Crystals Manual

Chapter 12: Obsolete Commands

12.1: Obsolete Commands

12.2: Least squares best planes and lines - \MOLAX

12.3: Thermal displacement parameter analysis - \ANISO

12.4: Principal atomic displacement directions - \AXES

12.5: Structure factors for a group of trial models - \TRIAL

The following Commands were available in earlier versions of CRYSTALS. They are retained for compatibility reasons, but have been suppressed or superceeded by new commands.
 

 Least squares best planes                      MOLAX
 Thermal displacement parameter analysis        ANISO
 Principal atomic displacement directions       AXES
 Structure factors for a group of trial models  TRIAL

 \MOLAX INPUTLIST=
 EXECUTE
 PUNCH
 ATOMS  W(1)  SPECIFICATION(1)  W(2)  SPECIFICATION(2) .
 PLOT
 PLANE
 LINE
 ANGLE  NP(1)  AND  NP(2)
 EVALUATE  ATOM SPECIFICATIONS . . . .
 REPLACE ATOM SPECIFICATIONS . . .
 SAVE
 QUIT
 END

 \MOLAX
 ATOM FIRST UNTIL LAST
 PLANE
 SAVE
 END

MOLAX is 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. It can be used to compute best lines and planes, and produce simple line printer plots of the atoms.

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, and the angles between normals to these planes or axes. Shape indices (Mingos M.P. and Rohl A.L. J Chem Soc Dalton Trans (1991) 3419) are computed.

Each time a line or plane is computed, the direction cosines of the relevent axis are stored as AXIS number 'n'. The 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)

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

      5   -  Default value
      10

 \
 \ these instructions define a plane
 \ involving n(1),n(2),c(1),c(2) and n(3) and
 \ prints the co-ordinates of all the atoms with
 \ respect to this plane.  the positions of the
 \ nitrogen atoms have double weight
 \
 \MOLAX
 ATOMS 2 N(1) UNTIL N(3)  1 C(1) C(2)
 PLANE
 EVALUATE ALL
 \
 \ this set of directives also calculates 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)
 ANGLE 1 AND 2
 END

 \ANISO INPUTLIST
 EXECUTE
 ATOMS   WEIGHT ATOM SPECIFICATIONS
 CENTRE   X=, Y=, Z=
 REJECT   NV=
 LIMITS   VALUE=   RATIO=
 TLS
 EVALUATE ATOM SPECIFICATIONS
 REPLACE ATOM SPECIFICATIONS . . .
 SAVE
 QUIT
 AXES
 DISTANCES  DL=   AL=
 ANGLES  AL=
 END

 \ANISO
 ATOM C(1) UNTIL C(6)
 TLS
 SAVE
 END

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).

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.
 

      5   -  Default value
      10

 \ANISO
 ATOMS O(12) UNTIL LAST
 AXES
 TLS
 DISTANCES
 END

 \AXES INPUTLIST=
 END

\AXES
 END

This routine calculates the magnitudes and directions of the principal axes of the atomic dispacement ellipsoid of an anisotropic atom. Atoms which are isotropic are ignored. Atoms with a negative principal axis generate a warning. The output gives the mean square displacement in angstroms squared along each of the principal axes, together with the direction cosines with respect to the orthogonalized axes and with respect to the real cell axes.

This routine can also be called from \ANISO to get the axes of specified atoms only.
 

      5   -  Default value
      10

This procedure is currently unsupported. It is kept in the code because it offers an opportunity for a new programmer to experiment with improved 'COST' functions.

At some stage during a structure determination, the orientation of a group of atoms may be known, but not their position in the unit cell. The routine described in this section provides a rapid method of calculating structure factors for a group of atoms at a series of points that fall on a grid in the unit cell. The algorithm used is similar to that employed in the slant fourier, (see the section of the user guide on 'Fourier routines') and is as follows :

The A part of the structure factor for the reflection with indices given by the vector H may be written as :

       A(H) = SUM[ G.SUM[ COS2PI(H'.S.X + H'.T) ] ]

With a similar expression for the B part. ( G Is the required form factor, modified by the temperature factor expression). Conventionally, the inner sum runs over the various symmetry operators that define the space group, and the outer sum runs over the number of atoms in the asymmetric unit. However, if the summation order is changed, it is possible to accumulate sums for all the atoms for each symmetry position :

       P(H,S) = SUM[ G.COS2PI(H'.S.X + H'.T) ]

With a similar expression for Q(H,S) for the B part. It is now possible to use a recurrence relationship for P and Q to give :

       P(H,S,2) = P(H,S,1)*2*COS2PI(H'.S.DX) - P(H,S,0)
 and
       Q(H,S,2) = Q(H,S,1)*2*COS2PI(H'.S.DX) - Q(H,S,0)

P(H,S,0) Is the original value of P for the symmetry position S for the reflection given by H . P(H,S,1) Is the corresponding value of P after a vector DX has been added to each set of coordinates, and P(H,S,2) is the corresponding term after a vector 2*DX has been added. Similar relationships hold for the Q terms. After the initial eight cosine and sine terms have been calculated, it is possible to calculate structure factors very rapidly as the group of atoms is moved about the unit cell, using the relationships given above.

Apart from an array to hold each section through the unit cell, it is necessary to store the eight cosine and sine terms, together with the three step vector cosines, for each reflection for each symmetry position. Because this imposes certain storage limitations, it is necessary to restrict the number of reflections that are used. In practice it is only the large reflections that must agree, and so the user is required to input a minimum Fo value, below which reflections are not used. The function that is displayed for each grid point is given by :

       SCALE*SUM[ Fo*Fc ]

Accordingly, the largest value printed represents the most likely solution. The SCALE term may be calculated by the program to give numbers in a reasonable range, or input by the user. The time for each calculation is proportional to the number of reflections used, the number of symmetry operators in LIST 2, and the number of grid points calculated. (A calculation in a non-centro space group takes twice as long as a calculation in the corresponding centro space group). The atoms to be moved around are taken directly from LIST 5.

      X1 = X0 + X-COMPONENT
      Y1 = Y0 + Y-COMPONENT
      Z1 = Z0 + Z-COMPONENT

 \TITLE MOVE 2 SULPHURS AROUND
 \LIST 5
 READ NATOM=2
 ATOM S 1 X=0.00 0.15 0.37
 ATOM S 2 X=0.13 0.05 0.24
 \ call '\trial' with a min. fO of 250
 \TRIAL
 MAP Fo-MIN=250
 \ initial origin shift
 DISPLACEMENT 0 0 -0.3
 \ plot half of y down the page
 DOWN 26 0 0.02 0
 \ plot half of x across the page
 ACROSS 26 0.02 0 0
 \ plot half of z up the page negatively
 THROUGH 51 0 0 -0.01
 \FINISH