Disorder

Introduction

• 3 types of disorder– Substitutional disorder– Static positional disorder– Dynamic positional disorder

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.

Substitutional disorder

• The same site may be occupied by different elements in different unit cells– i.e. two or more conformations may be

possible which are no better or worse than each other

• Consider the following example…

Substitutional disorder

Q: If you knew there was a nitrogen atom in the ring, in which position might it lie, A or B?

A B

Substitutional disorder

• Answer…– Possibly both

• As 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.

Substitutional Disorder

• Spotting substitutional disorder– As 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.

Subsitiutional Disorder

• Solvent molecules– Often 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.

Positional disorder

• Positional disorder is much more common than substitutional.

• Two types can occur…– Static– Dynamic

Static Disorder

• Two (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

Static Disorder

Static disorder

• Even 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.

Dynamic disorder

• This 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

Dynamic disorder

Appears shorter than expected

Appears longer than expected

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 chain

• Thermal parameters can indicate thermal motion.– Two ways to interpret

• Allow large thermal parameters as they may provide a more realistic description.

• Use multiple parts to describe several discrete positions.

Dynamic Disorder

• Example, tertiary butyl groups– Often spin freely in a structure.

Which description is better?

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 parameters

• If 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.

END OF PART 1

Disorder recap

Present in 100%Of unit cellsOccupancy = 1

Present in 33% of unit cellsOccupancy is 0.333

Present in 66% of unit cellsOccupancy is 0.667

Constraints vs. Restraints

• Restraints allow some freedom constraints allow none

• Restraints are preferable as they allow the data to affect the result, constraints do not.

Restraints

• Why use restraints– False (local) minima– Allow for inclusion of additional empirical data

E

r

Refinement sticks here

We want to be here

Restraints

• Distance– DFIX

• Restrain distance to a value given

– SADI• SAme DIstance, two or more distances are

restrained to be the same as one another

DFIX

User specified value

SADI

Restraints

• FLAT– Atoms are restrained to be coplanar

• SAME– 1,2 and 1,3 distances are restrained to be

similar

FLAT

SAME

Restraints

• SIMU– For atoms listed the entire 3x3 U matrix

describing atomic displacements is restrained to be similar

– Direction will become similar, size will become similar

Restraints

• DELU– For atoms listed only the components

describing atomic displacements along the bond (or interatomic vector) are restrained to be similar

– Direction will not change, size only along vector will become similar

Restraints

• ISOR– The anisotropic atom is restrained to have

isotropic behaviour.– Rubgy ball shaped ADP will become more

spherical

Constraints

• Same position– EXYZ C1 O1

• Same thermal parameters– EADP C1 O1

• Rigid hexagon– AFIX 66

• Many many more, see shelx manual

PARTS

• PART x y– This 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.

Worked examples

• The example following is taken from…– “Crystal Structure Refinement – A

crystallographer’s guide to SHELXL”P. Muller et al.