# Examples of geometries using symmetry
Below are examples of the use of the [SYMMETRY directive](SYMMETRY----Symmetry-Group-Input.md) in the compound
[GEOMETRY directive](Geometry.md). The *z* axis is
always the primary rotation axis. When in doubt about which axes and
planes are used for the group elements, the keyword `print` may be added
to the `SYMMETRY` directive to obtain this information.
## *Cs* methanol
The *σh* plane is the *xy* plane.
```
geometry units angstroms
C 0.11931097 -0.66334875 0.00000000
H 1.20599017 -0.87824237 0.00000000
H -0.32267592 -1.15740001 0.89812652
O -0.01716588 0.78143468 0.00000000
H -1.04379735 0.88169812 0.00000000
symmetry cs
end
```
## *C2v* water
The z axis is the *C2* axis and the *σv* may be either the *xz*
or the *yz* planes.
```
geometry units au
O 0.00000000 0.00000000 0.00000000
H 0.00000000 1.43042809 -1.10715266
symmetry group c2v
end
```
## *D2h* acetylene
Although acetylene has symmetry *D∞h* the subgroup *D2h*
includes all operations that interchange equivalent atoms which is what
determines how much speedup you gain from using symmetry in building a
Fock matrix.
The *C2* axes are the x, y, and z axes. The σ planes are the xy, xz
and yz planes. Generally, the unique atoms are placed to use the z as
the primary rotational axis and use the xz or yz planes as the σ plane.
```
geometry units au
symmetry group d2h
C 0.000000000 0.000000000 -1.115108538
H 0.000000000 0.000000000 -3.106737425
end
```
## *D2h* ethylene
The *C2* axes are the x, y, and z axes. The σ planes are the xy, xz
and yz planes. Generally, the unique atoms are placed to use the z as
the primary rotational axis and use the xz or yz planes as the σ plane.
```
geometry units angstroms
C 0 0 0.659250
H 0 0.916366 1.224352
symmetry d2h
end
```
## *Td* methane
For ease of use, the primary *C3* axis should be the x=y=z axis. The
3 *C2* axes are the x, y, and z.
```
geometry units au
c 0.0000000 0.0000000 0.0000000
h 1.1828637 1.1828637 1.1828637
symmetry group Td
end
```
## *Ih* buckminsterfullerene
One of the *C5* axes is the z axis and the point of inversion is the
origin.
```
geometry units angstroms # Bonds = 1.4445, 1.3945
symmetry group Ih
c -1.2287651 0.0 3.3143121
end
```
## *S4* porphyrin
The *S4* and *C2* rotation axis is the z axis. The reflection
plane for the *S4* operation is the xy plane.
```
geometry units angstroms
symmetry group s4
fe 0.000 0.000 0.000
h 2.242 6.496 -3.320
h 1.542 4.304 -2.811
c 1.947 6.284 -2.433
c 1.568 4.987 -2.084
h 2.252 8.213 -1.695
c 1.993 7.278 -1.458
h 5.474 -1.041 -1.143
c 1.234 4.676 -0.765
h 7.738 -1.714 -0.606
c 0.857 3.276 -0.417
h 1.380 -4.889 -0.413
c 1.875 2.341 -0.234
h 3.629 3.659 -0.234
c 0.493 -2.964 -0.229
c 1.551 -3.933 -0.221
c 5.678 -1.273 -0.198
c 1.656 6.974 -0.144
c 3.261 2.696 -0.100
n 1.702 0.990 -0.035
end
```
## *D3h* iron penta-carbonyl
The *C3* axis is the z axis. The *σh* plane is the xy plane.
One of the perpendicular *C2* axes is the x=y axis. One of the
*σv* planes is the plane containing the x=y axis and the z axis.
(The other axes and planes are generated by the *C3* operation.)
```
geometry units au
symmetry group d3h
fe 0.0 0.0 0.0
c 0.0 0.0 3.414358
o 0.0 0.0 5.591323
c 2.4417087 2.4417087 0.0
o 3.9810552 3.9810552 0.0
end
```
## *D3d* sodium crown ether
The *C3* axis is the z axis. The point of inversion is the origin.
