Crystallography Online: the website of the International Union of Crystallography

Christian suggested an extension of the local axis system
to provide for the bisector of a bond angle being defined 
as an axis (potentially useful in applying site symmetry).

This can already be done using a suitable dummy atom, but
it would require a manual calculation of coordinates. I
propose the dictionary definition could be extended as 
follows.

Paul. 


_atom_local_axes_ax1

Name

'_atom_local_axes_ax1'

Category: atom_local_axes

Data type: char

Must appear in a looped list containing '_atom_local_axes_atom_label'

Permitted values:

x
X
y
Y
z
Z
+x
+X
+y
+Y
+z
+Z
-x
-X
-y
-Y
-z
-Z
mxy
mXY
myz
mYZ
mzx
mZX
+mxy
+mXY
+myz
+mYZ
+mzx
+mZX
-mxy
-mXY
-myz
-mYZ
-mzx
-mZX


Definition

   Specifies 'ax1' in the definition of a local axis frame.
   The definition employs three atom site labels 'atom0', 'atom1'
   and 'atom2', and two axis labels 'ax1' and 'ax2' having values
   '+/-X', '+/-Y' or '+/-Z'. For the atom defined by
   '_atom_local_axes_atom_label', whose nuclear position is taken
   as origin, local axis 'ax1' is the vector from the origin to
   atom0, axis 'ax2' is perpendicular to 'ax1' and lies in the
   plane of 'ax1' and a vector passing through the origin parallel 
   to the vector atom1 -> atom2 (its positive direction making an 
   acute angle with the vector parallel to atom1 -> atom2), and a 
   right-handed orthonormal vector triplet is formed from the vector 
   product of the vectors with labels 'ax1' and 'ax2'. In most cases 
   atom1 will be the same as the atom specified by 
   '_atom_local_axes_atom_label'. One or more 'dummy' atoms (with 
   arbitrary labels) may be used in the vector definitions, 
   specified with zero occupancy in the _atom_site_ description.  
   The values of *_atom0, *_atom1 and *_atom2 must be identical to 
   values given in the _atom_site_label list.
   
   Alternatively, 'ax1' may have values '+/-mXY', '+/-mYZ' or 
   '+/-mZX'. In this case "m" signifies "median" and ax1 is formed 
   from the sum of vectors origin -> atom0 and a vector parallel to 
   the vector atom1 -> atom2, i.e. axis 'ax1' bisects the angle 
   between these two vectors. Its label is taken as '+/-X', '+/-Y' 
   or '+/-Z' respectively. Axis 'ax2' is defined as above, its label 
   being taken as the last character in 'ax1'. 

  ------------------------------------------------------------------------