D3d. I get an error that D3d is not a subgroup of Oh, when in fact it truly is a subgroup (see here).

This is a very basic operation, so am I missing something here? Or is this an error in GTP?

Answered question

You are correct, D3d is a subgroup of Oh. However, keep in mind that a specific representation of the group depends on the chosen coordinate system. You install Oh and D3d using GTInstallGroup. This command installs the groups taking the z-axis as the principle axis. In that form Oh, does not have a three-fold rotation about the z-axis, but D3d. You would need to generate D3d for a threefold rotation axis in correspondence to Oh, e.g., the alpha-axis. The module you need is GTGroupFromGenerators. See an example below:

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Johan Liebert

Ah, I see!
Is there a way to do this without having to look up and enter the symmetry generators by hand each time it occurs?

Matthias Geilhufe

Unfortunately not yet. Right now I don’t see a good general way of implementing this. A subgroup can occur in multiple realizations within a group (e.g. Oh has 4 three-fold rotation axes). Any ideas?

Johan Liebert

I noticed the same issue occurs with D4h and D2h, which should both have the z-axis as the primary axis. Is the convention for z still different between the two in gtpack?

Perhaps this problem is impossible to solve, you really have to do things by hand each time

Matthias Geilhufe

Good point. The implementation seems to be inconsistent here, D2h is installed with the x-axis as principle axis. I will consider this for the next GTPack update. For now, you would need to generate the corresponding D2h with e.g. {C2z, IEe, C2x}.