# Symmetry determination with Pointless

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The program Pointless can determine Laue group symmetry, and possibly the space group, and write an output file in the most probable (or chosen) Laue group or space group, suitable for input to Scala. In cases where alternative indexing schemes are possible, it will find the indexing scheme which is consistent with a previously processed reference file. Multiple files from eg Mosflm can be combined. Files from XDS, Scalepack, SHELX and SAINT (from version 1.4.3) can also be read by Pointless: some other formats can be read by the program Combat.

Note that strictly a Laue group is the *point group* symmetry of the diffraction pattern, *ie* the crystal point group plus a centre of inversion at the origin of the reciprocal lattice: here we include the lattice centring type (P, I, F, C, R) in the "Laue group" definition, equivalent to the Patterson space group

The **Find or match Laue group** task has four main mode options selected by buttons on the first line.

## Contents |

## [edit] Option 1: Determine Laue group

The indexing of the lattice in an integration program such as Mosflm is based on the lattice geometry, with no regard for the symmetry of the diffraction pattern, which can only be determined after integration. This option scores potential symmetry operators in the diffraction pattern, and ranks the possible Laue groups (point groups), and also inspects axial reflections for possible systematic absences which may indicate a likely space group. Be careful, the presence of pseudo-symmetry may suggest a higher symmetry than the truth. Pointless tries to allow for this possibility, but inspection of the scores for individual symmetry elements may help to indicate the correct space group in difficult cases.

### [edit] Running the task

One or more input files may be chosen, either MTZ files from Mosflm, XDS files (XDS_ASCII.HKL or INTEGRATE.HKL), or unmerged files from Scalepack. If an output file is selected, this will be written after choosing the most probable space group, or point group if no space group can be chosen. Another option overrides the default of IUCr standard settings for primitive orthorhombic and centred monoclinic spacegroups: this convention sets a<b<c for all primitive orthorhombic, *eg* it allows P 2_{1} 2 2_{1} rather than the "reference" setting P 2_{1} 2_{1} 2, and also chooses I2 in place of C2 if it gives a smaller β angle. Other less common options may be set in the closed panels, including exclusion of batches, choice of resolution, and tolerance on cell dimensions used to determine the potential lattice symmetry.

#### [edit] Multiple input files

By default, multiple files will be assigned to the same dataset, whose name may be changed from that in the input file. Different input files may optionally be assigned to different datasets, eg for different wavelengths in a MAD dataset. Multiple files will be checked for consistent indexing (if relevant, see below) unless the button *Assume all files have same indexing (faster)* is checked: this saves time if you are confident that they are consistently indexed. In the output file, batch numbers must be unique, and this is automatically enforced by adding a multiple of 1000 if necessary.

### [edit] Program output

The program reads data from all input files, then the maximum possible lattice symmetry is determined from the cell dimensions, within a given tolerance (default 2° or equivalent on lengths), ignoring the symmetry specified in the input file. It then does a rough normalisation by making <E^{2}> = 1.0 in all resolution ranges. Weak high resolution data is not used in the scoring: the resolution is cut where <I>/σ < 6 (by default).

#### [edit] Scoring individual symmetry elements

Each possible symmetry operator in the lattice is scored separately, by a pairwise correlation coefficient (CC) between E^{2} for observations related by that operator, and also by an R-factor, R_{meas}. The CC is used to estimate a probability, allowing for possible small samples by comparing it with the distribution CCs of equal sized samples of unrelated observation pairs. This separate scoring is useful in cases of pseudo-symmetry to indicate the true symmetry, in cases where the program gets it wrong. In the example on the left, the true symmetry is C222, but because of the accidental combination of cell lengths, *b* ≈ √3 *a*, the lattice can be indexed as hexagonal. The scores show that three orthogonal dyads are present, but the other potential operators of the hexagonal lattice are absent.

#### [edit] Scoring Laue groups

The scores from the individual elements are then combined into a joint score for all possible Laue groups which are subgroups of the lattice group. A high score for a symmetry element which is present in the lattice group but not in the Laue group will count against that group (the CC-, Zc- and R- columns in the table). Note that in this example, the pseudo-hexagonal lattice can accommodate three possible Cmmm settings, 60° apart: the one chosen randomly (ReindexOperator [h,k,l]) by the original indexing was wrong here.

