 
 
 
 
 
 
 
  
 methanol
 methanol
 water
 water
 acetylene
 acetylene
 ethylene
 ethylene
 methane
 methane
 buckminsterfullerene
 buckminsterfullerene
 porphyrin
 porphyrin
 iron penta-carbonyl
 iron penta-carbonyl
 sodium crown ether
 sodium crown ether
 ammonia
 ammonia
 benzene
 benzene
 
  
 ferrocene
 ferrocene
 
  
 trans-dichloroethylene
 trans-dichloroethylene
 
  
 cyclopentadiene anion
 cyclopentadiene anion
 gold tetrachloride
 gold tetrachloride
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.
 methanol
 methanol
The  plane is the xy plane.
 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
 water
 water
The z axis is the  axis and the
 axis and the  may be either the xz or the
yz planes.
 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
 acetylene
 acetylene
Although acetylene has symmetry  the subgroup
 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.
 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
 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
 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.
 
plane.
  geometry units au
    symmetry group d2h
    C      0.000000000    0.000000000   -1.115108538
    H      0.000000000    0.000000000   -3.106737425
  end
 ethylene
 ethylene
The  axes are the x, y, and z axes.  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
 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.
 
plane.
  geometry units angstroms
    C 0 0 0.659250 
    H 0 0.916366 1.224352 
    symmetry d2h
  end
 methane
 methane
For ease of use, the primary  axis should be the x=y=z axis.
The 3
 axis should be the x=y=z axis.
The 3  axes are the x, y, and z.
 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
 buckminsterfullerene
 buckminsterfullerene
One of the  axes is the z axis and the point of inversion is the origin.
 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
 porphyrin
 porphyrin
The  and
 and  rotation axis is the z axis.  The reflection plane 
for the
 rotation axis is the z axis.  The reflection plane 
for the  operation is the xy plane.
 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
 iron penta-carbonyl
 iron penta-carbonyl
The  axis is the z axis.  The
 axis is the z axis.  The  plane is the xy plane.  One of
the perpendicular
 plane is the xy plane.  One of
the perpendicular  axes is the x=y axis.  One of the
 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
 
planes is the plane containing the x=y axis and the z axis.  (The 
other axes and planes are generated by the  operation.)
 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
 sodium crown ether
 sodium crown ether
The  axis is the z axis. The point of inversion is the origin. One of
the perpendicular
 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
 axes is the x=y axis. One of the  planes
is the plane containing the -x=y axis and the z axis.
 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
 ammonia
 ammonia
The  axis is the z axis. One of the
 axis is the z axis. One of the  planes is the 
plane containing the x=y axis and the z axis.
 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
 benzene
 benzene
The  axis is the z axis.  The point of inversion is the origin.  One
of the 6 perpendicular
 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
 axes is the x=y axis. (-x=y works as a 
 axis.)  The
 axis.)  The  plane is the xy plane.  The
 plane is the xy plane.  The  planes contain the
 
planes contain the  axis and the z axis.  The
 axis and the z axis.  The  planes 
contain the
 planes 
contain the  axis and the z axis.
 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
 axis is the z axis.  The  plane is the xy plane.
 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
 ferrocene
 ferrocene
The  axis is the z axis.  The center of inversion is the origin.
One of the perpendicular
 axis is the z axis.  The center of inversion is the origin.
One of the perpendicular  axes is the x axis.  One of the
 axes is the x axis.  One of the  planes is the yz plane.
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
 axis is the z axis.  The  planes are the yz and the xz
planes.  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.
 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
 trans-dichloroethylene
 trans-dichloroethylene
The  axis is the z axis.  The origin is the inversion center.
The
 axis is the z axis.  The origin is the inversion center.
The  plane is the xy plane.
 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 is the z axis (z is also the  axis).  The x and y axes
are the perpendicular
 axis).  The x and y axes
are the perpendicular  s. The
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.
 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
 cyclopentadiene anion
 cyclopentadiene anion
The  axis is the z axis (z is also the
 axis is the z axis (z is also the  axis).  The y axis is one
of the perpendicular
 axis).  The y axis is one
of the perpendicular  axes.  The
 axes.  The  plane is the xy plane and
one of the
 plane is the xy plane and
one of the  planes is the yz plane.
 planes is the yz plane.
  charge -1
  geometry units angstroms
    symmetry d5h
    c 0 1.1853 0 
    h 0 2.2654 0 
  end
 gold tetrachloride
 gold tetrachloride
The  axis is the z axis (z is also the
 axis is the z axis (z is also the  axis).  
The
 axis).  
The  axes are the x and y axes and 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
 axes are the x=y axis
and the x=-y axis.  The inversion center is the origin.  The  plane is the xy plane.  The
plane is the xy plane.  The  planes are the xz and yz planes and
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.
 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
 
 
 
 
 
 
