chem cryst
CRYSTALS manual
University of Oxford

Crystals Manual

Chapter 9: Analysis Of Results

9.1: Scope of this section of the user guide

9.2: Analysis of residuals - \ANALYSE

9.3: Distance angles calculations - \DISTANCES

9.4: Distance-angles symmetry operations

9.5: Void Location - \VOIDS

9.6: TLS analysis, best planes and lines - \GEOMETRY

9.7: Torsion angles - \TORSION

9.8: Publication listing of the atomic parameters - \PARAMETERS

9.9: Publication listing of reflection data - \REFLECTIONS

9.10: Summary of data lists - \SUMMARY

9.11: CIF lists - \CIF

9.12: Graphics - CAMERON

  Analysis of residuals                          ANALYSE
  Distance and angles calculations               DISTANCES
  Void search                                    VOIDS
  Global Geometry (planes,lines & libration)     GEOMETRY
  Torsion angles                                 TORSION
  Publication listing of the atomic parameters   PARAMETERS
  Publication listing of the reflections         REFLECTIONS
  Summary of data lists                          SUMMARY
  CIF files                                      CIF
  Graphics                                       CAMERON
 

This analyses the residual, Fo-Fc, for systematic trends, which might either indiacate an incomplete model, or an unsatisfactory weighting scheme. It is described in the chapter Structure Factors and Least Squares.

 

  \DISTANCES INPUTLIST=
  OUTPUT MONITOR=  LIST= PUNCH= HESD=
  SELECT ALLDIST= COORD= SORTED= TYPE= RANGE= SYMM= TRANS=
  LIMITS DMINIMUM= DMAXIMUM= AMINIMUM= AMAXIMUM=
  E.S.D.S COMPUTE= CELL=
  INCLUDE atoms
  EXCLUDE atoms
  ONLY atoms
  PIVOT atoms
  BONDED atoms
  END
 
  \DIST
  E.S.D YES
  END
 

The distance angles routine is completely general with respect to crystal and lattice symmetry. For distances, the user may either use elemental radii specified in LIST 29 (see section 4.15 for input details), or specify minimum and maximum limits, and the program then calculates all possible contacts within these limits. All symmetry operations and unit cell translations are automatically generated. For the angles, LIST 29 or a separate set of distance limits may be used. At a given atom, angles are then calculated between all the atoms which bond to the central atom within the given limits.

The distance-angles routines can calculate the estimated standard deviations of the distances and angles that they produce. These e.s.d.'s are based upon the matrix stored in LIST 11 (see section 7.49), and as many variance and covariance terms as are present are used. (For a full matrix, therefore, the full variance-covariance matrix is used). For this reason, the calculation of e.s.d.'s takes at least ten times as long as a simple distance angles calculation.

When a set of e.s.d.'s are calculated, the variance-covariance matrix for the cell parameters (LIST 31, section 4.5) may also be used.
 

       5   -  Default value
       10
 

       OFF         -  no output
       DISTANCES   -  only monitors distances. (Default)
       ANGLES      -  only monitors angles.
       ALL         -  monitors distances and angles.
 

       OFF
       LOW   -  Default
       HIGH
 

 No H   No 

       ALL      - (Default) Output all bond length and angle standard
                  uncertainties (if requested) to the CIF (if requested),
                  including those of bonds to fixed atoms (i.e. to atoms on
                  special positions, or to atoms that are not refined).
       NONFIXED - Exclude standard uncertainties of bond distances and angles
                  to Hydrogen atoms that have not been refined. (as
                  required by Acta's notes for authors).
 

       NO   -  Default value
       YES
 

       NO   -  Default value
       YES
 

       NO   -  Default value
       YES
 

       ALL   -  Default value
       INTRA
       INTER
 

       COVALENT      Use 'covalent' radii from LIST 29.
       VANDERWAALS.  Use 'VanderWaals' radii from LIST 29, but angles are
                     suppressed.
       IONIC.        Use 'ionic' radii from LIST 29.
       LIMITS.       Use specified or default ranges set by the LIMIT directive.
 

