Faculty for Chemistry and Pharmacy - Group of Prof. Zipse

The Ci Point Group

This point group contains only two symmetry operations:

E the identity operation
i inversion through a center of symmetry

A simple example for a Ci symmetric molecule is 1,2-dichloro-1,2-difluoroethane (C2H2Cl2F2) in its staggered conformation displaying an anti-conformation of chloro and fluoro substituents. Here the HF/6-31G(d) optimized structure:

#P HF/6-31G(d) opt=(Z-Matrix,tight)

HF/6-31G(d) opt Ci 1,2-dichloro-1,2-difluoroethane

0 1
X2  1  1.0
C3  1  r3  2  90.0
C4  1  r3  2  90.0  3  180.0
Cl5  3  r5  1  a5  2  0.0
Cl6  4  r5  1  a5  2  180.0
F7  3  r7  5  a7  4  d7
F8  4  r7  6  a7  3  -d7
H9  3  r9  5  a9  7  d9
H10  4  r9  6  a9  8  -d9


In this case the symmetry of the system is reflected in the Z-Matrix through positioning of dummy atom X1 at the center of inversion (also the origin of the coordinate system), and the use of identical variables for the positioning of identical pairs of atoms. This reduces the number of independent structural variables from 18 (for an asymmetric, non-linear molecule containing eight centers) to 9.

Molecular orbitals as well as harmonic vibrations (if calculated) are labeled according to their symmetry properties as belonging to one of the two irreducible representations (Ag and Au) of the Ci point group. Those properties belonging to irreducible representation Ag are symmetric to both the identity operation E as well as reflection through the center of inversion. Those properties belonging to irreducible representation Au are symmetric with respect to the identity operation E but antisymmetric with respect to reflection through the center of inversion.