#### [edit] Systematic absences

Within a chosen Laue group, space groups (all chiral groups apart from the pairs I222 and I2_{1}2_{1}2_{1}, and I23 and I2_{1}3) may be distinguished by the presence or absence of screw axes along the cell edges. A screw axis leads to systematic absences along an axis of the reciprocal lattice *eg* a 2_{1} screw along **b** in space group P2_{1} makes axial reflections 0k0 present only when k is even. Detecting systematic absences may be unreliable because the axial reflections may be few in number, or missing from the dataset if they lie along the spindle rotation axis in the data collection (in the blind region), or may be misleading if there are approximate non-crystallographic screw axes, but in many cases they can suggest the space group, to be confirmed later: the space group remains a hypothesis until the structure is satisfactorily solved. In Pointless, a Fourier analysis is used to detect periodicity, on I'/σ: the intensity I' used here is adjusted by subtraction of a small fraction (default 0.02) of the intensity of the neighbouring reflection along the axis, to allow for possible overlap of a nearby strong reflection (see plot on right).

#### [edit] Choice of space group or point group

Possible space groups are ranked according to their total probability = Laue group probability × Systematic absence probability. If there is a unique solution with the highest total probability, this will be chosen as a "space group" solution. If there some of the potential systematic absence data is missing, as in the example on the right, then more than one space group has the same score, and the point group will be chosen, in this case P 4 2 2. Enantiomorphic space groups will have the same score, so the first one is chosen as a space group solution.
As well as the scores, a "confidence" score is calculated for both the Laue group and the space group, defined as √[Score × (Score - NextBestScore)]: these values are printed in a summary table as the *Best Solution* (see right). If you prefer a different solution to that chosen by the program, you can rerun the program with the **Choose a previous solution** option.

## [edit] Option 2: Match index to reference

In some point-groups there are more than one (typically two or four) valid but non-equivalent indexing possibilities. For your first crystal, you may choose any of these, but subsequent crystals must match the first. This problem generally arises in cases where the point group symmetry is less than the lattice symmetry: the alternative indexing schemes are related by the symmetry operators present in the lattice but not in the point group. These are the same point groups which may lead to merohedral twinning, eg point group P3 has four possible indexing schemes in the lattice point-group P622 (further explanation). Within multiple datasets from the same crystal (eg MAD), you can avoid this problem by only autoindexing one set, & using the same indexing matrix for the others, but different crystals must be explicitly checked for consistent indexing. Reindexing ambiguities may also arise in lower-symmetry point-groups in case of accidental coincidences or relationships between cell dimensions (*eg* a ≈ b in orthorhombic or the pseudo-hexagonal C222 example above).

### [edit] Running the task

The observed "test" dataset is tested against a previously processed "reference" file (merged or unmerged), by ranking the correlation coefficients for each possible alternative indexing schemes, to put the test dataset on a consistent scheme. Multiple test files may be read (see example above right), and the tolerance for different unit cells may be changed from the default 2°. The output file will be written in the space group of the reference file.

### [edit] Program output

A ranked table of scores for each possible indexing scheme is printed. The example on the left is unusually complicated: the true space group is rhombohedral, R3, but the lattice is pseudo-cubic; in the rhombohedral axis system (with a = b = c, α = β = γ) the angles are close to 90°. This means that in addition to the usual ambiguity in R3 with alternative indexing [k,h,-l] (in the hexagonal setting *aka* H3) , there are four possible directions for true 3-fold axis, along the body-diagonals of the cubic lattice, leading to a total of eight possible indexing schemes.

## [edit] Option 3: Choose a previous solution

This option allows an explicit choice of indexing or symmetry. The **Choose solution from search** options perform the usual search, but selects the given solution even if it does not have the highest score. The **Specify Laue group name** or **Specify space group name** use the given groups without doing the searches, *ie* the program just changes the group, with an option to reindex.

## [edit] Option 4: Just combine input files

This option just sorts one or more input files for Scala (equivalent to the program Sortmtz)

## [edit] Program documentation

The latest version of the documentation is available here. This provides information on program keywords which may be used from the command line.

This page describes Pointless version 1.6.18 (CCP4 version 6.3.0+) but earlier versions are not substantially different

## [edit] References

P.R.Evans, *Scaling and assessment of data quality*, Acta Cryst. **D62**, 72-82 (2006).

P.R.Evans, *An introduction to data reduction: space-group determination, scaling and intensity statistics*, Acta Cryst. **D67**, 282-292 (2011)