       SPACEGROUP  -  Default value. The full spacegroup symmetry is used in
                                     all computations
       PATTERSON.     A centre of symmetry in introduced, and the translational
                      parts of the symmetry operators are dropped.
       NONE.          Only the identity operator is used.
 

       NO   -  Default value
       YES
 

       NO   -  Default value
       YES
 

Accompanying each atom in a distance or angle calculation with LIST equal to HIGH are the symmetry operators that are necessary to bring the atom into the correct position in the cell to make a contact with the central atom. These symmetry operations are divided into six parts, which are indicated by five flags. These are explained in the section on Atomic and Structural Parameters.

  \
  \ distances from 0 to 2.5
  \ angles from 0 to 2.0
  \ the e.s.d.'s of the distances and angles are calculated
  \ distances from each atom to all other atoms are printed
  \ transformed coordinates are printed
  \ the distances are sorted in order of increasing magnitude
  \
  \DISTANCES
  SELECT ALL=YES,COORD=YES,SORT=YES,RANGE=LIMITS
  LIMITS DMAX=2.5, AMAX=2.0
  E.S.D. YES
  END
 

  \DIST
  EXCLUDE ALL
  ONLY C(1) C(3) C(4)
  END
 

  \VOIDS INPUTLIST=
  DISTANCE
  TOLERANCE
  CONTACTS
  RESOLUTION
  END
 
  \VOIDS
  DISTANCE 2.2
  END
 

This utility searches for the asymmetric unit for points which lie outside the known atoms. The 'radii' of the known atoms is independent of type, and in an input value. A pseudo atom in inserted at every point on a search grid outside the known atoms. The pseudo atoms are given a 'TYPE' dependant upon the number of neighbouring pseudo atoms. Atoms of type R are at the core of large voids, type L are intermediate, and M at the surface.
 

       5   -  Default value
       10
 

  \GEOMETRY INPUTLIST=
   ATOMS  W(1)  SPECIFICATION(1)  W(2)  SPECIFICATION(2) .
   PLANE
   LINE
   AXES
   TLS 
   EXECUTE
   EVALUATE  ATOM SPECIFICATIONS . . . .
   REPLACE ATOM SPECIFICATIONS . . .
   PUNCH
   SAVE
   DIHEDRAL  NP(1)  AND  NP(2)
   QUIT
   CENTRE   X=, Y=, Z=
   REJECT   NV=
   LIMITS   VALUE=   RATIO= 
   MODL L(11), L(22) L(33) L(23) L(13) L(12)
   MODT T(11), T(22) T(33) T(23) T(13) T(12)
   ZEROS
   DISTANCES  DL=   AL=
   ANGLES  AL=
   PLOT
   END
 

  \GEOMETRY
  ATOMS FIRST UNTIL LAST
  PLANE
  EXECUTE
  SAVE
  ATOMS FIRST UNTIL LAST
  TLS
  EXECUTE
  ANGLE 1 AND 2
  EXECUTE
  DISTANCES
  END
 

GEOMETRY is used for computing the following global derived parameters:

       Centroid (centre of gravity)
       Inertial Tensor
       Best Plane
       Best Line
       Shape Indices
       Principal Axes of adps
       Librational and Translational Thermal Tensors
       Dihedral Angles
 

It replaces the old \MOLAX, \AXES and \ANISO commands

PLANE & LINE are used for computing the principal axes of inertia through groups of atoms using the routines described in Computing Methods in Crystallography, edited by J. S. Rollett, Pergamon Press, 1965, p67-68.

