The D2h Point Group

This point group contains the following symmetry operations:

E    the identity operation
C2   a twofold principal symmetry axis
2 * C2   two twofold symmetry axes orthogonal to the principal axis
i     inversion through a center of symmetry
σh   a horizontal mirror plane intersecting the principal symmetry axis
2 * σv   two vertical mirror planes aligned with the principal symmetry axis

A simple example for a D2h symmetric molecule is ethylene (C2H4), here in its HF/6-31G(d) optimized structure:
#P RHF/6-31G(d) opt=(Z-Matrix,tight)

RHF/6-31G(d) opt min ethylene D2h sym.

0 1
X2  1  1.0
C3  2  r3  1  90.0
C4  2  r3  1  90.0 3  180.0
H5  3  r5  2  a5  1  -90.0
H6  3  r5  2  a5  1  90.0
H7  4  r5  2  a5  1  -90.0
H8  4  r5  2  a5  1  90.0



In this case the symmetry of the system is reflected in the Z-Matrix through the use of identical variable names for hydrogen atoms H5 - H8 and through constraining all atoms to the symmetry plane. This reduces the number of independent structural variables from 12 (for an asymmetric, non-linear molecule containing six centers) to 3 and thus accelerates geometry optimizations.

Molecular orbitals as well as harmonic vibrations (if calculated) are labeled according to their symmetry properties as belonging to one of the eight irreducible representations ( Ag, Au, B1g, B2g, B3g, B1u, B2u, B3u, ) of the D2h point group.

last changes: 08.06.2006, HZ
questions & comments to: