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Item _space_group.transform_Qq_xyz

Description

 
           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 premultiplication 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.

Category

Item Examples

Example 1:

R3:r to R3:h

-x/3+2y/3-z/3, -2x/3+y/3+z/3, x/3+y/3+z/3

Example 2:

Pnnn:1 to Pnnn2

x+1/4,y+1/4,z+1/4

Example 3:

Bbab:1 to Ccca:2

z+1/2,x+1/2,y+1/2

Mandatory Code

Data Type Code

 

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