The best plane for a series of N atoms whose positions have varying reliability, such that they can be assigned weights, w(1), w(2), . . . w(n), is defined as that for which the sum of the squares of the distances (in angstroms) of the atoms from the plane, multiplied by the weights, w(i), of the atomic positions, is a minimum. Note that the normal to the 'worst plane' is the 'best line', and if masses are used for weights, then the calculation gives the principal inertial axes.

The atomic positions are taken from LIST 5, possibly modified by symmetry information, to compute inertial axes & deviations of atoms from the planes or lines.

Each time a line or plane is computed, the direction cosines of the relevent axis are stored as AXIS number 'n'. The dihedral angles between these axes can be computed. Three geometry indices are also computed. The geometry is best described by the index closest to unity. (Mingos,D.P.M & Rohl,A.L., J.Chwm.Soc. Dalton Trans (1991) pp 3419 - 3425)

TLS. This routine calculates the overall rigid-body motion tensors T, L, S (Shoemaker and Trueblood, Acta Cryst. B24, 63, 1968) by a least-squares fit to the individual anisotropic temperature factor components, together with librational corrections to bond lengths and angles.

Shoemaker and Trueblood's conventions and reductions are followed throughout; in particular, the trace of S, which is indeterminant, is set to zero. The program therefore determines 20 overall tensor components - the upper triangles of T and L together with the whole of S apart from S(33). (See also: Johnson in Crystallographic Computing, ed R.Ahmed, Munksgaard, 1970, pp 207-219)

Even when the trace-of-S singularity has been removed, however, the nature of the rigid body problem is such that ill-conditioned and singular normal matrices are much more common than in structure refinement and the program therefore proceeds via the eigenvalues and eigenvectors of the normal matrix. In most cases the largest and smallest eigenvalues are output for inspection, but if the ratio of these quantities is less than the LIMITing RATIO, a full eigenvalue/vector listing is produced. Further, if any eigenvalue is itself less than the LIMITing VALUE, the corresponding parameter combination is set to zero, thus removing the near- singularity. These actions can be modified by the use of the LIMIT and REJECT directives described below. If the TLS calcuation cannot be stabilised by means of these filters, the user can modify either T, L or S directly before applying the REPLACE or PUNCH commands. Though here is some danger in this, especially if the supposed rigid group is infact flexible, it may be preferable to using a model yielding negative vibrational or librational amplitudes.

The direction cosines of the principal axis of L are stored for use in inter-axis angle comutations.

Immediate execution of a directive can be forced by issuing an EXECUTE directive.
 

       5   -  Default value
       10
 

  \
  \ these instructions compute a plane
  \ involving n(1),n(2),n(3) and c(1), and
  \ prints the co-ordinates of all the atoms with
  \ respect to this plane.  The positions of the
  \ nitrogen atoms have double weight
  \
  \GEOMETRY
  ATOMS 2 N(1) UNTIL N(3)  1 C(1) C(2)
  PLANE
  EVALUATE ALL
  \
  \ these instructions calculate another plane,
  \ printing only the co-ordinates of c(5) with respect to
  \ the second plane.  The angle between the two planes
  \ is then calculated
  \
  ATOMS C(1) S(1) N(1)
  PLANE
  EVALUATE C(5)
  DIHEDRAL 1 AND 2
  END
 

  \TORSION INPUTLIST=
  ATOMS  SPECIFICATIONS
  PUBLICATION  PRINT=
  END
 
  \TORSION
  ATOM C(1) C(2) C(3) C(4)
  END
 

The routines described in this section calculate torsion angles which are defined as follows. The torsion angle about the bond j-k is the angle the bond k-l is rotated from the ijk plane. It is positive when, on looking from ij to kl, the rotation is clockwise.

