Reindexing (CCP4: General)


reindexing - information about changing indexing regime


General Remarks

It is quite common to find that the diffraction from subsequent crystals for a protein do not apparently merge well. There are many physical reasons for this, but before throwing the data away it is sensible to consider whether another indexing regime could be used. For illustrations and examples see HKLVIEW-examples below. For documentation on re-indexing itself, and some hints, see also REINDEX.

For orthorhombic crystal forms with different cell dimensions along each axis you can usually recognise if the next crystal is the same as the last and see how to transform it (remember to keep your axial system right-handed!).

In P1 and P21 there are many ways of choosing axes, but they should all generate the same crystal volume. Use MATTHEWS_COEF or some other method to check this - if the volumes are not the same, or at least related by integral factors, you have a new form. If they are the same it is recommended to plot some sections of the reciprocal lattice; you can often see that the patterns will match if you rotate in some way (see HKLVIEW-examples below). A common change in P21 or C2 where the twofold axis will be constant, is that a*new = a*old + c*old, and c*new must be chosen carefully. One very confusing case can arise if the length of (a*+nc*) is almost equal to that of a* or nc*, but it should be possible to sort out from the diffraction pattern plots.

Confusion arises mostly when two or more axes are the same length, as in the tetragonal, trigonal, hexagonal or cubic systems. In these cases any of the following definitions of axes is equally valid and likely to be chosen by an auto-indexing procedure. The classic description of this is that these are crystals where the Laue symmetry is of a lower order than the apparent crystal lattice symmetry.
real axes:(a,b,c)or(-a,-b,c)or (b,a,-c)or(-b,-a,-c)
reciprocal axes:(a*,b*,c*)or(-a*,-b*,c*)or (b*,a*,-c*)or(-b*,-a*,-c*)
N.B. There are alternatives where other pairs of symmetry operators are used, but this is the simplest and most general set of operators. For example: in P4i (-a,-b,c) is equivalent to (-b,a,c), or in P3i (-a,-b,c) is equivalent to (-b,a+b,c).

N.B. In general you should not change the hand of your axial system; i.e. the determinant of the transformation matrix should be positive, and only such transformations are discussed here.

The crystal symmetry may mean that some of these systems are already equivalent:
For instance, if (h,k,l) is equivalent to (-h,-k,l), the axial system pairs [(a,b,c) and (-a,-b,c)] and
[(b,a,-c) and (-b,-a,-c)] are indistinguishable. This is the case for all tetragonal, hexagonal and cubic spacegroups.
If (h,k,l) is equivalent to (k,h,-l), the axial system pairs [(a,b,c) and (b,a,-c)] and
[(-a,-b,c) and (-b,-a,-c)] are indistinguishable. This is true for P4i2i2, P3i2, P6i22 and some cubic spacegroups.
If (h,k,l) is equivalent to (-k,-h,-l), the axial system pairs [(a,b,c) and (-b,-a,-c)] and
[(-a,-b,c) and (b,a,-c)] are indistinguishable. This is only true for P3i12 spacegroups.
See detailed descriptions below.

A real monoclinic example

Two datasets from the same crystal with apparently the same cell dimensions:
run1 55.76 84.62 70.96 90 112.71 90
run2 56.04 85.11 71.57 90 113.15 90
However, the Rmerge from Scala was around 40% Viewing the k = constant sections in HKLVIEW showed that the diffraction patterns were rotated with respect to each other. A reindexing transformation of -h, -k, h+l was inferred. In terms of the real-space cell, the new axes are constructed as follows:

cell axes transformation

Some basic trigonometry shows the new cell dimensions to be:

run1 (reindexed) 55.76 84.62 71.33 90 113.42 90
The new dimensions are slightly closer to those of run2. The previous similarity is shown to be a coincidence.

Note the transformation -h, -k, h+l preserves the hand, i.e. the corresponding matrix has a determinant of +1.

Lookup tables

Here are details for the possible systems:

Changing hand


Test to see if the other hand is the correct one:
Change x,y,z for (cx-x, cy-y, cz-z)
Usually (cx,cy,cz) = (0,0,0).

Remember you need to change the twist on the screw-axis stairs for P3i, P4i, or P6i!

P21 - to P21; For the half step of 21 axis, the symmetry stays the same.

P31 - to P32
P32 - to P31

P41 to P43
(P42 - to P42: Half c axis step)
P43 -to P41

P61 to P65
P62 - to P64
(P63 - to P63)

In a few non-primitive spacegroups, you can change the hand and not change the spacegroup by a cunning shift of origin:

(x,y,z) to (-x,1/2-y,-z)
(x,y,z) to (-x,1/2-y,1/4-z)
(x,y,z) to (1/4-x,1/4-y,1/4-z)

Plus some centric ones:

(x,y,z) to (1/4-x,1/4-y,-z)
(x,y,z) to (1/4-x,1/4-y,-z)
(x,y,z) to (1/4-x,1/4-y,-z)
(x,y,z) to (1/4-x,1/4-y,-z)


Full size versions of the example pictures can be viewed by clicking on the iconised ones.

HKLVIEW Barnase pH6 A P32 data set indexed h,k,l
HKLVIEW Barnase pH6 indexed -h-kl The same P32 data set, reindexed -h,-k,l
HKLVIEW Barnase pH6 indexed -k-hl The same P32 data set, reindexed -k,-h,l
HKLVIEW Barnase pH6 indexed kh-l The same P32 data set, reindexed k,h,-l
HKLVIEW Hipip h2l Monoclinic data set, HKLVIEW h,2,l
HKLVIEW Hipip reindexed The same monoclinic data set, reindexed -h,-k,h-l


Eleanor Dodson, University of York, England
Prepared for CCP4 by Maria Turkenburg, University of York, England
Some additional material from Martyn Winn, Daresbury Lab.


G. Bernardinelli and H. D. Flack (1985). Least-squares absolute-structure refinement. Practical experience and ancillary calculations. Acta Cryst. A41, 500-511.