## 6.3.2.3. IMPOSING SYMMETRY

next, previous Section / Table of Contents / Index 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" returns immediately to submenu SS. 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 discarded without prompting. [,] 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 returns to submenu SS. > [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. next, previous Section / Table of Contents / Index