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Chapter 7: Structure Factors And Least Squares
- 7.1: Scope of the structure factors and least squares section
- 7.2: Refinement
- 7.3: Special positions
- 7.4: Atomic parameter refinement
- 7.5: Overall parameter refinement
- 7.6: Scale factor definitions
- 7.7: Structure factor calculation control list - LIST 23
- 7.8: Printing the SLFS control list
- 7.9: Special position constraints - \SPECIAL
- 7.10: Printing the special position information
- 7.11: Refinement directives - LIST 12
- 7.12: Obsolete Refinement directives
- 7.13: Defining the least squares matrix
- 7.14: Printing of LIST 12
- 7.15: Creating a null LIST 12
- 7.16: Processing of LIST 12
- 7.17: Restraints - LIST 16
- 7.18: Parameter, atom, bond and angle specifications
- 7.19: General restraints
- 7.20: General restraints
- 7.21: Debugging restraints
- 7.22: Printing the contents of LIST 16
- 7.23: Creating a null LIST 16
- 7.24: The special restraints - LIST 17
- 7.25: Printing and punching LIST 17
- 7.26: Creating a null LIST 17
- 7.27: Checking restraints - CHECK
- 7.28: Weighting schemes for refinement- LIST 4
- 7.29: Weighting for refinement against Fo
- 7.30: Weighting for refinement against Fsq
- 7.31: Weights stored in LIST 6
- 7.32: Weighting schemes
- 7.33: Dunitz Seiler weighting - scheme 13
- 7.34: Chebychev weighting schemes 10, 11
- 7.35: Robust-resistant weighting schemes 14, 15
- 7.36: Statistical Weights, 16
- 7.37: Printing LIST 4
- 7.38: Weighting the reflections - WEIGHT
- 7.39: Reflection restriction list - LIST 28
- 7.40: Creating a null LIST 28
- 7.41: Printing the contents of LIST 28
- 7.42: Structure Factor Least Squares Calculations - \SFLS
- 7.43: Definitions
- 7.44: Unstable refinements
- 7.45: Sorting of LIST 6 for structure factor calculations
- 7.46: Processing of the refinement directives
- 7.47: Analysis of residuals - \ANALYSE
- 7.48: Least squares absorption correction - \DIFABS
- 7.49: Internal workings
- 7.2: Refinement
[Top] [Index] Manuals generated on Wednesday 8 November 2006
7.1: Scope of the structure factors and least squares section
This section describes the necessary LISTS and explains how structure factor
calculation and
least squares refinement can be carried out.
Refinement
LIST 23 - Structure factor calculation control list (7.7)
SPECIAL - Special positions constraints (7.9)
LIST 12 - Input of refinement directives (7.11)
LIST 16 - Input of the restraints (7.17)
LIST 4 - Weighting the reflections (7.28)
LIST 28 - Reflection restriction list (7.39)
CHECK - Checking the refinement and restraint directives
SFLS - Structure factor least squares calculations (7.42)
ANALYSE - Systematic comparisons of Fo and Fc
DIFABS - Least squares absorption correction
Internal workings
LIST 22 - Refinement parameter map (7.49)
LIST 17 - Input of the special restraints (7.24)
LIST 11 - The least squares matrix (7.49)
LIST 24 - The least squares shift list (7.49)
LIST 26 - Restraints in internal format (7.49)
[Top] [Index] Manuals generated on Wednesday 8 November 2006
7.2: Refinement
Before a stucture factor-least squares calculation is performed, the
following lists must exist in the .DSC file
LIST 1 Cell parameters (section 4.2)
LIST 2 Symmetry inforamation (section 4.8)
LIST 3 Scattering factors (section 4.11)
LIST 4 Weighting scheme
LIST 5 Atomic and other model parameters (section 6.3)
LIST 6 Reflection data (section 6.3)
LIST 12 Refinement definitions (section 7.11)
LIST 16 Restraints (section 7.17)
LIST 17 Special position restraints (section 7.24)
LIST 23 Structure factor control list (section 7.7)
LIST 25 Twin laws, only for twinned refinements (section 10.0)
LIST 28 Reflection control list (section 7.39)
LISTS 12,16 and 17 (constraints 7.11, restraints
!flabel!LIST16! and special restraints !RLIST17
)
are not required if structure factors
are only going to be calculated.
The refinement directives specify which model
parameters are to be refined, and the control directives control the
terms in the minimisation function.
During structure factor least squares calculations, the partial derivatives with respect to each of the parameters is calculated for each structure factor and added into the 'normal equations'. This system of equations may be represented in matrix notation as :
A.x = b
WHERE :
A 'A' is a symmetric n*n matrix. an element
'A(i,j)' of 'A'is given by :
A(i,j) = Sum [ w(k)*Q(i,k)*Q(j,k) ] over k.
n number of parameters being refined.
k indicates reflection number 'k'.
w(k) weight of reflection k.
Q(i,k) the partial differential of Fc(k) with
respect to parameter i.
x a column vector of order n, containing
the shifts in the parameters.
b also a column vector, an element
of which is given by :
b(i) = Sum [ w(k)*DF(k)*Q(i,k) ] over k.
DF(k) delta for reflection k, given by :
DF(k) = [Fo(k) - Fc(k)]
As the matrix A is symmetric, only (n(n+1))/2 of its elements need to be calculated and stored, together with a few house keeping items.
In some cases, because of either storage or time considerations, it is impractical to use the full normal matrix A . In this situation, it is necessary to use a 'block diagonal approximation' to the full matrix, in which interactions between parameters which are known not to be highly correlated are ignored. The effect of ignoring such interactions is to leave blank areas of the full matrix, related symmetrically across the diagonal, which do not need to be stored or accumulated. A common (but not very efficient or stable) example of this approach is to place one atom in each of the blocks used to approximate the normal matrix, so that each block is of order either 4 (x, y, z and u[iso]) or 9 (x, y, z and the anisotropic thermal parameters).
One of the main purposes of the refinement directives is to describe the areas of the matrix A that are to be calculated. If the matrix A is approximated by m blocks of order n(1), n(2),.....n(m), The total amount of memory needed to hold the matrix and vector is:
Elements = 12 + 4*m + Sum n(i)*(5 +n(i))/2,
i = 1 to m
Currently (June 2003) elements=8,388,608, giving over 4000
parameters in a single block.
The formation of the blocks that are to be used to approximate the normal matrix A is controlled in the refinement directive list by a series of BLOCK directives, each of which contains the coordinates that are to be included in the newly specified block. Further control instructions for the current block may appear on subsequent directives until a new BLOCK directive is found, when the formation of another block with its associated parameters is started.
Two special directives are provided to allow for the most common cases required, full matrix refinement (a FULL directive) and one atom per block (a DIAGONAL directive). For all these cases only the parameters specified on the control directives and the following directives are refined.
Highly correleated parameters MUST be refined together. Refining them in different cycles or different blocks will lead to an incorrect structure.
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 must 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. This dummy temperature factor should not be confused with the 'overall temperature factor' which is a temperature factor that applies to all the atoms and is therefore just a convenience and requires no special treatment.
For further details, Computing Methods in Crystallography, edited by J. S. Rollett, page 50, and Crystalographic Computing, ed Ahmed, 1970, page 174.