The program uses atomic positions taken from LIST 5. These can be modified by the space group symmetry operators stored in LIST 2 (space group information, see section 4.8)
 

       5   -  Default value
       10
 

       NO   -  DEFAULT.  There is no publication listing
       YES    There is a publication listing sent to the PUNCH file
       CIF    The listing is in CIF format
 

  Example.
  \ the torsion angle about C(3)-C(4) is calculated
  \ two torsion angles about C(4)-C(5) are calculated
  \
  \TORSION
  ATOMS N(2) C(3) C(4) C(5)
  ATOMS C(3) C(4) C(5) C(6) O(1)
  END
 

  \PARAMETERS
  LAYOUT INSET= ATOM= DOUBLE= CHOOSE= FLOAT= NCHAR= NLINE= LISTAXES= ESD=
  COORDINATES NCHAR= NDECIMAL= SELECT= TYPE= DISPLAY= PRINT= PUNCH=
  U'S NCHAR= NDEC= SELECT= TYPE= DISPLAY= PRINT= PUNCH=
  END
 

  \PARAMETERS
  LAYOUT ATOM-NAME=6,DOUBLE=YES
  END
 

This routine sends the atomic parameters to the PUNCH file in a suitable format for publication or binding into a thesis. As well as the current atomic parameters in LIST 5, the estimated standard deviations derived from the least squares normal matrix are also printed. THIS ROUTINE WILL NOT WORK if LIST 5 is modified in any way since the last round of refinement. If any changes, including renaming, are made, a further round of refinement must be done. If you wish to preserve parameter values, and create a valid matrix without changing the parameter values, compute a refinement cycle but set all the shifts to zero.

       \SFLS
       REFINE
       SHIFT GENERAL = 0.0
       END
 

The output is in two halves, the first containing the positional coordinates and any isotropic temperature factors, and the second containing all the anisotropic temperature parameters.

For the first part, a page is split into 6 separate fields. The first field is blank, and is an offset so that the information is centred on the page. The remaining fields contain the atom type and serial number, the three positional parameters, and a temperature factor. This will be the value of U(iso) with its e.s.d for isotropic atoms, otherwise U(equiv), without an e.s.d, for anisotropic atoms. U(equiv) is not simply related to the diagonal elements of U(aniso), and may be computed as either the arithmetic or geometric mean of the principal axes of the ellipsoid. See \SET UEQUIV in the chapter on IMMEDIATE commands. The width of each type of field may be altered by the user, using respectively the INSET , ATOM-NAME , and NCHARACTER parameters. The default length of a page of this type of output is that required for A4 paper.

The second part contains the anisotropic temperature factors, and each page is split into eight fields. As for the atomic coordinates, the first field is blank and represents an offset. The second field contains the atom type and serial number, and the remaining six fields contain the components of the anisotropic temperature factors. The width of each type of field may be adjusted by the user, using respectively the INSET , ATOM-NAME and NCHARACTER parameters. If a different value for INSET or ATOM-NAME is required in the first and second parts of the output, the job must be run twice. Depending upon the width across the page, the second part of the output occupies one sheet of A4 paper either across the page or down the page.

For both types of output, the user can select double spacing down the page with the DOUBLE parameter. Similarly for each of the numeric fields, the user can choose the number of decimal places to be printed (the NDECIMAL parameter), and whether the numbers are printed as integers or in floating point with a decimal point. (The FLOATING parameter). The e.s.d.'s are printed to the same accuracy as the atomic parameters, so that if the chosen field is too small and an e.s.d. appears to be zero, it will be omitted in exactly the same way as for a parameter that has not been refined. A parameter printed with 4 decimal places might thus appear as :

  0.0123(4)
  OR
     123(4)
 

Depending upon the format. In either case, the numbers are right justified in their field.

As an alternative to the user selecting the number of decimal places that should be printed, it is possible to get the program to choose the number of decimal places required for each parameter automatically. (The CHOOSE parameter). If the parameters are to be printed in floating point, the number of decimal places is chosen so that the e.s.d. Can be represented as a one digit number in the last decimal place. For numbers that are to be printed as integers, the field used is never less than that given by the NDECIMAL parameter. If the required field is larger than that defined by these s, a decimal point is inserted and the required number of extra digits is output. For example, if the number of decimal places required is four, but the e.s.d. is too small, it would appear as :

  0.12345(6)
  OR
   1234.5(6)
 

Depending upon whether floating point or integer output was required. For either type, if the parameter has not been refined, the number of decimal places is that given by the NDECIMAL instruction.

