C2nv

C2nv is a designation that appears in discussions of molecular symmetry and group theory, belonging to the broader Cnv family. In this family, a molecule or object has a principal rotation axis of order n (Cn) and n vertical mirror planes that contain that axis. The value of n therefore encodes both the rotational symmetry and the number of vertical reflection planes. In standard references, the family is denoted Cnv, with specific members such as C2v, C3v, C4v, and so on.

In a symmetry-theoretic sense, Cnv groups are isomorphic to the dihedral group Dn. They consist of n rotations around the principal axis (E, Cn, Cn^2, ..., Cn^(n-1)) and n reflections (sigma_v, Cn sigma_v, ..., Cn^(n-1) sigma_v). The total number of symmetry operations is 2n. This structure underpins many applications in spectroscopy and vibrational analysis, where the group determines selection rules, degeneracies, and the character of infrared or Raman active modes.

The notation C2nv is not widely used in standard literature. When encountered, it is typically a nonstandard or context-specific variant, or a misprint for Cnv with n = 2, i.e., C2v. The practical cases most often discussed are Cnv with n = 2, 3, 4, etc., each corresponding to familiar point groups observed in molecules with a polar axis and vertical mirror planes.

See also: Cnv, Dihedral group, Point group, Molecular symmetry.