Although it is possible to input an overall temperature factor as one of the overall parameters, it is not possible to use it under all circumstances. The structure factor routines always take the temperature factor of an individual atom as the value or values stored for that atom. If the overall temperature factor is to be refined, the system will ensure that the current value of the overall temperature factor is inserted for the temperature factor of all the atoms. When the new parameters are computed after the solution of the normal equations, this substitution is again made, so that all the atoms have the same overall isotropic temperature factor. However, if the overall temperature factor is not refined, or no refinement is done, the individual temperature factor for each atom will be used, and the overall temperature factor ignored.
It should be noted that if a set of anisotropic atoms are input with no
U[ISO] key and U[ISO] data, then the default value of 0.05 will be
inserted by the sfls routines. This implies that all such atoms are
isotropic, so that the anisotropic temperature factors will be set to
zero, and the calculation will proceed for isotropic atoms.
Several strategies are available for refining hydrogen atoms. Which you use is probably a matter of taste.
Note that the different methods can be mixed in any way, with some
hydrogens placed geometrically, and others refined.
R = 100*Sum[//Fo/-/Fc//]/Sum[/Fo/]
The summation is over all the reflections accepted by LIST 28. This
definition is used for both conventional and F-squared refinement.
100*Sqrt(Sum[ w(i)*D'(i)*D'(i) ]/SUM[ w(i)*Fo'(i)*Fo'(i) ])
D' = Fo'-Fc'
Fo' = Fo for normal refinement, Fsq for F-squared refinement.
Fc' = Fc for normal refinement, Fc*Fc for F-squared refinement.
MINFUNC = Sum[ w(i)*D(i)*D(i) ]
D', Fo', Fc' defined above.
[Top] [Index] Manuals generated on Wednesday 8 November 2006
7.3: Special positions
The second major purpose of the refinement directives is to allow for atoms on special positions. For example, the atom at the Wyckoff site H in the space group P6(3)/mmc (no. 194) has coordinates X,2X,Z . In a least squares refinement, the X and Y coordinates of this atom must be set to the same variable, i.e. they become equivalent. The command \SPECIAL (section 7.9) can be used to generate the necessary constraints or restraints, and may be invoked automatically before structure factor calculations by setting the appropriate parameters in LIST 23 (structure factor control settings, see section 7.7) The user can do this manually via the refinement directives, LIST 12. The relationship is set up by an EQUIVALENCE directive, which sets all the parameters on the directive to the same least squares parameter. In this example, it is also necessary to alter the contribution of the Y coordinates to the normal matrix by multiplying the derivatives by 2. This facility is provided by the WEIGHT directive, which should not be confused with the weight ascribed to each reflection in the refinement. For a full treatment of atoms on special positions, see Crystallographic Computing, edited by F. R. Ahmed, page 187, or Computing Methods in Crystallography, page 51.
Similar relationships also hold for the anisotropic temperature factors.
The relationships between the variable parameters in a refinement may also be defined by RESTRAINTS. These are held in LIST 17 (see 7.24), and are particularly usefull if a complex matrix has been defined (e.g. using RIDE, LINK, EQUIVALENCE, WEIGHT, BLOCK, GROUP or COMBINE).
[Top] [Index] Manuals generated on Wednesday 8 November 2006
7.4: Atomic parameter refinement
Atomic parameters may be specified in three different ways. Firstly, there is an IMPLICIT definition, in which parameters for all the atoms are specified simply by giving the appropriate key or keys.
Hydrogen atoms are automatically excluded from implicit definitions.
Secondly, there is an EXPLICIT definition, in which the parameters of one atom are specified by giving the atom name followed by the appropriate keys.
Lastly, the parameters for a continuous group of atoms in LIST 5 may be specified by an UNTIL sequence. This type of parameter definition is taken to be implicit.
Parameter definitions of all three types may appear on any directive in any desired combination.
EXAMPLE
LIST 5 contains FE(1) C(1) C(2) C(3) C(4) C(5) C(6) N(1)
\LIST 12
BLOCK X'S C(1,U[ISO]) UNTIL C(6) FE(1,U'S)
END
This refines x,y,z of all atoms, u[11]...u[12] of iron, and
u[iso] of the other atoms.
The following parameter keys may be given in an atom definition :
OCC X Y Z U[ISO] SIZE DECLINAT AZIMUTH U[11] U[22] U[33] U[23] U[13] U[12] X'S Indicating X,Y,Z U'S Indicating U[11],U[22],U[33],U[23],U[13],U[12] UII'S Indicating U[11],U[22],U[33] UIJ'S Indicating U[23],U[13],U[12]
[Top] [Index] Manuals generated on Wednesday 8 November 2006
7.5: Overall parameter refinement
Overall parameters, apart from the layer scale factors and the element scale factors, are specified simply by their keys. Such a specification is considered to be an explicit definition. The following overall parameter keys may be given :
SCALE OU[ISO] DU[ISO] POLARITY ENANTIO EXTPARAM
[Top] [Index] Manuals generated on Wednesday 8 November 2006
7.6: Scale factor definitions
The OVERALL scale factor is always applied to the structure factor calculation, though it need not necessarily be refined. LAYER and BATCH scale factors are applied only if indicated in LIST 23 (structure factor control settings, see section 7.7), and ELEMENT scales only if the crystal is marked as being twinned in LIST 13. Note that all of these scale factors can be expected to be correlated with each other, and the overall parameters.
The layer scale factors, batch scale factors and the element scale factors may be given in three different ways, all of which are considered to be explicit :
[Top] [Index] Manuals generated on Wednesday 8 November 2006
7.7: Structure factor calculation control list - LIST 23
\LIST 23 MODIFY ANOM= EXTINCT= LAYERSCALE= BATCHSCALE= PARTIAL= UPDATE= ENANTIO= MINIMISE NSINGULARITY= F-SQUARED= REFLECTIONS= RESTRAIN= REFINE SPECIAL= UPDATE= TOLERANCE= ALLCYCLES MIN-R= MAX-R= *-WR= *-SUMSQ= *-MINFUNC= U[MIN]= INTERCYCLE MIN-DR= MAX-DR= *-DWR= *-DSUMSQ= *-DMINFUNC= END
\LIST 23 MODIFY EXTINCTION=YES, ANOMALOUS=YES END
This LIST controls the structure factor calculation. The default calculation involves the minimum of computation (atomic parameters and overall sale factor). More extensive calculations have to be indicated by entries in this list. The presence of a parameter in the parameter list (LIST 5) does not automatically mean that it will be included in the structure factor calculation.
This list also controls the treatment of atoms on special positions, the use of F or Fsq, and the use of restraints.
The presence of information in the DSC file does
not ensure that it will be used by the structure factor
routines. Thus, the operations corresponding to
RESTRAIN , ANOMALOUS , EXTINCTION , PARTIAL , BATCHSCALES,
LAYERSCALES and ENANTIO are not performed unless they are explicitly
asked for in a LIST 23.
This directive controls modifications that can be applied to Fo and Fc.
NO - Default value
YES
If ANOMALOUS is YES , the imaginary part of the anomalous dispersion
correction, input in LIST 3 (see section 4.11, will be included in
the s.f.l.s. calculations.
For computational efficiency, it is recommended only to use the value YES
towards the end of a refinement. Note that the value YES should be used
even for centro-symmetric crystals if they contain a heavy atom.
NO - Default value
YES
If EXTINCTION is YES , the calculated structure factors are modified
to allow for the effects of extinction by the method of A. C. Larson.
See Atomic and Structural Parameters for the definition.
