[berg1029]

Why would trans-1,2-dichloroethylene be C2h while cis-1,2-dichloroethylene would be C2v?  Would they both not have a sigma h plane of reflection?  In other words, why does trans-1,2-dichloroethylene not have a sigma h plane of reflection?  Is there a good way to think about this that I am just missing?

[Yggdrasil]

The principle axes of the two compounds are different, so the plane in which all the carbon and chlorine atoms lie is perpendicular to the principle axis in one case and parallel to it in the other.

[semper erectus]

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.


This point group contains four symmetry operations:

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

[alkufi]

cis form is like hydrogen peroxide

[sjb]

cis form is like hydrogen peroxide

Maybe 1,3-dichloro-1,3-propadiene is like hydrogen peroxide, yes, but not cis-1,2-dichloroethylene. At least not isolated molecules. The time averaged structure may be more C2v (like water, rather), but at any given time it's more like a the spine of an half-open book, with the bottom edge of one page, and the top of the facing one as your O-H bonds

[Rudi]

but at any given time it's more like a the spine of an half-open book, with the bottom edge of one page, and the top of the facing one as your O-H bonds

True.. H2O2 does not exhibit C2v symmetry but C2 symmetry.