Crystals Primer

Chapter 16: Advanced Refinements

16.1: Mixed isotropic and anisotropic refinement

16.2: Large structures.

16.3: Tied parameters

16.4: Rigid groups refinement.

16.5: Pseudo-symmetry.

16.6: Absolute Configuration

16.7: Enantiomorphic Space Groups

CRYSTALS was originally conceived as a refinement program, and continuing developments have maintained it as one of the best. The following examples illustrate some common situations. Remember that constraints are set in LIST 12, and restraints in LIST 16. They can be combined in almost any resonable fashion. An important principle to remember in building constraints is that it is not parameters which are refined, but sfifts in parameters. Parameters cn be linked to have the same shift, even if the staring values are (and will remain) different.
 

      !\LIST 12
      !BLOCK      SCALE X'S
      !CONTINUE   C(1,U'S) UNTIL O(42)
      !CONTINUE   P(1,U[ISO]) UNTIL F(6)
      !END
      !\LIST 22
      !END

These commands define a single matrix block containing the overall scale factor, the positions for all atoms, the anisotripic temperature factors for the first group of atoms, and isotropic for the second. The command LIST 22 converts the symbolic LIST 12 into an internal format, and checks for syntactic consistency. It should always be issued if LIST 12 is complex, so that potential errors can be detected before least squares are started. It also informs the user of the space which will be needed for the matrix in the .DSC file. It is generated internally if the user forgets.
 

The user can refine different groups of parameters is sucessive refinement cycles, by issuing a new LIST 12 command between each cycle. It is also possible to define a multi block refinement, a very effective method if the blocks are carefully chosen. Each block should contain correlated parameters. As a rough guide, the following groups of parameters are in general highly correlated and should be refined in the same block if possible :

 1.  Temperature factors, scale factors, the extinction  parameter,
     the polarity parameter and the enantiopole parameter.
 2.  Coordinates of bonded atoms.
 3.  Non-orthogonal coordinates of the same atom.
 4.  U(11), U(22) and U(33) of the same atom.

If it is necessary to split the temperature factors and scale factor into different blocks, their interactions must not be neglected but be allowed for by using a 'dummy overall isotropic temperature factor'. In this case, the scale factor and the dummy temperature factor must be put into a block of order 2 by themselves, and the program will make the appropriate corrections to all the temperature factors.

      !\LIST 12
      !BLOCK X'S
      !BLOCK U'S SCALE
      !END

This defines a two block matrix. The scale factor should be with the temperature factors.

      !\LIST 12
      !BLOCK C(1,X'S,U'S) UNTIL O(36)
      !BLOCK C(37,X'S,U'S) UNTIL N(61)
      !BLOCK SCALE DU[ISO]
      !END

This defines a three block matrix for a structure containing two uncorrelated (i.e. not related by pseudo -symmetry) fragments or molecules.
 

Parameters can be tied individually, on a per atom basis, or for whole groups of atoms.

      !\LIST 12
      !FULL X'S
      !EQUIVALENCE C(10,OCC) CL(11,OCC) CL(12,OCC)
      !RIDE        C(17,X'S) H(171,X'S) H(172,X'S) H(173,X'S)
      !LINK        C(1,X'S,U[ISO])   UNTIL C(13)   AND
      !CONTINUE    C(101,X'S,U[ISO]) UNTIL C(113)
      !EQUIV       K(1,OCC) NA(1,OCC)
      !WEIGHT   -1 NA(1,OCC)

The first command IMPLIES the positions of all atoms. Subsequent commands EXPLICITLY refer to parameters, and over ride the implicit definitions. The second command ties the occupancies of the atoms in dichloromethane. The third defines a methyl group with riding hydrogen positions. The fourth, which continues onto two lines, ties all the parameters in one group with the corresponding parameters in the second. The final equivalence ties the two occupancies, but the weight card negates the shift applied to sodium. The total of their occupancies is therefore constant.
 

Initial refinements of large or disordered structures are best done by defining groups of atoms with well known geometries as regid groups. The geometry of the groups should first be idealised with \REGULAR. Each atom may not occur in more than one group, though restraints can be applied to any atoms, in or out of groups.

      \LIST 12
      FULL FE(1,X'S) P(1,X'S) CL(1,X'S) CL(2,X'S)
      CONTINUE U'S
      GROUP C(1) UNTIL C(5)
      RIDE  C(1,U'S) UNTIL C(5)
      GROUP C(6) UNTIL C(11)
      RIDE  C(6,U'S) UNTIL C(11)
      GROUP C(12) UNTIL C(17)
      RIDE  C(12,U'S) UNTIL C(17)
      GROUP C(18) UNTIL C(23)
      RIDE  C(18,U'S) UNTIL C(23)
      END

Four groups are refined together with 4 other atom positions and all the anisotropic temperature factors. Each GROUP is given linked anisotropic temperature shifts. They do not have to have the same starting temperature factor values.
 

When a structure contains whole groups of highly correlated coordinates, for example when a symmetry operator is lowered by generating atoms and removing a symmetry operator, the refinement will be unstable. This can often be controlled with:

      \LIST 16
      LIMIT .1 X
      LIMIT .1 Y
      LIMIT .1 Z
      END
      \LIST 12
      FULL
      COMBINE C(1,X'S) UNTIL C(23)  AND C(101,X'S) UNTIL C(123)
      END

The LIMIT restraints prevent wild divergence on the first round of least squares, and the COMBINE card combines the parameters from the original fragment with those from the generated fragment - see the reference Manual.
 

CRYSTALS permits the refinement of either the Rogers eta or the Flack x parameter. The Flack parameter is more stable, and has a physical interpretation throughout its permitted range (0 to 1). Its refinement seems to be robust against DIFABS treatment, but does require an extinction correction to be applied if necessary, and may also require the inclusion of very weak refections. Note that these are often systematically over-estimated. The listing file for a cycle of refinement including the Flack parameter contains a list of 'enantiomer sensitive' reflections. F+ is Fcalc for the current model, F- for the inverse, and Fo is the observed value. Fo should tend to F+ or F-. If it is consistently stronger or weaker, suspect the data collection.

If the material is expected to be chirally pure, once the hand has been determined x should be set to 0.0, and enantio removed from LIST 12 and turned off in LIST 23. If the material is twinned, enantio must remain in the refinement.
 

 
Interpretation of the Flack Parameter

      Flack      e.s.d      interpretation
     ~0.0         <.05      Hand is correct
     ~1.0         <.05      Hand need inverting
     ~0.5         <.05      Well characterised twin.
     ~0.0         >0.5      Hand undertermined
     ~1.0         >0.5      Hand undertermined
     ~0.5         >0.5      Twinning undertermined

      P 61      -  P 65                   P 41       -  P 43
      P 62      -  P 64                   P 41 2 2   -  P 43 2 2
      P 61 2 2  -  P 65 2 2               P 41 21 1  -  P 43 21 1
      P 62 2 2  -  P 64 2 2               P 41 3 2   -  P 43 3 2

                        P 31      -  P 32
                        P 31 1 2  -  P 32 1 2
                        P 31 2 1  -  P 32 2 1