NO - Default value
YES
If either SCALE key is YES , the corresponding scale factors stored in
LIST 5 (the model parameters) are
applied to the reflection data. If this parameter is omitted, the
scale factors are not applied, even if they exist in LIST 5
NO - Default value
YES
If PARTIAL is YES , the fixed partial contributions stored in LIST 6
(section 5.3) are
added in during the calculation of Fc and the phase.
The partial contributions must already be present in LIST 6, and should
have the keys A-PART and B-PART . The atoms which have contributed to
the partial terms should be omitted from LIST 5 whenever PARTIAL is
YES .
NO - Default value
YES
If UPDATE is YES , the contributions of the atoms to A and B are
output to LIST 6 with the keys A-PART and B-PART . If UPDATE is
NO , its default value, the partial contributions are not changed
during structure factor calculations.
This requires that LIST 6 contain the keys A-PART and B-PART.
NO - Default value
YES
If ENANTIO is YES, then Fc is computed with
Fc = SQRT( (1-x)*F(h)**2 + x*F(-h)**2 )
Where x is the enantiopole parameter from LIST 5. Once the correct
enantiomer has been established, set this parameter back to NO.
This directive controls modifications made to the minimisation function during s.f.l.s.
NO - Default value
YES
If F-SQUARED is NO, the traditional minimisation function is:
Minimisation function = Sum[ w*(Fo - Fc)**2 ]
If F-SQUARED is YES , the minimisation function is:
Minimisation function = Sum[ w*(Fo**2 - Fc**2)**2 ]
If F-SQUARED is YES , the weights given by w in the above expression
are assumed to be on the correct scale and to refer to Fsq
rather than Fo's. Note that refinement can be against Fo or Fsq independent of
whether the input was Fo or Fsq.
NO
YES - Default value
If REFLECTIONS is YES, the reflections stored in LIST 6 (and subject to the
checks in LIST 28) are used for computing structure factors and the
derivatives added into the matrix if required.
If REFLECTIONS is NO, LIST 6 is not used, whether it is present or not. This setting could be used for refinement against restraints only. See the section DLS, 'Distance Least Squares'.
Floating origins are controlled by restraining the center of gravity of the structure along the axis to remain fixed.
X
SPECIAL = NO No action
= TEST Displays but does not store any restrictions
= ORIGIN Tests for and restrains floating origins
= RESTRAIN Creates and stores restraints
= CONSTRAIN (Default) Attempt to create constraints
UPDATE = NO Nothing updated
= OCCUPATION Site occupancies modified
= PARAMETERS (Default) All adjustable parameters modified
NO - Default value
YES
GROUPS is automatically set to YES if LIST 12
contains any GROUP directives. It forces the group derivatives
to be recalculated between each cycle or refinement.
Not currently used
SUMSQ = SQRT(SIGMA(SHIFT/ESD))/N)
The default values
of MIN-SUMSQ and MAX-SUMSQ are 0.03 and 10000.0, .
MIN-MINFUNC= MAX-MINFUNC= The minimisation function, on the scale of Fo, must lie between MIN-MINFUNC and MAX-MINFUNC, otherwise the refinement is terminated after the current cycle. The default values of MIN-MINFUNC and MAX-MINFUNC are 0.0 and 1000000000000000.0.
This directive refers to conditions that must be obeyed before the next cycle of least squares refinement can proceed. (A quantity undergoes a positive change if OLD - NEW is positive, not NEW - OLD ). The definitions are similar to ALLCYCLES. The abbreviation '*' represents MIN and MAX .
[Top] [Index] Manuals generated on Wednesday 8 November 2006
7.8: Printing the SLFS control list
[Top] [Index] Manuals generated on Wednesday 8 November 2006
7.9: Special position constraints - \SPECIAL
\SPECIAL ACTION= UPDATE= TOLERANCE=
END
\SPECIAL
END
\SPECIAL can be issued at any time to get information about atoms on special positions. However, normally it is called automatically by setting the SPECIAL keyword in LIST 23 (section 7.7).
Atoms on special positions may be constrained through LIST 12
(section !flabel!LIST12!), or restrained through LIST 17 (section !RLIST17
).
CRYSTALS will attempt to generate the special position conditions when
requested via the
SPECIAL command, and also update coordinates of atoms on
special positions.
If the RESTRAIN option is chosen, then the special conditions are imposed on the refinement by restraints, which are generated without reference to what is being specified in LIST 12, the refined parameter definition list.
If the CONSTRAIN option is chosen, then CRYSTALS examines the site restrictions as it processes LIST 12. If an atom on a special position is being refined without any user defined conditions (EQUIVALENCE, RIDE, LINK, COMBINE, GROUP, WEIGHT), and the related coordinates are in the same matrix block, then the internal representation of LIST 12 (LIST 22) is dynamically modified to include the necessary constraints. If the atom is already the object of a constraint, then LIST 12 cannot safely be modified, and the special condition is applied as a restraint. In either case, CRYSTALS warns the user about what is being done.
The origins of polar space groups are always fixed by restraints, since this produces a better conditioned matrix than one from just fixing atomic coordinates.
The UPDATE directive controls whether parameters of atoms near special positions will be modified to make them exact. The routine will update just the site occupancies, or the occupancies and the other variable parameters. The crystallographic site occupancy is held temporarily in the key SPARE, leaving the key OCC available for a refinable chemical occupancy. Take care if an atom refines onto (or off) a special position.
The function SPECIAL is actioned automatically for every round of least squares refinement. Its action is then determined by values held in LIST 23 (structure factor control, see section 7.7)
ACTION = NONE No action
= TEST Displays but does not store any restrictions
= ORIGIN Tests for and restrains floating origins
= RESTRAIN Creates and store a LIST 17
= CONSTRAIN Attempt to create constraints.
= LIST23 (Default) Takes the action defined in LIST 23
UPDATE = NONE Nothing updated
= OCCUPATION Site occupancies modified
= PARAMETERS All adjustable parameters modified
= LIST23 (Default) Takes action defined in LIST 23
TOLERANCE is the maximum separation, in Angstrom, between nominally equivalent sites. The default is 0.6A.
[Top] [Index] Manuals generated on Wednesday 8 November 2006
7.10: Printing the special position information
Force the atom parameter list (LIST 5) to be updated and send it to the PCH file.
\SPECIAL TEST PARAMETER
END
\PUNCH 5 (to get a listing with 5 decimal places)
END
[Top] [Index] Manuals generated on Wednesday 8 November 2006
7.11: Refinement directives - LIST 12
This list defines the parameters to be refined in the least squares calculation, and specifies relationships between those parameters.
\LIST 12 BLOCK PARAMETERS ... FIX PARAMETERS ... EQUIVALENCE PARAMETERS ... RIDE ATOM_PARAMETER SPECIFICATIONS ... LINK PARAMETER_LIST AND PARAMETER_LIST AND PARAMETER_LIST. COMBINE PARAMETERS_LIST AND PARAMETERS_LIST GROUP ATOM SPECIFICATIONS WEIGHT F1 PARAMETERS F2 PARAMETERS ... FULL PARAMETERS DIAGONAL PARAMETERS PLUS PARAMETERS END
\LIST 12 BLOCK SCALE X'S U'S END
x' = x1 + x2
x" = x1 - x2
where x1 and x2 are physical parameters,
and x' and x" are least squares parameters.
Such a re-parameterisation is useful for dealing with certain sorts of ill-
conditioning, such as that due to pseudo-symmetry,
of the normal matrix (see Edward Prince, Mathematical Techniques in
Crystallography and Material Science, 1982, Springer-Verlag, page 113).
