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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
- 12.2: Least squares best planes and lines - \MOLAX
[Top] [Index] Manuals generated on Wednesday 8 November 2006
12.1: Obsolete Commands
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
[Top] [Index] Manuals generated on Wednesday 8 November 2006
12.2: Least squares best planes and lines - \MOLAX
\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
This forces the execution of preceding directives.
This directive causes the orthogonal coordinates of the atoms of any plane or
line computed in following tasks to be output to the 'punch' file.
This specifies atoms to be used in the calculation of the
best plane.
W(1) Is the weight assigned to the atoms
contained in the first atom specification, W(2) is the weight
assigned to the second group of atoms, and so on.
If W(1) is omitted, a default value of 1 is used,
but any other W(I) term applies to all the atoms following it,
until another W is found or the end of the directive is
encountered.
At least one ATOM directive must precede each PLANE or PLOT directive.
An ATOM directive will over-rule an immediately preceding ATOM directive. If an
input line is not long enough for the full atom list, use CONTINUE.
This directive causes the orthogonal coordinates of the atoms of any plane or
line computed or EVALUATED in the current task to be output to the 'punch'
file.
This directive, (or PLANE or LINE)
must follow immediately after an ATOM directive and
causes the calculation of inertial axes.
Details of the computation are suppressed on the Monitor,
but a line drawing projected onto the best plane is produced.
MOLAX Can thus be used as a means of displaying some or all
of the atoms in a structure.
This directive, (or LINE or PLOT)
must follow immediately after an ATOM directive and
causes the calculation of a least squares best plane.
This directive, (or PLANE or PLOT)
must follow immediately after an ATOM directive and
causes the calculation of a least squares best line.
If present, thus directive must follow at least
two ATOMS/PLANE (ATOMS/LINE, ATOMS/PLOT) directive sequences.
It causes the program
to calculate the angle between the axes with serial numbers
NP(1) and NP(2) .
The AND must be present.
If present, this directive
must appear after a PLANE, LINE or PLOT directive,
and causes the co-ordinates of the atoms specified
to be calculated and printed with respect to the least squares axial system.
if present, this directive
must appear after a PLANE, LINE or PLOT directive,
and causes the co-ordinates of the atoms specified to be modified so that
they lie on the previously defined plane. The LIST 5 in core is immediately
updated, so that the new coordinates will be used for any subsequent
computation. A LIST 5 is only written to the disc on a satisfactory exit from
MOLAX.
This directive causes the latest plane defining matrix and
vector to be stored in LIST 20. A LIST 20 is only written to the disc on
a satisfactory exit from MOLAX.
This directive abandons the calculation without modifying the disc LISTs.
\ \ 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
[Top] [Index] Manuals generated on Wednesday 8 November 2006
12.3: Thermal displacement parameter analysis - \ANISO
\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
This causes immediate execution of the previous directive, otherwise
directives are executed on input of a new directive (or END).
This parameter specifies the set of atoms to be used for the following calculation.
WEIGHT. The default weight of 1.0 is used for all atoms except those
following a WEIGHT value. Any decimal number on the ATOM directive
is taken as a weight and applied to any following atoms.
A subsequent atom directive over rules all previous atom directives.
If the full atom specification cannot be got on one directive, use CONTINUE.
The atom specifications are in the usual form with symmetry
operators and UNTIL sequences permitted. An ATOM directive resets the CENTRE to
its default value, 0,0,0.
This directive specifies the centre of libration,
in crystal fractions, to be used in the original derivation of
the overall motion tensors. The program derives and uses a unique
origin at a later stage in the calculations. This directive
is optional, the default centre being (0,0,0).
If a centre of (0,0,0) is given or set by default, the program computes
and uses the mean position of the given atoms, INCLUDING any which are
isotropic, even though these are not used to compute TLS. The stored CENTRE
is updated during TLS, and a second TLS computation may be performed using
this new value as CENTRE. This may help stabilise certain forms of
ill-conditioning.
Overrides normal action and sets the parameter combination
corresponding to eigenvector number nv to zero.
Eigenvectors are numbered in ascending order of their eigenvalues,
so that nv
is in the range 1 to 20 inclusive and will usually have been obtained
from a full eigenvalue/vector listing produced in
a previous run.
If an eigenvalue is less than VALUE or its size is less than
RATIO * (the next bigger), it is eliminated from the analysis.
VALUE is currently .000001 and RATIO .01 .
This causes the TLS calculation to be initiated. It MUST have been preceded
by an ATOM directive.
This may be used after a successfull TLS calculation to list Ucalcs for
the specified atoms. The atom list is not modified.
If present, his directive
must appear after a TLS directive,
and causes the co-ordinates of the atoms specified to be modified so that
they have U's defined by the current T, L, and S matrices.
The LIST 5 in core is immediately
updated, so that the new coordinates will be used for any subsequent
computation if a new ATOM directive is issued.
The updated LIST 5 is only written to the disc on a satisfactory exit from
ANISO.
This directive is optional. If it follows a TLS directive, it
causes the latest L matrix and CENTRE to be stored in LIST 20. If it
follows an AXES directive, the direction cosines and centre if the ellipse FOR
THE LAST ATOM are stored in LIST 20.
A LIST 20 is only written to the disc on
a satisfactory exit from ANISO.
This directive abandons the calculation without modifying the disc LISTs.
This directive (like \AXES) computes the principal axis lengths
and directions for the atoms specified on a preceding ATOM directive.
This directive calculates all interatomic distances less than
DL angstroms with librational corrections. If this directive is omitted,
no distances are calculated; if DL is absent, a default value of 1.8 is
inserted. If AL is present, angles between atoms separated by less than AL
angstroms are computed.
This directive calculates angles between all bonds less than AL angstroms. If this directive is omitted, no angles are calculated; if AL is absent, a default value of 1.8 is inserted.
*********************** WARNING *************************
The directive DISTANCE may only be followed by ATOM, EXECUTE, or END.
\ANISO ATOMS O(12) UNTIL LAST AXES TLS DISTANCES END
[Top] [Index] Manuals generated on Wednesday 8 November 2006
12.4: Principal atomic displacement directions - \AXES
\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.
This command initiates the routine for calculating the principal atomic vibration directions, and requires no other directives.
5 - Default value
10
The default value is 5.
[Top] [Index] Manuals generated on Wednesday 8 November 2006
12.5: Structure factors for a group of trial models - \TRIAL
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.
This is the command which initiates the routine to calculate structure factors for a group of trial models.
This directive determines which reflections will be used in the calculations and how the map will be printed.
This directive defines a vector which is added to each set of coordinates in LIST 5 before the structure factor calculation starts. DELTA-X , DELTA-Y And DELTA-Z thus correspond to an initial origin shift for the group in LIST 5.
The default values for these parameters are zero, indicating no initial origin shift before the structure factor calculation.
This directive specifies the printing down the page.
X1 = X0 + X-COMPONENT
Y1 = Y0 + Y-COMPONENT
Z1 = Z0 + Z-COMPONENT
Where 1 and 0 define successive points down the page.
These are the corresponding values across the page.
These are the values that define the change from section to section.
These shift vectors allow any change of position for the group to be plotted out.
\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
[Introduction To The System | Definitions And Conventions | The Crystals Database | Initial Data Input | Reflection Data Input | Atomic And Structural Parameters | Structure Factors And Least Squares | Fourier Routines | Analysis Of Results | Twinned Crystals | Matrix Calculations | Obsolete Commands]