One of the perpendicular *C2* axes is the x=y axis. One of the
*σd* planes is the plane containing the -x=y axis and the z
axis.
Note that the oxygen atom is rotated in the x-y plane 15 degrees away
from the y-axis so that it lies in a mirror plane. There is a total of
six atoms generated from the unique oxygen, in contrast to twelve from
each of the carbon and hydrogen atoms.
```
geometry units au
symmetry D3d
NA .0000000000 .0000000000 .0000000000
O 1.3384771885 4.9952647969 .1544089284
H 6.7342048019 -0.6723850379 2.6581562148
C 6.7599180056 -0.4844977035 .6136583870
H 8.6497577017 0.0709194071 .0345361934
end
```
## *C3v* ammonia
The *C3* axis is the z axis. One of the *σv* planes is the
plane containing the x=y axis and the z axis.
```
geometry units angstroms
N 0 0 -0.055
H 0.665 0.665 -0.481
symmetry c3v
end
```
## *D6h* benzene
The *C6* axis is the z axis. The point of inversion is the origin.
One of the 6 perpendicular *C2'* axes is the x=y axis. (-x=y works
as a *C2''* axis.) The *σh* plane is the xy plane. The
*σd* planes contain the *C2''* axis and the z axis. The
*σv* planes contain the *C2'* axis and the z axis.
```
geometry units au
C 1.855 1.855 0
H 3.289 3.289 0
symmetry D6h
end
```
## *C3h* H3BO3
The *C3* axis is the z axis. The *σh* plane is the xy plane.
```
geometry units au
b 0 0 0
o 2.27238285 1.19464491 0.00000000
h 2.10895420 2.97347707 0.00000000
symmetry C3h
end
```
## *D5d* ferrocene
The *C5* axis is the z axis. The center of inversion is the origin.
One of the perpendicular *C2* axes is the x axis. One of the
*σd* planes is the yz plane.
```
geometry units angstroms
symmetry d5d
fe 0 0 0
c 0 1.194 1.789
h 0 2.256 1.789
end
```
## *C4v* SF5Cl
The *C4* axis is the z axis. The *σv* planes are the yz and
the xz planes. The *σd* planes are: 1) the plane containing the
x=y axis and the z axis and 2) the plane containing the -x=y axis and
the z axis.
```
geometry units au
S 0.00000000 0.00000000 -0.14917600
Cl 0.00000000 0.00000000 4.03279700
F 3.13694200 0.00000000 -0.15321800
F 0.00000000 0.00000000 -3.27074500
symmetry C4v
end
```
## *C2h* trans-dichloroethylene
The *C2* axis is the z axis. The origin is the inversion center. The
*σh* plane is the xy plane.
```
geometry units angstroms
C 0.65051239 -0.08305064 0
Cl 1.75249381 1.30491767 0
H 1.14820954 -1.04789741 0
symmetry C2h
end
```
## *D2d* CH2CCH2
The *C2* axis is the z axis (z is also the *S4* axis). The x and y
axes are the perpendicular *C2's*. The *σd* planes are: 1)
the plane containing the x=y axis and the z axis and 2) the plane
containing the -x=y axis and the z axis.
```
geometry units angstroms
symmetry d2d
c 0 0 0
c 0 0 1.300
h 0.656 0.656 1.857
end
```
## *D5h* cyclopentadiene anion
The *C5* axis is the z axis (z is also the *S5* axis). The y axis
is one of the perpendicular *C2* axes. The *σh* plane is the
xy plane and one of the *σd* planes is the yz plane.
```
charge -1
geometry units angstroms
symmetry d5h
c 0 1.1853 0
h 0 2.2654 0
end
```
## *D4h* gold tetrachloride
The *C4* axis is the z axis (z is also the *S4* axis). The
*C2'* axes are the x and y axes and the *C2''* axes are the
x=y axis and the x=-y axis. The inversion center is the origin. The
*σh* plane is the xy plane. The *σv* planes are the xz
and yz planes and the *σd* planes are 1) the plane containing
the x=-y axis and the z axis and 2) the plane containing the x=y axis
and the z axis.
```
geometry units au
Au 0 0 0
Cl 0 4.033 0
symmetry D4h
end
```