Crystals Primer

Chapter 8: Refinement

8.1: Structure factor control list

8.2: Refinement definition

8.3: Special positions

8.4: Treatment of reflections

8.5: Weighting the reflections

8.6: Restraints

8.7: Least Squares

CRYSTALS was originally developed to perform difficult or complex refinements, and was subsequently modified to simplify the treatment of routine cases. There are seven components of a refinement strategy.
 

The default values in this list are usually suitable. Some switches may be reset automatically by CRYSTALS. You will be told when this happens.

For disordered structures, you may need to inhibit special position checking, or reduce the tolerance for atom matching.

  e.g.
      !\LIST 23
      !REFINE         SPECIAL=TEST      UPDATE=NO
      !END
or
      !\LIST 23
      !REFINE        TOLERANCE = .1
      !END

Defining the parameters to be refined. This information is held separately from the atom coordinates, in LIST 12. This list also contains information about the matrix blocking, constrained parameters, riding parameters, rigid groups and other special processes.

The release version of CRYSTALS will refine about 5,000 atoms by large -block diagonal methods, or 1400 selected parameters full matrix. The parameters to be refined are specified in LIST 12. See the note above on atomic parameters and parameter names.

  e.g.
      !\LIST 12
      !FULL     X'S U[ISO]
      !END


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


      !\LIST 12
      !FULL     X'S
      !CONTINUE     FIRST(U'S) UNTIL C(30)
      !CONTINUE     H(1,U[ISO]) UNTIL LAST
      !END

The first example gives full matrix isotropic refinement, the second full matrix anisotropic refinement. The third is a mixed aniso-iso refinement. FULL always implies refinement of the over all scale factor. The matrix will be large, so you may need to extend the .DSC file if automatic extension is not enabled. See the sections on ADVANCED REFINEMENT and on CRYSINIT files.
 

Treatment of atoms on special positions. This can be done automatically, by a switch in LIST 23, on demand by issuing \SPECIAL, or manually in LIST 12.

CRYSTALS automatically applies the constraints or restraints necessary for the treatment of atoms on special positions, and adjusts the site occupancy. Default actions are set in LIST 23, and if these are disabled they can be set on demand with \SPECIAL. The user needs only be concerned with partial occupancy due to disorder, etc.
 

 e.g.
      !\LIST 28
      !MINIMA RATIO=3.0
      !READ NOMISSION=2
      !OMIT 2 0 0
      !OMIT 0 2 2
      !END

The default, unit, weights are suitable for initial refinement.

      !\LIST 4
      !END

Once the model is fully parameterised (all atoms found) and more or less converged, alternative weights should be chosen to obtain the most realistic estimated standard deviations. The SCRIPT \SCRIPT WEIGHTS gives some help in the choice. Otherwise, for F refinement try

      !\LIST 4
      !SCHEME NUMBER = 14, NPARAM=3
      !END
      !\WEIGHT
      !END
      !\ANALYSE
      !END

For Fsq refinement, try

      !\LIST 4
      !SCHEME 16 NPARAM=3
      !PARAM .001 3.0 1.0
      !END

The ANALYSE command produces an analysis of residuals. The column headed <w*deltasq> should be more or less constant for suitable weights.
 

Treatment of restraints. These are stored in LIST 16, and applied or not depending on a switch in LIST 23.

CRYSTALS offers many restraints. They are stored in symbolic form in LIST 16, and are converted to computable format by \LIST 26.

 e.g.
   !\LIST 16
   !DIST       1.39, .01 = C(10) TO C(11), C(10) TO C(15)
   !DIST       0.0 , .01 = MEAN  C(1) TO C(2), C(1) TO C(6)
   !PLANAR     C(101) UNTIL C(106)
   !VIBRATION  0.0 , .01 = MEAN  C(1) TO C(2), C(1) TO C(6)
   !SUM        Ca(1,OCC) FE(1,OCC) Al(1,OCC)
   !END
   !\CHECK
   !END

The CHECK command produces a listing of the observed and calculated values for the restraints. The atom specifications can include symmetry indicators.

The distance and angle restraints using the mean value of the observed molecular parameters is especially valuable for imposing molecular symmetry without the user being required to know the target values.

 e.g. for a phenyl group bonded though C(1)
       !\LIST 16
       !DIST 0.0, .001 = MEAN C(1) to C(2), C(1) TO C(6)
       !DIST 0.0, .001 = MEAN C(2) to C(3), C(6) TO C(5)
       !DIST 0.0, .001 = MEAN C(3) to C(4), C(5) TO C(4)
       !ANGLE 0.0, .02 = MEAN C(1) to C(2) to C(3),
       !CONTINUE           C(1) to C(6) to C(5)
       !ANGLE 0.0, .02 = MEAN C(2) to C(3) to C(4),
       !CONTINUE           C(6) to C(5) to C(4)
       !END

If there are several phenyl groups, all equivalent bonds can be added into the same mean.
 

Least squares are initiated once the preparations are completed. For large structures it is sensible to do the preparations interactively, and run the LS in batch. If refinement converges or diverges before the specified number of cycles, refinement is terminated. The user can always demand one cycle.

      !\SFLS
      !SCALE
      !REFINE
      !REFINE
      !CALCULATE
      !END