Index

Core dictionary version 3.3.0

_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.

Type: Text

Category:
space_group