NOTE that only one AND can be given.
Because of the linearisation algorithm used, some distortion of the group will occur if there are large parameter shifts. Use REGULARISE to re-form it.
[Top] [Index] Manuals generated on Wednesday 8 November 2006
7.12: Obsolete Refinement directives
The following directives may be removed in some future release.
BLOCK SCALE PARAMETERS
CONTINUE PARAMETERS after the BLOCK directive.
[Top] [Index] Manuals generated on Wednesday 8 November 2006
7.13: Defining the least squares matrix
Parameters may be referred to either implicitly, by just giving the parameter name (in which case that parameter is referenced for all atoms), or explicitly by specifying the parameter for an atom or group of atoms. All implicit specifications ignore H atoms.
e.g.
IMPLICIT: x, u's
EXPLICIT C(1,X), O(1,U'S) UNTIL O(14)
A parameter may not be referenced more than once either explicitly or implicitly. A parameter may be referenced both implicitly and explicitly, in which case the explicit reference takes precedence.
e.g.
BLOCK x's (implicit reference)
FIX Pb(1,y) (explicit reference)
This establishes the refinement of z,y,z for all atoms
except Pb(1), for which only x and z are refined.
EXAMPLES :
1. BLOCK SCALE X
FIX C(1,X) ALLOWED
2. BLOCK SCALE X
FIX X NOT ALLOWED
The refinement directives are read and stored on the disc. Before the structure factor least squares routines can use the information in LIST 12 (constraint directives), it is validated against LIST 5 (the model parameters) and stored symbolically as a LIST 22. This is done automatically by the SFLS routines (section 7.42), but the user can force the verification of LIST 12 by issuing the command \LIST 22.
[Top] [Index] Manuals generated on Wednesday 8 November 2006
7.14: Printing of LIST 12
LIST 12 may be listed with either
or
LIST 12 may be punched with
[Top] [Index] Manuals generated on Wednesday 8 November 2006
7.15: Creating a null LIST 12
A null LIST 12, containing no refinement directives, may be created with
[Top] [Index] Manuals generated on Wednesday 8 November 2006
7.16: Processing of LIST 12
LIST 12 is processed to greate a LIST 22 with
Examples.
1. Full matrix isotropic refinement of a structure without H atoms
\LIST 12
BLOCK SCALE X'S U[ISO]
END
2. Full matrix anisotropic of a structure with C(25) as the last
non-hydrogen, not refining the H atoms.
\LIST 12
BLOCK SCALE FIRST(X'S,U'S) UNTIL C(25)
END
3. Refine all positions, aniso non-H, iso H atoms
\LIST 12
BLOCK SCALE X'S
CONTINUE FIRST(U'S) UNTIL C(25)
CONTINUE H(1,U[ISO]) UNTIL LAST
END
4. Ride H(1) positions on C(21) positions, etc. There are 2 H on C(25)
\LIST 12
BLOCK SCALE X'S
CONTINUE FIRST(U'S) UNTIL C(25)
CONTINUE H(1,U[ISO]) UNTIL LAST
RIDE C(21,X'S) H(1,X'S)
RIDE C(22,X'S) H(2,X'S)
RIDE C(23,X'S) H(3,X'S)
RIDE C(24,X'S) H(4,X'S)
RIDE C(25,X'S) H(51,X'S) H(52,X'S)
END
5. A fragment is distributed over 2 sites. The fragments are
C(100) C(101) O(102) C(103) and C(200) C(201) O(202) C(203)
\LIST 12
BLOCK SCALE X'S
... ...
EQUIVALENCE C(100,OCC) UNTIL C(103) C(200,OCC) UNTIL C(203)
WEIGHT -1 C(200,OCC) UNTIL C(203)
END
[Top] [Index] Manuals generated on Wednesday 8 November 2006
7.17: Restraints - LIST 16
This list defines the restraint to be used as supplemental observations.
\LIST 16 DISTANCES VALUE, E.S.D= BOND1, BOND2 DISTANCES VALUE, E.S.D= MEAN BOND1, BOND2 DISTANCES VALUE, E.S.D= DIFFERENCE BOND1, BOND2 NONBONDED VALUE, POWERFACTOR= BOND1, BOND2 ANGLES VALUE, E.S.D= ANGLE1, ANGLE2 ANGLES VALUE, E.S.D= MEAN ANGLE1, ANGLE2 ANGLES VALUE, E.S.D= DIFFERENCE ANGLE1, ANGLE2 VIBRATIONS VALUE, E.S.D= BOND1, BOND2 U(IJ)'S VALUE, E.S.D= BOND1, BOND2 PLANAR E.S.D FOR 'ATOM SPECIFICATIONS' LIMIT E.S.D FOR 'PARAMETER SPECIFICATIONS' ORIGIN E.S.D FOR 'PARAMETER SPECIFICATIONS' SUM E.S.D FOR 'PARAMETER SPECIFICATIONS' AVERAGE E.S.D FOR 'PARAMETER SPECIFICATIONS' SAME BOND-ESD ANGLE-ESD FOR GROUP-1 AND GROUP-2 AND ... RESTRAIN VALUE, E.S.D= TEXT DEFINE NAME = TEXT COMPILER EXECUTION END
\LIST 16 DIST 1.39 , .01 = C(1) to C(2), C(2) to C(3), C(3) to C(4) DIST 0.0 , .01 = MEAN C(1) to C(2), C(2) to C(3), C(3) to C(4) VIBR 0.0 , .01 = C(1) to C(2), C(2) to C(3), C(3) to C(4) U(IJ) 0.0 , .02 = C(1) to C(2), C(2) to C(3), C(3) to C(4) PLANAR C(1) until C(6) SUM K(1,OCC), K(2,OCC) K(3,OCC) SUM ELEMENT SCALES (twin element scale factors) LIMIT U[11] U[22] U[33] END
The restraints that can be applied under this system are of a type originally described by J. Waser, Acta Cryst. 1963, 16, 1091. A good summary of the present facilities and aims is provided by J.S. Rollett in Crystallographic Computing, p170.
In this method of restraints, the user provides a set of physical or chemical restraints that are to be applied to the proposed model. These restraints are usually based upon observations of similar compounds (for example, bond lengths or bond angles) or upon known physical laws (for example, the difference in mean square displacement of two atoms along the bond that joins them). These restraints are not rigidly applied to the model, but each restraint has associated with it an e.s.d., which is used to calculate a weight so that the restraint can then be added into the normal equations. (The e.s.d.'s are provided on an absolute scale, and rescaled by the program onto the same scale as the xray data). In this way, the importance of the restraints, which are treated as extra observations, can be varied with respect to the importance of the X-ray data. If the structure is required to adhere closely to the proposed model, the restraints are given high weights (i.e. small e.s.d.'s) otherwise they can be given smaller weights.
If, at the end of a refinement, the restraints are not compatible with the Xray data, this is shown by a discrepancy between the requested value for the restraint, and that computed from the refine parameters. If this is found, the validity of the restraints that have been imposed should be carefully checked.
In order that the restraint routines should be completely general, each atom that is part of a restraint can be modified by a set of symmetry operators before the restraint is applied. (This is vital for molecules that lie across a symmetry element, as all the atoms that constitute the molecule are not present in LIST 5).
