ORCA labels orbitals in an abelian subgroup, so its MO diagrams never correlate #147

What happens

An ORCA calculation on methane, run with symmetry enabled, produces an MO diagram with no correlation at all. The diagram's own note says why:

The fragment orbitals and the calculation's labels do not span the same representation (2A + 2B1 + 2B2 + 2B3 reported, 2A1 + 6T2 from symmetry)

The orbitals are labelled 2A, 1B₁, 1B₂, 1B₃ — which are D2 irreps — while the heading reads Td.

Why

ORCA says so itself:

Point group                           .... Td
Symmetry-adapted orbitals             .... D2
   Irrep    A has    7 symmetry adapted basis functions (ofs=   0)
   Irrep   B1 has    5 symmetry adapted basis functions (ofs=   7)

ORCA only symmetry-adapts orbitals in abelian point groups. It detects the full group correctly and then works in the largest abelian subgroup — D2 for Td, and in general D2h or one of its subgroups.

So ORBSYM for any ORCA calculation carries labels from an abelian subgroup, not from the group ECCE detects on the structure. MoDiagramPanel builds its fragment columns in the structure's group, the two label sets cannot match, and correlation falls back to composition — which is not wired up (#132), so nothing is drawn.

This affects every ORCA calculation of a molecule whose point group is not already abelian. Water (C2v) is abelian and works; methane (Td), ammonia (C3v), benzene (D6h) and every coordination complex do not.

Not a regression, but newly visible

Until now ORCA jobs were generated with symmetry off by default, so they had no orbital labels at all and failed the same way for a simpler reason. Defaulting symmetry on means they now have labels — from a different group.

What a fix looks like

The diagram should be built in the group the calculation actually used, not the one the structure has, whenever the calculation's labels are irreps of an abelian subgroup of it. The machinery is largely present: MoFragments already has subgroupOf() and nameSubgroup(), added for splitting ethene across a subgroup, and MoDiagram::reconcile() already handles axis-convention disagreements within one group.

What is needed is the step before those: recognising that {A, B1, B2, B3} is D2, that D2 is a subgroup of Td, and rebuilding the fragment columns in D2 so the two sides speak the same language. A methane diagram in D2 is less informative than one in Td — the t₂ set splits into b₁+b₂+b₃ — but it is correct, and it is what the calculation computed.

Worth stating in the diagram when that happens, so nobody reads a D2 diagram as a Td one.

Reproducing

Any ORCA calculation of a non-abelian molecule with "Use symmetry" ticked. The point group and the adapted group are both printed near the top of the ORCA output, a few lines apart.