Symmetry dictionary (symCIF) version 1.0.1

_space_group.transform_Qq_xyz

Name:
'_space_group.transform_Qq_xyz'

Definition:

   This item specifies the transformation (Q,q) of the atomic
   coordinates from the setting used in the CIF [(x,y,z) referred
   to the basis vectors (a,b,c)] to the reference setting given in
   _space_group.reference_setting [(x',y',z') referred to the
   basis vectors (a',b',c')].

   The value given in Jones-Faithful notation corresponds to the
   rotational matrix Q combined with the origin shift vector q in
   the expression:

       (x',y',z') = Q(x,y,z) + q.

   Q is a pre-multiplication matrix of the column vector (x,y,z).
   It is related to the inverse transformation (P,p) by:

       P = Q^-1^
       p = Pq = -(Q^-1^)q,

   where the P and Q transformations are applied as follows:

   atomic coordinates  (x',y',z') = Q(x,y,z) + q
   Miller indices      (h',k',l') = (h,k,l)P
   symmetry operations         W' = (Q,q)W(P,p)
   basis vectors       (a',b',c') = (a,b,c)P + p

   This item is given as a character string involving the
   characters x, y and z with commas separating the expressions
   for the x', y' and z' components. The numeric values may be
   given as integers, fractions or real numbers. Multiplication
   is implicit, division must be explicit. White space within
   the string is optional.

Examples:

'-x/3+2y/3-z/3, -2x/3+y/3+z/3, x/3+y/3+z/3' R3:r to R3:h

x+1/4,y+1/4,z+1/4 Pnnn:1 to Pnnn:2

z+1/2,x+1/2,y+1/2 Bbab:1 to Ccca:2

Mandatory item: no

Category: space_group