Below are examples of the use of the SYMMETRY directive in
the compound GEOMETRY directive (Section 6).
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.
The
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
The z axis is the
axis and the
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
Although acetylene has symmetry
the subgroup
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
axes are the x, y, and z axes. The
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
plane.
geometry units au
symmetry group d2h
C 0.000000000 0.000000000 -1.115108538
H 0.000000000 0.000000000 -3.106737425
end
The
axes are the x, y, and z axes. The
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
plane.
geometry units angstroms
C 0 0 0.659250
H 0 0.916366 1.224352
symmetry d2h
end
For ease of use, the primary
axis should be the x=y=z axis.
The 3
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
One of the
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
The
and
rotation axis is the z axis. The reflection plane
for the
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
The
axis is the z axis. The
plane is the xy plane. One of
the perpendicular
axes is the x=y axis. One of the
planes is the plane containing the x=y axis and the z axis. (The
other axes and planes are generated by the
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
The
axis is the z axis. The point of inversion is the origin. One of
the perpendicular
axes is the x=y axis. One of the
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
The
axis is the z axis. One of the
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
The
axis is the z axis. The point of inversion is the origin. One
of the 6 perpendicular
axes is the x=y axis. (-x=y works as a
axis.) The
plane is the xy plane. The
planes contain the
axis and the z axis. The
planes
contain the
axis and the z axis.
geometry units au
C 1.855 1.855 0
H 3.289 3.289 0
symmetry D6h
end
The
axis is the z axis. The
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
The
axis is the z axis. The center of inversion is the origin.
One of the perpendicular
axes is the x axis. One of the
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
The
axis is the z axis. The
planes are the yz and the xz
planes. The
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
The
axis is the z axis. The origin is the inversion center.
The
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
The
axis is the z axis (z is also the
axis). The x and y axes
are the perpendicular
s. The
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
The
axis is the z axis (z is also the
axis). The y axis is one
of the perpendicular
axes. The
plane is the xy plane and
one of the
planes is the yz plane.
charge -1
geometry units angstroms
symmetry d5h
c 0 1.1853 0
h 0 2.2654 0
end
The
axis is the z axis (z is also the
axis).
The
axes are the x and y axes and the
axes are the x=y axis
and the x=-y axis. The inversion center is the origin. The
plane is the xy plane. The
planes are the xz and yz planes and
the
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