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
A
B
Q: If you knew there was a nitrogen atom in the ring,
in which position might it lie, A or 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 edensity 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 33% of unit cells
Occupancy is 0.333
Present in 100%
Of unit cells
Occupancy = 1
Present in 66% of unit cells
Occupancy 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
Refinement sticks here
r
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
SADI
User specified value
Restraints
• FLAT
– Atoms are restrained to be coplanar
• SAME
– 1,2 and 1,3 distances are restrained to be
SAME
similar
FLAT
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.