Twinning • Finish absolute configuration • Non-merohedral twinning • Merohedral twinning
How can a cell be enantiomorphic if the contents are racemic? • For non-polar accentric cells the contents are completely racemic yet the unit cell is enanitomorphic. • The arrangement of molecules in the unit cell creates the optical activity. • Is there a chemical analogy?
Consider Co(en)33+ • Obviously Co3+ nor ethylenediamine is optically active
Co(en)3 • Yet the ion is optically active • Note there is not a single enantiomorphic atom in the structure. The overall arrangement creates the optical activity.
Flack Parameter • If the Flack Parameter (x) refines to zero than the enantiomer is correct, while 1 is incorrect. • The Flack Parameter can take on values outside of 0 to 1. These are generally meaningless and suggest the anomalous scattering is too weak to provide the answer. • The s.u. in the Flack Parameter is important. • 0.2(1) suggests correct. • 0.2 (6) suggests nothing.
Flack Parameter • Advantages • Do not need Friedel pairs to calculate. • Provides a quantitative indicator of the absolute configuration. • Disadvantages • The Flack Parameter tends to correlate with other parameters when there is not much Friedel pair data. • It is not Chemist friendly
The Hooft Approach • Rob Hooft and Ton Spek worked on a new approach which was recently published. • They assumed that most of the Friedel data would be collected which is true for modern area detectors. • Their method is in PLATON as the Bijvoet calculation and appears in our table ent.txt
Hooft Method • Advantages • Very Quantitative • Chemist Friendly • Lower errors on the Hooft y Parameter than the Flack Parameter • Disadvantages • Requires Friedel pair data • Is very sensitive to how data is collected.
Twinning • At one time this meant something, today if simply means not a single crystal. • Basically there are two types • Simply a sample contains more than one crystal—non-merohedral twin • A crystal that is sort of a huge disorder that adds non-existent symmetry –merohedral twin
Racemic Twinning • In this case each unit cell is enantiomorphically pure but the crystal is made up of both d and l cells • This is rare for polar space groups but common in non-polar accentric cells. • The twinning will effect the r-factor and the adp's • Add two cards to SHELX .ins • TWIN • BASF 0.5 --this is the ratio of the two types of cells.
Non-merohedral Twins • These must be treated as multiple crystals. • They must be indexed so that the orientation matrices of each component must be determined. This cannot be done with DENZO. • Once this is done must recognize there are two types of diffraction spots. • Spots that are well defined and belong to a single component • Spots that overlap and belong to more than one component
Non-merohedral Twins • There are two types • Two or more random multiple crystals—unless sample is in short supply there is no reason to use such crystals. • Cases where the twinning is a 180° rotation around a reciprocal axis • This is only possible for triclinic or monoclinic crystals as a 180° rotation in higher symmetry takes an axis into -axis. • For some compounds this second type of twin is present in all the suitable crystals.
The twin law • Obviously there is a relationship between the two components. • This is called the twin law and is a 3x3 matrix that translates one cell into the other. • The programs that index twins provide the twin law.
Refining Twins • There are several approaches to refining twins. • The first is to simply ignore the twinning. • During data averaging some reflections will have contributions from multiple components this will result in large values of Rint. • There will also be some data where the intensity is too large because of overlap. The worst of these can be removed using OUTLIER • The final R factor will be somewhat larger than if the twinning is treated.
Rigorous Refinement • Must integrate the data set for each separate component • Scale the data using the program TWINABS. • This will produce two data sets • An HKLF 4 data set which is one component • An HKLF 5 data set which is for twins. • The next to last card in SHELX indicates the type of data • Solve with HKLF 4 and finish with HKLF 5 • Add a BASF card with HKLF 5
Another Approach in SHELX • If the twin law is know use it instead of HKLF 5 • Add a card TWIN followed by the nine numbers of the twin law. • Add a BASF card. • This will correct for overlap without an additional data set.
Merohedral Twins • A merohedral twin results when disorder adds symmetry to the crystal that is not there. • This makes the symmetry of the crystal look like it belongs to a higher class than it really is. • A simple example: an orthorhombic crystal where a and b are about equal. In this case it is possible that a and b may disorder making the crystal appear to be tetragonal.
As is • The coins in the wrappers are very disordered with respects to heads and tails and also to the orientation of the coin. • This is an example of a one dimensional crystal. • It is ordered along the wrapper but random in the other two dimensions.
Add Some Ordering • Lets put a nick in all the coins so we can ensure they face in the same directions. • If the crystals are all in the wrapper face up or face down then there is exact translational symmetry along the wrapper. This is the only symmetry. • Now imagine the coins are aligned in the wrapper but are placed in randomly with respect to face up or face down.
In this case each edge will be ½ heads and ½ tails. • The two faces will be identical. • In this case there will be a two-fold between the coins and in the middle of the coin. • This symmetry was created by the disorder and is not real. • This is a merohedral twin.
Recognizing Merohedral Twins • These will only contain one component and therefore will not appear to be twinned. • The data will look quite normal • There is no space group that fits the data. • The value of Rint for data averaging is bad. • Frequently it is impossible to solve.
Refinement • The HKLF 5 method will not work • Need to place the twin law on a TWIN card and add a BASF card. • Frequently this data goes nowhere even when it looks quit good. • Can sometimes get some ideas from PLATON or other software. • Send to Vic Young at U. of Minnesota.