  Index

# _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