If a structure uses symmetry related atoms to form bonds, the command \DISTANCE with OUTPUT PUNCH=RESTRAIN can be used to set up a proforma restraints list, including symmetry codes. The distances and e.s.ds will have to be edited to the correct target values. Use appropriate values on the SELECT, INCLUDE and EXCLUDE directives for DISTANCE to tailor the generated list.
Note that restraints may be used without diffraction data, see the chapter 'Distance Least Squares' for examples.
[Top] [Index] Manuals generated on Wednesday 8 November 2006
7.18: Parameter, atom, bond and angle specifications
Composite parameter specifications are not permitted ( e.g. U's), atom specifications are as in Chapter 4.
Two atoms that are bonded together are defined in the following way :
atom1 to atom2,
'atom1' and 'atom2' are standard atom specifications as described
in chapter 4, and are separated from any other text on the line by
at least one space. If there is more than one bond specification on a
line, it may be separated from another by either a space or a comma.
The 'TO' is mandatory, and is terminated by
one or more spaces.
The definition of an angle is an extension of the definition of a bond:
atom1 to atom2 to atom3,
The angle is defined as the angle subtended at atom2 by atom1
and atom3.
The restraints routines apply all the required symmetry if specified in
an atom definition, while still
conserving the partial derivatives in their correct form.
The restraints routines regard all continuation directives as part of the original directive, so that the column of a character on a continuation directive will have had '80*n' added to it, where 'n' is the number of directives between the current continuation directive and the start of the directive. The ',', '=' signs and separator 'MEAN' are mandatory if shown in the definition.
DELTA = MEAN + VALUE - BOND CALCULATED.
DELTA = VALUE + BOND(N) - BOND(M)
Where BOND(N) occurs after BOND(M) in
the directive.
Each such restraint is added into the normal equations with an e.s.d. Of E.S.D. . However, as each bond is restrained to each of the bonds that follow it, (N*(N-1))/2 separate restraints are generated. Many of these restraints involve the same bond lengths and are thus not independent. To be strictly accurate, a non-diagonal weight matrix should be used with this restraint but such a facility is not available.
The letters DIFFERENCE are terminated by one or more spaces and may be abbreviated to DIFF.
weight = 10000*(requested/observed)**(powerfactor*12)
When the observed equals the requested distance,
the weight corresponds to an e.s.d.
of .01. If the requested is less than the observed, the weight is reduced
slowly as a function of the discrepancy. If the requested is greater than the
observed, the weight rises rapidly with discrepancy. The function is like the
repulsive part of a 6-12 energy expression, having greatest effect on
anomalously short contacts. Powerfactors of between 1 and 4 seem to be
suitable.
Note that the atoms defining a 'bond' need not actually be bonded, but merely serve to define a direction. For really bonded atoms, try an esd of .002; for 1-3 atoms or diagonals of phenyl groups, try .005.
Examples :
PLANAR C(1,2) UNTIL C(6) C(9) C(10,2,2)
PLANAR 0.05 C(1) C(2) UNTIL C(6)
PLANAR 0.05 FOR C(1) C(2) UNTIL C(6)
PLANAR FOR C(1,2) UNTIL C(6)
Example
ORIGIN Y
overall parameters e.g. SCALE,
all atomic parameters of one type e.g. X, Y, U[11],
atomic parameters of one type for a group of atoms
e.g. NA(1,OCC) UNTIL RB(6),
Examples :
SUM 0.0001 NA(1,OCC) UNTIL RB(6)
SUM LAYER SCALES
SAME BOND-ESD ANGLE-ESD FOR GRUOP-1 AND GROUP-2 AND ...# The first group on the card is the 'target' all following groups are mapped onto it (in order specified) and the distances and angles restrained - using the connectivity of the first group.
The first two arguments are the e.s.d for bond length restraints and the e.s.d for angle restraints. Groups are seperated by the word 'AND'. NOTE the andence of the usual '=' sign. I.E:
SAME 0.01, 0.1 FOR RESI(1) AND RESI(2)
maps all atoms in resi(1) onto all the atoms in resi(2) - note that
although this shorthand is appealing, the order of resi(1) and resi(2)
must be identical in List 5, although the residues may interpenetrate.
SAME 0.01 , 0.1
CONT C(17) C(18) H(183) H(182) H(181) AND
CONT C(17) C(18) H(182) H(181) H(183)
imposes 3-fold symmetry on a single methyl group.
SAME 0.01 , 0.1
CONT C(17) C(18) H(183) H(182) H(181) AND
CONT C(17) C(19) H(193) H(192) H(191) AND
CONT C(8) C(9) H(93) H(92) H(91) AND
CONT C(8) C(10) H(103) H(102) H(101) AND
CONT C(14) C(15) H(153) H(152) H(151) AND
CONT C(14) C(16) H(163) H(162) H(161)
restrains six methyl groups to have the same geometry as each
other. Combining the last two restraints would make all the
methyls have 3 fold symmetry, and all be the same.
Errors are generated if
1) the size of any of the groups on the SAME card is not the
same as the first group.
2) the element type in a group does not match the corresponding
element type in the first group.
Warnings are printed if there are zero bonds to any of the atoms
in the first group.
The comma separating the e.s.d arguments, and the 'FOR' separating the
e.s.d.s from the atom specifications are optional.
The second e.s.d is optional, the default is 0.1 degrees.
The first e.s.d is optional unless you wish to specify the second, the
default is 0.01 Angstroms.
List 41 (bonds) is loaded by the restraint generating routine, if it
does not exist an error will occur. (By default L41 is kept up to date
with the current model.)
[Top] [Index] Manuals generated on Wednesday 8 November 2006
7.19: General restraints
The 'general restraint' enables the user to write out a restraining equation explicitly. The system automatically calculates the value of the restraint and then evaluates the partial derivatives for each of the refinable parameters
Thes restraints look like simple fortran statements involving operators and operands.
(
)
** must be followed by an operand.
* must join two operands.
/ must join two operands.
+ must precede an operand.
- must precede an operand.
An operand may be a simple variable or
an expression enclosed in parentheses.
The operators above assume their normal FORTRAN meanings, and the combination of operands and operators is the same as in standard FORTRAN, except that all calculations are done in floating point.
TYPE(SERIAL,S,L,TX,TY,TZ,KEY)
KEY Specifies the relevant coordinate of the
atom. The KEY is regarded as an
obligatory parameter, but for the remaining
symmetry parameters, the drop
out rules and default
settings described under the atom definition may be
applied, so that the simplest form of
coordinate definition is TYPE(SERIAL,KEY), similar to a LIST 12
definition .
The usual parameter keys are recognized.
The system has pre-stored various arrays and variables holding useful crystallographic information, and users may not define or declare new arrays. The addressing is done in the normal Fortran manner, except that the element required must be specified by numeric arguments, and not variables. Thus A(3,1) is allowed, but A(I,J) is illegal.
A(6) the cell parameters (angles in radians)
CV real cell volume
AR(6) reciprocal cell parameters (angles in radians)
RCV reciprocal cell volume
G(3,3) real metric tensor
GR(3,3) reciprocal metric tensor
L(3,3) real orthogonalization matrix
LR(3,3) reciprocal orthogonalization matrix
CONV(3) conversion factor for the 'U(ij)'s' from 'U[iso]'
RIJ(6) coefficients needed to calculate [sin(theta)/l]**2
ANIS(6) coefficients needed to calculate the temperature
factor from the anisotropic temperature factors
SM(3,4,p) symmetry matrix 'p', where the translational
part is stored in sm(i,4,p)
SMI(3,4,p) inverse symmetry operators
NPLT(3,n) non-primitive lattice translations
PI 3.141......... etc.
