Orientation of Local Atomic Coordinates

As discussed before the atomic positions are input with the key ATOMS. One option has thus far not been mentioned: the possiblity to redefine the local coordinate frame of an atom.

ATOMS {type of coordinates}
  {n} atomname coordinates {F=fragment} {Z=xx yy zz} {X=xx yy zz}
  ...
end

Except for the z= option all aspects have been examined already before.

z=xx yy zz

defines a reorientation of the local atomic z-axis; it is interpreted as a direction vector with components (xx,yy,zz) pointing away from the atom. In the local, reoriented frame the local atomic x-axis will be rotated to the plane defined by the directions of the molecular z-axis and the local atomic z-axis.
This feature can be used only for single-atom fragments (otherwise it is ignored). Its purpose is to give more flexibility in the analysis of the final molecular orbitals in terms of the atomic orbitals. In such a case it may be very helpful to redefine the orientation of say the p-orbitals of an atom. For instance, you may orient all p-orbitals towards the origin by specifying for each atom z= -x -y -z (with x,y,z the coordinates of that atom).
By default the local and molecular z-axes are identical.

x=xx yy zz

defines a reorientation of the local atomic x-axis; it is interpreted as a direction vector with components (xx,yy,zz) pointing away from the atom. Together with the z vector this defines the xz plane. The y axis is then given by the vector product z * x.
This is used for analysis (see orientation of the z-axis).