Glossary
A short reference for the symmetry and group-theory terms used throughout these docs. Many of these terms also appear with a dotted underline elsewhere on the site — hover over them for a one-line reminder.
Point group
The complete set of symmetry operations that leave a molecule's geometry
unchanged. Every molecule belongs to exactly one point group, written as a
Schoenflies symbol such as C₂ᵥ or D₆ₕ. This is the
central quantity pyrrhotite computes.
Symmetry operation
A geometric transformation — a rotation, reflection, inversion, or improper rotation — that maps a molecule onto an indistinguishable copy of itself.
Symmetry element
The geometric entity a symmetry operation acts around: a rotation axis, a mirror plane, or the inversion centre.
Proper rotation (Cₙ)
A rotation by 360°/n about an axis that leaves the molecule unchanged. The largest n is the principal axis and sets the molecule's orientation.
Reflection (σ)
A mirror operation through a plane. Labelled σₕ (horizontal, perpendicular to the principal axis), σᵥ (vertical, containing it), or σd (dihedral, a vertical plane bisecting two C₂ axes).
Inversion (i)
The operation that sends every atom at position r to −r through a central point (the inversion centre).
Improper rotation (Sₙ)
A rotation by 360°/n followed by a reflection through the plane perpendicular to that axis — a single combined operation.
Schoenflies symbol
The notation pyrrhotite uses for point groups (C₂ᵥ, D₆ₕ, T_d, O_h, …), common
in chemistry and spectroscopy. The alternative
Hermann–Mauguin notation is more common in
crystallography.
Hermann–Mauguin notation
The crystallographic "international" notation for symmetry groups (e.g. mmm,
4/mmm). pyrrhotite does not use it — it works entirely in Schoenflies
symbols.
Character table
The compact table that summarises a point group: its
irreducible representations, the characters
(traces) of each operation class, and the basis functions that transform under
each irrep. pyrrhotite can generate one for any of the 18 Schoenflies classes.
Irrep (irreducible representation)
A fundamental "symmetry species" of a point group — one row of the character table. Each molecular orbital, vibration, or rotation belongs to exactly one irrep, which is what makes irreps useful for predicting IR/Raman activity and orbital mixing.
Character
The trace of the transformation matrix representing a symmetry operation in a given irrep — the numbers that fill the body of a character table.
Basis function
A coordinate (x, y, z), rotation (Rx, Ry, Rz), or quadratic term (x², xy, …) listed against the irrep it transforms as — used to read off selection rules and orbital symmetries.
Conjugacy class
A set of symmetry operations that are equivalent under the group's own symmetry (e.g. the two rotations C₃ and C₃² of C₃ᵥ form one class "2C₃"). Character tables have one column per class, not one per operation.
Rotor class
A classification of a molecule by the degeneracy of its
principal moments of inertia — Linear,
Spherical Top, Prolate Symmetric Top, Oblate Symmetric Top, or Asymmetric
Top. pyrrhotite determines this first to narrow the symmetry search.
Principal moments of inertia
The three eigenvalues of the molecule's inertia tensor (Iₐ ≤ I_b ≤ I_c). Their pattern of equalities determines the rotor class.
Principal axes
The eigenvectors of the inertia tensor — the natural body-fixed axis frame in which the inertia tensor is diagonal.
.xyz file
A plain-text molecular geometry format: an atom count, a comment line, then one
element x y z line per atom (coordinates in Ångströms). The standard input to
pyrrhotite.
Next steps
-
Algorithm & Supported Groups
See these terms in action — how detection works and which groups are supported.
-
User Guide
The full Python API, with each concept put to use.
-
API Reference
The exact signatures, parameters, and return types for every public function and class.