TPI 2*Pi
TPIS 2*pi*pi
DTR conversion of degrees to radians
RTD conversion of radians to degrees
ZERO 0.0
The following functions
are also recognized :
SIN(ARG) COS(ARG) TAN(ARG) ACOS(ARG)
ASIN(ARG) ATAN(ARG) EXP(ARG) SQRT(ARG)
[Top] [Index] Manuals generated on Wednesday 8 November 2006
7.20: General restraints
There are two directives.
[Top] [Index] Manuals generated on Wednesday 8 November 2006
7.21: Debugging restraints
Debugging commands are available to help with the creation of general restraints
[Top] [Index] Manuals generated on Wednesday 8 November 2006
7.22: Printing the contents of LIST 16
The contents of LIST 16 may be listed with:
or
LIST 16 may be punched with:
[Top] [Index] Manuals generated on Wednesday 8 November 2006
7.23: Creating a null LIST 16
A null LIST 16, containing no restraints, may be created with
restrain a set of distances to 1.5 angstrom with an
e.s.d. of 0.03, note the use of symmetry indicators.
DISTANCE 1.5 , 0.03 = C(1) TO S(1) , C(1,5) TO S(1,5)
CONT S(1,7,1,-1) TO C(1,7,1,-1)
restrain the first distance above explicitly, by a user defined
restraint
RESTRAIN 1.5 , 0.03 = SQRT
CONT ((C(1,5,X)-S(1,5,X))*(C(1,5,X)-S(1,5,X))*G(1,1)
CONT +(C(1,5,X)-S(1,5,X))*(C(1,5,Y)-S(1,5,Y))*G(1,2)
CONT +(C(1,5,X)-S(1,5,X))*(C(1,5,Z)-S(1,5,Z))*G(1,3)
CONT +(C(1,5,Y)-S(1,5,Y))*(C(1,5,X)-S(1,5,X))*G(2,1)
CONT +(C(1,5,Y)-S(1,5,Y))*(C(1,5,Y)-S(1,5,Y))*G(2,2)
CONT +(C(1,5,Y)-S(1,5,Y))*(C(1,5,Z)-S(1,5,Z))*G(2,3)
CONT +(C(1,5,Z)-S(1,5,Z))*(C(1,5,X)-S(1,5,X))*G(3,1)
CONT +(C(1,5,Z)-S(1,5,Z))*(C(1,5,Y)-S(1,5,Y))*G(3,2)
CONT +(C(1,5,Z)-S(1,5,Z))*(C(1,5,Z)-S(1,5,Z))*G(3,3))
restrain some distances to their mean
DISTANCE 0.0 , 0.03 = MEAN O(1) TO S(1) O(2) TO S(1)
CONT O(1,2) TO S(1) O(1,7) TO S(1)
vibration restraints along a bond
VIBRATION 0.0 , 0.01 = S(1,5) TO O(1,5) S(1,7) TO C(1,7)
CONT S(1) TO O(1) S(1) TO C(1)
thermal similarity restraints
U(IJ) 0.0 , 0.01 = S(1,5) TO O(1,5) S(1,7) TO C(1,7)
CONT S(1) TO O(1) S(1) TO C(1)
user defined restraints to some of the U(IJ)'S. This might cure a npd
atom
RESTRAIN 0.0,0.01=S(1,U[11])-S(1,U[33])
RESTRAIN 0.0,0.01=S(1,U[12])
RESTRAIN 0.0,0.01=S(1,U[13])
RESTRAIN 0.0,0.01=S(1,U[23])
[Top] [Index] Manuals generated on Wednesday 8 November 2006
7.24: The special restraints - LIST 17
LIST 17 is generated automatically
by the command \SPECIAL (section 7.9),
and is intended to take care of floating
origins and atoms on special positions.
The user may create their own LIST 17, but this will be over written by
SPECIAL unless it this is deactivated.
[Top] [Index] Manuals generated on Wednesday 8 November 2006
7.25: Printing and punching LIST 17
or
It is punched with:
[Top] [Index] Manuals generated on Wednesday 8 November 2006
7.26: Creating a null LIST 17
A null LIST 17, containing no restraints, may be created with
[Top] [Index] Manuals generated on Wednesday 8 November 2006
7.27: Checking restraints - CHECK
The target values for the restraints can be checked against the calculated values by issuing the following command :
LOW Default value
HIGH
This command causes the restraints to be calculated,
but not added into the normal equations.
The observed and calculated values are output to the listing file,
with a summary on the terminal. If the LEVEL is LOW, only restraints
where the calculated value differs significantly from the target are
printed, otherwise all restraints are printed.
[Top] [Index] Manuals generated on Wednesday 8 November 2006
7.28: Weighting schemes for refinement- LIST 4
\LIST 4 SCHEME NUMBER= NPARAMETERS= TYPE= WEIGHT= MAXIMUM= PARAMETERS P= END \LIST 4 SCHEME 14 3 END
The weighting of least squares refinement is still very controversial. The matter is discussed at some length by Schwartzenbach et al in Statistical Descriptors, and further insights may be gleaned from Numerical Recipies. Weighting the refinement can serve several purposes, and the weighting may need to be changed as the refinement proceeds. The weighting of Fo and Fsq refinements will be different. To a first approximation,
w(Fsq) = w(Fo)/2Fo
note the problem as Fo approaches 0.0
Initially the analyst must choose a scheme which will hasten the rate of convergence, and reduce the risk of the refinement falling into a false minimum. Towards the end of the refinement, once all the parameters have been approximately refined, a different scheme will be necessary to generate reliable parameter s.u.s (e.s.d.s)
My advice (DJW,1996) is to use unit weights for Fo refinement (1./4Fsq for Fsq refinement) until the structure is fully parameterised, and then an empirical scheme for the final refinement. It seems that pure 'statistical' weights are rarely satisfactory. The crucial thing is to look at the analysis of variance (/ANALYSE). The weighted residual (see definition of Fo' etc above) w(Fo'-Fc')**2 should be invariant for any rational ranking of the data. If there are any trends, then either the model is wrong or the estimates of w are wrong. If the model is believed to be full parameterised and substantially correct, the trend in residual can be used to estimate the weights.
[Top] [Index] Manuals generated on Wednesday 8 November 2006
7.29: Weighting for refinement against Fo
This set of weighting schemes should be selected when the minimisation function that is to be used during the least squares process is given by :
SUM( w*(Fo - Fc)**2 )
Where the summation is over all the reflections.
[Top] [Index] Manuals generated on Wednesday 8 November 2006
7.30: Weighting for refinement against Fsq
Refinement against Fo or Fsq is also controversial. The controversy is not really concerned with negative observations, since Fo can be given the sign of Io. The real problem is that the error distribution for Fo is not the same as that of Fsq, and is not simply related to it for very weak reflections. However, the argument is academic, since the error estimates for Fsq are not really known.
CRYSTALS provides two different alternatives for the case in which the minimisation function is given by :
SUM( w*(Fo**2 - Fc**2)**2 )
In the first of these options, the weights are calculated normally for Fo,
and then converted so that they apply to Fsq
by the operation :
w' = w/(4*Fo*Fo)
Where w' is the weight for Fsq and w is the weight for Fo.
This option is selected by the parameter TYPE = 1/2Fo
in the SCHEME directive above.
