The C_2h Point Group

This point group contains four symmetry operations:

E the identity operation
C₂ a twofold symmetry axis
i a center of inversion
σ_h a horizontal mirror plane

A simple example for a C_2h symmetric molecule is trans -1,2-dichloroethylene, here in its HF/6-31G(d) optimized structure:

#P HF/6-31G(d) opt=(Z-Matrix,tight) test1 HF/6-31G(d) opt trans-1,2-dichloroethylene 0 1 Cl1 C2 1 r2 C3 2 r3 1 a3 Cl4 3 r2 2 a3 1 180.0 H5 3 r5 2 a5 1 0.0 H6 2 r5 3 a5 4 0.0 r2=1.729226 r3=1.310646 r5=1.070566 a3=121.7652 a5=123.8226

In this case the symmetry of the system is reflected in the Z-Matrix through the use of identical variable names for the C-Cl and C-H bond distances and the Cl-C-C and H-C-C bond angles. All atoms are also constrained to the horizontal mirror plane of the C2h point group. This reduces the number of independent structural variables from 12 (for an asymmetric, non-linear molecule containing 6 centers) to 5.

Molecular orbitals as well as harmonic vibrations (if calculated) are labeled according to their symmetry properties as belonging to one of the four irreducible representations (A_g, B_g, A_u, and B_u) of the C_2h point group.