Crystals User Guide

Chapter 9: Results

9.1: Difference electron density

9.2: Analysis of differences

9.3: Physical reasonableness

9.4: Thermal parameters

9.5: Computer Graphics

Increasingly, the aim of a crystal structure analysis is not to produce a detailed description of a single structure, but either to determine the gross structure of a compound, or obtain geometric details of a series of compounds. Few crystallographers now have the time to make friends with all their structures. Non the less, since most published structures now find their way into computer readable data banks, from which they may be retrieved by programs with less insight than human researchers, it has become more vital than ever that structures are processed in a well defined and documented way, and that the results are published without additional errors. CRYSTALS does watch what the user is doing, and may alert him to real or potential problems, but eventually the user is responsible for his own work. The following list gives some of the points to be checked, and the facilities available for doing this.
 

This provides a broad and largely unbiassed view in an intuitatively interpretable form of the differences between the observed and calculated structure factors. An entirely featureless map indicates that the model can simulate the observations well, though other models may do almost as well, and there may be errors in the data that it would be preferable that the model didn't emulate (e.g. temperature factors concealing the need for an absorption correction). In any case, since most refinements will be conducted with some sort of weighting of the observations, it is unlikely that the map will be without features of any kind. What is important is that any features observed can be explained.
 

For a formally valid least squares refinement, the average value of w(Fo-Fc)**2 must be constant for any systematic sectioning of the data. In CRYSTALS the instruction \ANALYSE provides an analysis by sectioning as a function of h, k, l, parity, class, /Fo/ and sign(theta). The entries in the column <w(Fo-Fc)**2> should be approximately constant throughout the table. If this condition is not satisfied, then systematic variations in <(Fo-Fc)> as a function of one or more of the sectinings may throw light on serious failures in the model. For example, if Fo is less than Fc for strong reflections and also for low angle reflections, then an extinction correction may be necessary. Systematic variations as a function of index may indicate the need for an absorption correction or an anisotropic extinction correction.

A refinement which converges to physically unreasonable parameter values cannot be regarded as satisfactory. Positional parameters usually need translating into molecular parameters before their significance becomes apparent. Several translations available in CRYSTALS.
 
\DISTANCES

This instruction computes inter and intra atomic distances and angles. All necessary symmetry operators are automatically applied to ensure that values within the specified limits are generated. The user should check that there are no inexplicably short inter molecular contacts, as well as checking the ususal bond lengths and angles. The program will also compute e.s.d.s from the full covarience matrix (including symmetry effects). The information for this is taken from the least squares matrix, and the program will not permit this information to be applied to any other LIST 5 than that produced be the corresponding round refinement. It is thus fairly important to give your atoms systematic names and serial numbers, and to get the list into a convenient order AS SOON AS POSSIBLE. Even just changing the serial of an atom will inhibit the linking of the LIST 5 and the matrix.
 
\MOLAX

This procedure computes the principal axes of inertia of a group of atoms. If they have unit weights or weights derived from their standard deviations, then the shortest axis is parallel to the normal to the best plane, and the longest is parallel to the best line.
 
\TORSION

This procedure computes the torsion angles for the specified atoms. e.s.d.s are not currently computed.
 
\CHECK

This procedure compares the current values of parameters with those requested in the restraint definitions. Current values differing significantly from those required should be carefully reappraised, since they indicate a conflict between the diffraction data and the hypothesese.

The six components of the anisotropic temperature factor can be transformed to define a three dimensional ellipsoid representing the harmonic motion of the atom. If free refinement of the U's leads to an ellipsoid with a negative volume, then the transformation becomes meaningless, usually indicating that there are grave deficiencies in the model or the data. For data collected at very low temperatures, the volume may go marginally negative, and restraints on the U's should stabilise the situation. The procedure AXES is called automatically after every round of refinement, to give warning of non-positive definite U's. Refinement will however continue even if some atoms are unsatisfactory. The result is generally a rapidly diverging process with rapidly increasing R factors.
 
\ANISO

This procedure tries to fit the atomic temperature factors to a rigid body composite temperature factor. This is partitioned into three parts, T representing the rectilinear vibration of the body, L representing its torsional libration, and S representing the coordination between these two parts. There are 20 independant terms to be evaluated in TLS for an unsymmetrical fragment not lying on a symmetry operator, so that a rigid body of this sort cannot be defined for less than 4 atoms. For a body of six atoms, the calculation might just be meaningfull, though there are problems with the conditioning of the matrix if the atoms lie close to a conic section. Under these conditions the maths cannot distinguish two correlated motions in T space from a corresponding libration in L space. The user should be aware that good agreement between U(obs) and U(calc) does not mean that the values of T, L and S have any physical significance.

There are no real graphical facilities as part of CRYSTALS. However, we have built an interface to the progran SNOOPI to facilitate visualisation of structures. A structure that 'looks' wrong often is wrong, and interactive graphical facilities enable the user to look frequently and easily at his structure.