For example, pseudo unit weights are selected by the input :
\LIST 4
SCHEME 9 0 1/2Fo
END
This option may be used with any of the weighting schemes above.
The second option also uses the weighting scheme types for Fo, except that Fsq is substituted for Fo in the equations. This option is selected by the parameter TYPE = Fo**2 in the SCHEME directive above. This choice would be suitable for the Chebychev weighting schemes.
NORMAL
1/2Fo
Fo**2
CHOOSE - Default value
The value of NORMAL indicates that the weighting scheme type
is for refinement against Fo.
If TYPE is 1/2Fo or Fo**2 the weighting scheme type is for
refinement against Fsq (see above).
If TYPE equals CHOOSE, one of the three previous type is chosen depending on the scheme number and the refinement type set in LIST 23 (structure factor control, see section 7.7).
W = 1/[1+Fo**WEIGHT].
Thus if WEIGHT is equal to zero, all the weights will be the same and equal
to 0.5.
The default value is 2.0
The parameters that are to be used to compute the weight for a given reflection are specified with this directive.
The parameters must always be provided on the scale of Fo, not on the scale of Fc. For example, the agreement analysis programs can work on the scale of Fc, so that constants derived from such output must be put on the scale of Fo by multiplying them by the scale factor in LIST 5 (the model parameters).
[Top] [Index] Manuals generated on Wednesday 8 November 2006
7.31: Weights stored in LIST 6
If w is the weight to be applied to a reflection in the least squares refinement, the value to be stored in LIST 6 (section 5.3) is sqrt(w), given the key SQRTW. If weights are computed by some external utiity, then either is should generate sqrt(w), or the values be converted after input to CRYSTALS - see scheme 5 below.
[Top] [Index] Manuals generated on Wednesday 8 November 2006
7.32: Weighting schemes
In the equations and explanations below, NP is an abbreviation of NPARAMETERS , the number of parameters required to define the weighting scheme, P(1) is the first such parameter and P(NP) the last parameter.
The available weighting schemes are :
1. sqrt(W) = Fo/P(1), Fo < P(1) OR Fo = P(1)
sqrt(W) = P(1)/Fo, Fo > P(1)
2. sqrt(W) = 1 , Fo < P(1) OR Fo = P(1)
sqrt(W) = P(1)/Fo, Fo > P(1)
3. sqrt(W) = sqrt(1/(1 + [(Fo - P(2))/P(1)]**2))
4. sqrt(W) = sqrt(1/[P(1) + Fo + P(2)*Fo**2 + . . + P(NP)*Fo**NP])
try P(1) = 2*FMIN and P(2) = 2/FMAX,
Cruickshank, Computing Methods and the Phase
Problem, Pepinsky et al, 1961, page 45
5. sqrt(W) = SQRT(data with the key 'SQRTW' in list 6)
6. sqrt(W) = (data with the key 'SQRTW' in list 6)
7. sqrt(W) = SQRT(1/(data with the key 'sigma(Fo)' in LIST 6))
8. sqrt(W) = 1/(DATA WITH THE KEY 'SIGMA(Fo)' IN LIST 6)
** remember that for schemes 7 & 8, LIST 6 **
** must store both weight and sigma. **
9. sqrt(W) = 1.0 (Unit weights, default)
10. sqrt(W) = sqrt(1.0/[A[0]*T[0]'(X) + A[1]*T[1]'(X) . .
+A[NP-1]*T[NP-1]'(X)])
Chebychev weighting - see below for details
11. As for 10, but only applying previously determined parameters.
12. sqrt(W) = sqrt([SIN(THETA)/LAMBDA]**P(1))
If NP is zero, a value of -1 is assumed for P(1) .
13. sqrt(W) = sqrt([weight] * exp[8*(p(1)/p(2))*(pi*s)**2])
Dunitz Seiler weighting - see below for details
14. sqrt(W) = sqrt(W' * (1. - (delta(F)/ 6* del(F)est)**2)**2)
W' = 1.0/[A[0]*T[0]'(X) + A[1]*T[1]'(X) . .
+A[NP-1]*T[NP-1]'(X)]
Robust-resistant refinement - see below
15. As for 14, but only applying previously determined parameters.
16. sqrt(W) = Sheldrick SHELX-97 weights (page 7-31). The P1-P6
correspond to Sheldricks parameters a-f, but are not
refined automatically. Fo and Fc replace Fosq and
Fcsq for Fo refinement.
Use 0.1 0 0 0 0 .333 to get Sheldrick defaults.
[Top] [Index] Manuals generated on Wednesday 8 November 2006
7.33: Dunitz Seiler weighting - scheme 13
[Top] [Index] Manuals generated on Wednesday 8 November 2006
7.34: Chebychev weighting schemes 10, 11
A[i] are the coefficients of a Chebyshev series in t[i]'(x), where x = Fo/Fo(max). (There is an account of CHEBYSHEV series in Computing Methods in Crystallography, edited by J.S. Rollett, p40). For this weighting scheme, the coefficients a[i] are calculated by the program using a least squares procedure which minimizes sum[(Fo - Fc)**4] over all the reflections. The resulting coefficients are stored in a new LIST 4 as weighting scheme type 11 (see below), and then used to calculate the weights for each of the reflections. It is recommended that several different values of NP are used (e.g 3 to 5), so that series of various orders are tested to see which gives the best fit. If negative or very small reciprocal weights are computed (i.e. the computed curve fall close to or crosses the ordinate axis), the parameter MAXIMUM can be used to restrict the maximum weight. For data on 'ordinary' scales, this will require a value of about 100. (This is best seen by computing an agreement analysis once the new weights have been calculated). The parameters P(i) need not be given, because they are to be computed. When the Chebyshev coefficients have been determined, p(1) is overwritten by the value determined for a[1]. (Carruthers and Watkin, Acta Cryst (1979) A35, 698). Scheme 10 generates the parameters needed for a scheme 11.
[Top] [Index] Manuals generated on Wednesday 8 November 2006
7.35: Robust-resistant weighting schemes 14, 15
[Top] [Index] Manuals generated on Wednesday 8 November 2006
7.36: Statistical Weights, 16
[Top] [Index] Manuals generated on Wednesday 8 November 2006
7.37: Printing LIST 4
of LIST 4 may be printed with:
There is no command for punching LIST 4.
Example
\ Weighting scheme type 10 (Chebyshev) with 3 parameters
\LIST 4
SCHEME NUMBER = 10,NPARAM = 3
END
[Top] [Index] Manuals generated on Wednesday 8 November 2006
7.38: Weighting the reflections - WEIGHT
If the weighting scheme is changed, new weights are automatically computed for the next structure factor calculation. The computation of weights can be forced at any time with \WEIGHT.
[Top] [Index] Manuals generated on Wednesday 8 November 2006
7.39: Reflection restriction list - LIST 28
\LIST 28 MINIMA COEFFICIENT(1)= COEFFICIENT(2)= ... MAXIMA COEFFICIENT(1)= COEFFICIENT(2)= ... READ NSLICES= NOMISSION= NCONDITION= SLICE P= Q= R= S= T= TYPE= OMIT H= K= L= CONDITION P= Q= R= S= T= TYPE SKIP STEP= END
\LIST 28 MINIMA RATIO=3 READ NOMIS=1 OMIT 2 0 0 END
LIST 6 (section 5.3) should contain all the reflections, including negative ones. LIST 28 can then be used to dynamically select which ones are to be omitted from a calculation. Several conditions may be specified, and ALL the conditions must be satisfied for a reflection to be used, i.e. the conditions are ANDed together.
