Glossary
- Block
The dense matrix \(X_{ij}^{\bm L}\) of an operator between the orbitals of atom \(i\) and atom \(j\) translated by \(\bm L\).
- Copy
One instance of an irrep inside a feature;
16x1ohas sixteen copies of the vector irrep. Invariant scalings act on whole copies.- Coupled irreps
The irreps of the packed edge vector covering every species pair,
${layout.coupled_irreps}; the readout target of recipes.- Directed periodic edge
The triple \((i,j,\bm L)\). Both \((i,j,\bm L)\) and \((j,i,-\bm L)\) are stored and predicted.
- Edge class
Onsite (\(i=j,\bm L=0\)), shifted self (\(i=j,\bm L\ne0\)) or offsite (\(i\ne j\)).
- Envelope
An invariant radial factor \(E_p(r)\) multiplying predicted blocks of species pair \(p\).
- Hermitian projection
\(X_{ij}^{\bm L}\leftarrow\tfrac12(X_{ij}^{\bm L}+(X_{ji}^{-\bm L})^\dagger)\).
- Irrep
Irreducible representation \((\ell,p)\) of O(3), written
"2e","1o"…- Mapper
BlockIrrepMapper, the Clebsch–Gordan change of basis between blocks and irrep vectors for every species pair.- Observable guidance
Training terms on quantities derived from predicted operators: \(\Tr(DH)\), \(\Tr(DS)\) and band eigenvalues.
- Pipeline
The ordered, typed list of stages of an E3GNN (
FeaturePipeline).- Recipe
A YAML configuration with an explicit
pipelinesection.- Slot
A named feature in a pipeline; written once by one stage.
- Snapshot
One geometry with its H, S, D operators and metadata (
Snapshot).- Stage
One transformation in a pipeline:
id,transform,inputs,outputs,options.- Support
The index set of an edge-like feature (
output,message, …). Features on different supports cannot be combined.