Since this routine prints the e.s.d.'s, it is vital that the least squares matrix (LIST 11, see section 7.49) belongs to the current LIST 5 (the model parameters). If LIST 5 has been modified in any way since the last Least Squares, this routine will abort.

When anisotropic atoms are present in LIST 5, U[EQUIV] is calculated according to the current setting of \SET UEQUIV.

 

  NO   No output is displayed on the terminal.
  YES  Output is displayed on the terminal.
 

  NO       No output is sent to the listing file
  YES      Output is sent to the listing file
 

  NO       No output is sent to the punch file
  YES      Output is sent to the punch file
  CIF      Output is in CIF format
 

  OFF   No output is displayed on the terminal.
  HIGH  Output is displayed on the terminal.
 

  NO       No output is sent to the listing file
  YES      Output is sent to the listing file
 

  NO       No output is sent to the punch file
  YES      Output is sent to the punch file
  CIF      Output is in CIF format
 

 \REFLECTIONS INPUT=
 LAYOUT NCOLUMNS= NLINES= INSET= NSPACE= SCALE= NCHARACTER=
 OUTPUT PRINT= PUNCH= LIST28=
 END
 

This routine prints the reflection data in LIST 6 (section 5.3) in a suitable format for publication or binding into a thesis. The information printed falls into one or more columns, each of which contains h, k, l, /Fo/, /Fc/, and the phase angle in degrees. Each column is 18 characters wide. Although the user has no control over the contents of each column, it is possible to vary the number of blank spaces at the start of each line, the number of columns across the page, the number of spaces between successive columns, and the number of lines per page. (The INSET , NCOLUMNS , NSPACE and NLINES parameters, respectively). /Fo/ and /Fc/ are both put on the same scale of /Fc/, using the scale factor in LIST 5, and both these two numbers may be modified by a scaling constant before they are printed. (The SCALE parameter). However, all the values of both /Fo/ and /Fc/ must be less than 10000 when they are printed.

LIST 28 is used for checking whether or not to print a reflection. Remember that if LIST 28 was used to reject some reflections when structure factors were last calculated, removing these restrictions before printing LIST 6 will mean that some reflections will have incorrect values of Fc and phase.

       6      Default
       7      Alternative reflection list
 

  NO       No output is sent to the listing file
  YES      Output is sent to the listing file
 

       NO       No output is sent to the punch file
       YES      Output is sent to the punch file
 

  \SUMMARY OF= TYPE= LEVEL=
 
  \SUMMARY LIST 5 HIGH
  END
  \SUMMARY EVERYTHING
  END
 

This command produces a summary on the terminal of the contents of a list. Use \PRINT if you need full details.
 

       n  a four-digit number giving the number of references to follow. 
          Other text on the line is ignored.
 Next items repeated 'n' times:
       m  a three digit number preceded by a 'hash' symbol used as an 
          identifier for the reference. The numbers must be unique, not 
          necessarily in any order, with the largest one equal to 'n'
       
       The full reference. References are put in the file in alphabetic 
       order.
 

 (1) if one adopts esd values to one digit precision (rule of 9) the values
 
       5.548(1)      1.453(2)  3.921(3)  1.2287(8)  are acceptable.
 
 (2) if one permits two digits precision with a limit of 19 (rule of 19)...
 
       5.5483(9)     1.4532(16)  3.921(3)  1.2287(8)  are acceptable.
 
 (3) if one permits two digits precision with a limit of 29 (rule of 29)...
 
       5.5483(9)     1.4532(16)  3.9214(28)  1.2287(8)  are acceptable.