3 First things first… What is a crystal? A 3-D ordered array of molecules.Defined by discrete unit cells, the smallest repeating unit from which the crystal structure can be reconstructed when combined with the crystal lattice.Unit cell contents should be identical in a perfect crystal. Often imperfections complicate matters.Disorder describes a case where unit cell contents are not 100% identical.
4 Substitutional disorder The same site may be occupied by different elements in different unit cellsi.e. two or more conformations may be possible which are no better or worse than each otherConsider the following example…
5 Substitutional disorder Q: If you knew there was a nitrogen atom in the ring,in which position might it lie, A or B?
6 Substitutional disorder Answer…Possibly bothAs neither position has a clear advantage over the other, (i.e. both can form hydrogen bonds, neither changes steric interactions, etc.) it is equally possible that a molecule might be found in either conformation.This results in the superposition of both atom types onto the same site creating a problem the crystallographer must address.
7 Substitutional Disorder Spotting substitutional disorderAs X-rays diffract from electrons, electron density and therefore the atomic number, z, is important.Thermal parameters enlarge in order to reduce e- density if too large an element is assigned and shrink if too small an element is assigned.In general thermal parameters will be similar for an atom and its neighbours. If they are significantly different there may be an issue with an atom’s element assignment.
8 Subsitiutional Disorder Solvent moleculesOften be partially occupied which increases thermal parameters.BUT They are often highly mobile in the crystal lattice which also imparts high thermal parameters.In general only reduce occupancy for VERY large solvent molecules and be mindful of the effect on your R-factor, charge balance (if not a neutral species) and resultant thermal parameters.
9 Positional disorderPositional disorder is much more common than substitutional.Two types can occur…StaticDynamic
10 Static DisorderTwo (or more) equally plausible conformations may be possible in a structure.Some unit cells may contain one conformation and the rest the other.Results in the superposition of the two possibilities which may look chemically unreasonable and are difficult to interpret
12 Static disorderEven simple two position disorder can be very difficult to interpret.Avoid anisotropic refinement early on.Pay attention to ellipsoid shapes and size.Atoms which are not fully occupied will refine to have larger thermal parameters.If necessary refine relative occupancy of the components.
13 Dynamic disorderThis type of disorder is usually the result of our data giving us a time averaged picture of structure.The time scale on which we conduct the experiment is many many times more than the timescale of atomic motion.This is probably the more difficult case to treat.Thermally induced motion can occur which leads to electron density which is smeared out and thus difficult to refine.Sometimes it is possible to freeze out the disorder and is one reason we collect data at low temperature
14 Dynamic disorder Appears shorter than expected Appears longer than expected
15 Dynamic disorder Interpretation of electron density can be difficult. Electrons are spread out and so finding atoms can be difficult or impossible.Thermal parameters can vary wildly along the chainThermal parameters can indicate thermal motion.Two ways to interpretAllow large thermal parameters as they may provide a more realistic description.Use multiple parts to describe several discrete positions.
16 Dynamic Disorder Example, tertiary butyl groups Often spin freely in a structure.Which description is better?
17 Disorder refinement General principles If two interpretations exist, try both and compare the result.Use restraints when necessary which is often the case with disorder.Pay attention to thermal parametersIf you suspect disorder, refine only isotropic thermal parameters or switch back to isotropic refinement for these atoms.Anisotropic refinement will often obscure disorder.Check anisotropic thermal ellipsoid shapes to see if they are consistent with your model and expected thermal motion.Pay particular attention to ellipsoids near unaccounted for electron density (i.e. Q-peaks).Sometimes particularly with solvent molecules you may be unable to produce a ‘good’ model. Simply do your best to give a sensible and chemically reasonable explanation. For solvents you may consider using the Squeeze routine in Platon.
19 Disorder recap Present in 33% of unit cells Occupancy is 0.333
20 Constraints vs. Restraints Restraints allow some freedom constraints allow noneRestraints are preferable as they allow the data to affect the result, constraints do not.
21 Restraints Why use restraints False (local) minima Allow for inclusion of additional empirical dataERefinement sticks hererWe want to be here
22 Restraints Distance DFIX SADI Restrain distance to a value given SAme DIstance, two or more distances are restrained to be the same as one anotherDFIXSADIUser specified value
23 Restraints FLAT SAME Atoms are restrained to be coplanar 1,2 and 1,3 distances are restrained to be similarSAMEFLAT
24 RestraintsSIMUFor atoms listed the entire 3x3 U matrix describing atomic displacements is restrained to be similarDirection will become similar, size will become similar
25 RestraintsDELUFor atoms listed only the components describing atomic displacements along the bond (or interatomic vector) are restrained to be similarDirection will not change, size only along vector will become similar
26 RestraintsISORThe anisotropic atom is restrained to have isotropic behaviour.Rubgy ball shaped ADP will become more spherical
27 Constraints Same position Same thermal parameters Rigid hexagon EXYZ C1 O1Same thermal parametersEADP C1 O1Rigid hexagonAFIX 66Many many more, see shelx manual
28 PARTSPART x yThis instruction can be placed into the ins file before a group of atoms and will assign them to the given part number, x, until the next part instruction.y specifies the occupancy these atoms will have. It is not required but saves manually changing each individual atom.All atoms are in PART 0 by default. Atoms in this part will bond to all other parts. PART 1 will only bond to other atoms in PART 1 and atoms in PART 0 but no others.
29 Worked examples The example following is taken from… “Crystal Structure Refinement – A crystallographer’s guide to SHELXL”P. Muller et al.