```6.3.2.3.  IMPOSING SYMMETRY

Option [S] selected from the structure option menu S, see Sec. 6.3.2, allows
you to impose additional point symmetries on the cluster. The cluster will be
completed by adding equivalent atoms (if needed) to achieve the required
symmetry. Further, coinciding atoms produced by previous group operations may
be removed with the present option. The cluster symmetry menu SS reads

====================================================================

Global symmetry:  [C]axis  [M]irror  [I]nvers  [R]educe  [D]max(dc)
[X]plot  [?,]esc
============================================================== 81 ==

allowing to define an n-fold rotation axis, a mirror plane, inversion
symmetry, and to reduce the cluster by removing coinciding atoms. The value
dc determines the present coincidence distance which is the maximum distance
between two atoms to be considered to coincide in the above point symmetry
transformations.

>   [C]  selected from submenu SS imposes N-fold rotation symmetry on the
cluster. The rotation axis is defined by an origin (x,y,z) (on the
axis) and a direction vector (xd,yd,zd). The prompt

Rotation origin  NC,X,Y,Z ("-1,0,0,0"=esc) :

asks for four numbers defining the rotation origin given either in
absolute coordinates (0,x,y,z) or denoting the center of an
existing atom na by (na,0,0,0). Dummy input "-1,0,0,0" returns
immediately to submenu SS. Then the prompt

Rotation axis, order (X,Y,Z, N) :

asks for four numbers defining the direction vector components
(xd,yd,zd) and the order N of the rotation axis. The direction
vector does not need to be normalized.

>   [M]  selected from submenu SS imposes mirror symmetry on the cluster.
The mirror plane is defined by an origin (x,y,z) (on the plane) and
a plane normal vector (xn,yn,zn). The prompt

Mirror origin  NC,X,Y,Z ("-1,0,0,0"=esc) :

asks for four numbers defining the mirror plane origin given either
in absolute coordinates (0,x,y,z) or denoting the center of an
existing basis atom na by (na,0,0,0). Dummy input "-1,0,0,0"
returns immediately to submenu SS. Then the prompt

Mirror plane normal (X,Y,Z) :

asks for three numbers defining the vector components (xn,yn,zn) of
the plane normal. The normal vector does not need to be normalized.

>   [I]  selected from submenu SS imposes inversion symmetry on the cluster.
The inversion is defined by an origin (x,y,z). The prompt

Inversion origin  NC,X,Y,Z ("-1,0,0,0"=esc) :

asks for four numbers defining the inversion origin given either in
absolute coordinates (0,x,y,z) or denoting the center of an
existing basis atom na by (na,0,0,0). Dummy input "-1,0,0,0"

After successful definition of the symmetry the respective operation is
applied to all atoms of the cluster and new atoms are added if needed
which is concluded by

Symmetry checked, no new atoms

if the symmetry operation did not result in new atoms or by

Symmetry operation yields nn new atom(s)

if nn new atoms have been generated by the symmetry operation and BALSAC
returns to the structure option menu S, see Sec. 6.3.2.

If a new atom generated by the symmetry operation coincides with an
existing cluster atom (within the limit given by the coincidence
distance, see below) the new atom will not be included in the cluster.
For coinciding atoms of different nuclear charge a warning

WARNING: symmetry copy of XX atom (n1) and YY atom (n2) coincide
no or partial symmetry applied to atom no. n1

will be issued where n1 denotes the number of the atom (XX its element
name) where the symmetry operation was applied and n2 is the number of
the existing cluster atom (YY its element name).

>   [R]  selected from submenu SS checks all atoms of the cluster for
coincidence and allows you to discard respective atoms. Here two
atoms are considered to coincide if their relative distance is
smaller than a limit given by the coincidence distance which can be
set freely, see below. For each pair of coinciding atoms a prompt

Xyz,R,Id( n1,V1) :   x    y    z ,  rad1 ,  nuc1
Xyz,R,Id( n2,V2) :   x    y    z ,  rad2 ,  nuc2

Discard atom:  [F]irst  [S]econd  [A]utosec   [?,]esc

appears where n1/2 gives the atom pointers, V1/2 denotes the
visibilities of the two atoms ("T" = visible, "F" = hidden),
(x,y,z) denotes their (identical) positions, rad1/2 their atom
radii, and nuc1/2 their nuclear charges (element names). Here
selecting option

[F]  removes the first atom of the pair, atom no. n1 (lower
number), from the cluster.

[S]  removes the second atom of the pair, atom no. n2 (higher
number), from the cluster.

[A]  continues in automatic discard mode where of all pairs of
coinciding atoms the second, no. n2 (higher number), is

[,]  stops the search for coinciding atoms returning to the
structure option menu S, see Sec. 6.3.2.

The coincidence check is concluded by the message

np atoms coincide,      nrem atoms removed

giving the number np of pairs of coinciding atoms and the number
nrem of atoms removed from the cluster. If coincidence checking was
interrupted by selecting [,] above the number np may be smaller
than the actual number of coincidence pairs of the cluster. Note
that the atom removal of this option is final and cannot be undone.

>   [D]  selected from submenu SS resets the coincidence distance which is
the maximum distance between two atoms to be considered to coincide
in the above symmetry transformations. The prompt

Atom coincidence distance  ( dc) :

shows the present value of the coincidence distance
(default = 0.01) and asks for a new value after which BALSAC

>   [X]  selected from submenu SS plots the cluster (switching to graphics
mode (DOS) or opening a graphics window (Unix)) or lists its atom
coordinates depending on the plot/list mode defined in the graphics
option, see Sec. 6.2.7.

>   [,]  selected from submenu SS returns immediately to the structure
option menu S, see Sec. 6.3.2.