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 C_2h 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.

last changes: 25.10.2004, HZ
questions & comments to: zipse@cup.uni-muenchen.de