It is also possible to specify individual reflections which are to be omitted.
TAKE CARE WHEN CHANGING LIST 28. If the conditions are relaxed, reflections
may become acceptable for which Fc and phase have not been recomputed
because they were rejected at an earlier stage. Recompute them all.
This defines the coefficients whose minimum values are to be restricted.
H K L /FO/
SQRTW FCALC PHASE A-PART
B-PART TBAR FOT ELEMENTS
SIGMA(F) BATCH INDICES BATCH/PHASE
SINTH/L**2 FO/FC JCODE SERIAL
RATIO THETA OMEGA CHI
PHI KAPPA PSI CORRECTIONS
FACTOR1 FACTOR2 FACTOR3 RATIO/JCODE
This defines the coefficients whose maximum values are
to be restricted. See MINIMA above.
This gives the number of conditional directives to follow.
This directive selects reflections to those giving values of (h*p + k*q + l*r) in the range s to t. The number of such directives is specified on the READ directive above. TYPE indicates whether the selected reflections are accepted or rejected. The records are processed in the order given. If a reflection matches the conditions, the specified action is taken and no further slice directives are considered. This enables quite fancy intersections to be specified.
For example, a single layer of reciprocal points, or a set of adjacent layers, oriented in any desired crystallographic direction, can be selected.
REJECT (default) causes rejection of selected reflections.
ACCEPT accepts reflections
This directive causes the reflection with the indices H, K, and L to be omitted.
This directive causes selection of reflections giving values of (h*p + k*q + l*r + s) exact multiples of 't'. TYPE indicates whether the selected reflections are accepted or rejected. The number of such directives is specified on the READ directive above. The records are processed in the order given. If a reflection matches the conditions, the specified action is taken and no further slice directives are considered. This enables quite fancy intersections to be specified.
For example, l odd layers can be rejected by setting 'r' and 's' to 1, 't' to 2.
REJECT (default) causes rejection of selected reflections.
ACCEPT accepts reflections
This directive can be used sample the data by skipping through LIST 6, (reflections, section 5.3) and may be usefull to speed up initial refinement.
[Top] [Index] Manuals generated on Wednesday 8 November 2006
7.40: Creating a null LIST 28
\LIST 28 END
Allows all the reflections in LIST 28 to be used.
[Top] [Index] Manuals generated on Wednesday 8 November 2006
7.41: Printing the contents of LIST 28
LIST 28 may be listed by the command :
There is no command for punching LIST 28.
Example 1
\LIST 28
\ Set the minimum ratio I/sigma(i) to 3.0,
\ a maximum Fo to 1000
\ and omit the 0 2 0 reflection
\
MINIMA Ratio=3
MAXIMA Fo=1000
READ NOMIS = 1
OMIT 0 2 0
END
Example 2. To reject h and k simultaneously even:
condit p=1 s=1 t=1 type=accept \lets ALL with h odd through
condit q=1 s=1 t=1 type=accept \lets ALL with k odd through
condit s=1 t=1 type=reject \rejects remaining.
Example 3. To reject all k=0, k=2:
slice q=1 s=0 t=0 type=reject
slice q=1 s=2 t=2 type=reject
Example 4. To reject all k=0, k=2 but keep the l=0 row:
slice r=1 s=0 t=0 type=accept
slice q=1 s=0 t=0 type=reject
slice q=1 s=2 t=2 type=reject
Example 5. To only allow specific zones, the ones wanted are
selected, and then the rest rejected, eg for h=0:
slice p=1 s=0 t=0 type=accept \ accept the h00 zone
slice p=1 q=1 r=1 s=-500 t=500 type=reject \ reject everything else
[Top] [Index] Manuals generated on Wednesday 8 November 2006
7.42: Structure Factor Least Squares Calculations - \SFLS
\SFLS INPUT= CALCULATE LIST= MAP= /Fo/= THRESHHOLD= SCALE LIST= MAP= /Fo/= REFINE LIST= MAP= /Fo/= PUNCH= MATRIX= MONITOR= INVERTOR= SHIFT KEY= KEY= MAXIMUM KEY= KEY= FORCE KEY= KEY= SOLVE MONITOR= MA=P /Fo/= PUNCH= MATRIX= VECTOR MONITOR= MAP= /Fo/= PUNCH= MATRIX= END
\SFLS REFINE REFINE END
[Top] [Index] Manuals generated on Wednesday 8 November 2006
7.43: Definitions
Minimisation function = Sum[ w*(Fo**2 - Fc**2)**2 ]
Minimisation function = Sum[ w*(Fo - Fc)**2 ]
R = 100*Sum[//Fo/-/Fc//]/Sum[/Fo/]
The summation is over all the reflections accepted by LIST 28. This
definition is used for both conventional and F-squared refinement.
100*Sqrt(Sum[ w(i)*D'(i)*D'(i) ]/SUM[ w(i)*Fo'(i)*Fo'(i) ])
Fo' = Fo for normal refinement, Fsq for F-squared refinement.
Fc' = Fc for normal refinement, Fc*Fc for F-squared refinement.
D' = Fo'-Fc'
The weighted R-factor stored in LIST 6 (section 5.3) and LIST 30
(section 4.17) is that computed
during a structure factor calculation. The conventional R-factor is
updated by either an SFLS calculation or a SUMMARY of LIST 6.
Fo' = Fo for normal refinement, Fo*Fo for F-squared refinement.
Fc' = Fc for normal refinement, Fc*Fc for F-squared refinement.
D' = Fo'-Fc'
MINFUNC = Sum[ w(i)*D(i)*D(i) ]
Good references to the theory and practice of structure factor least squares are in the chapters by J. S. Rollett and D. W. J. Cruickshank in Crystallographic Computing, edited by F. R. Ahmed, and chapters 4, 5 and 6 in Computing Methods in Crystallography, edited by J. S. Rollett.
[Top] [Index] Manuals generated on Wednesday 8 November 2006
7.44: Unstable refinements
If a refinement 'blows up', i.e. diverges rapidly, the user should
seek out the physical cause (wrong space group, pseudo symmetry,
incorrect data processing, disorder, twinning etc). If the cause of the
divergence is simply that the model is too inaccurate, the divergence
can by controlled by limiting the shifts applied in the first few
cycles. The modern way to do this is via 'shift limiting restraints'
(Marquardt modifier) in LIST 16. An older method was to use partial
shift factors. These are set up by directives to the \SFLS command
(section 7.42).
During the solution of the normal equations, the user may specify
that more or less than the whole calculated shift should be
applied.
Alternatively, the program can be instructed to scale the shifts so that
the maximum shift for any parameter group is limited to a given value.
(The SHIFT , MAXIMUM and FORCE directives).
[Top] [Index] Manuals generated on Wednesday 8 November 2006
7.45: Sorting of LIST 6 for structure factor calculations
During a structure factor least squares calculation, the values for the real and imaginary parts of A and B and their derivatives are computed and stored. These values are then taken and formed into Fc and its derivatives, which are added into the normal matrix. Between reflections, the values for A and B and their derivatives are retained. If the next reflection in LIST 6 (section 5.3) has a set of indices which are equivalent to the last reflection, the same values for the real and imaginary parts of A and B and their derivatives can be used.
This type of situation can arise either when anomalous scatterers are present, implying that F(h,k,l) is not equal to F(-h,-k,-l), or when an extinction parameter is being refined and formally equivalent reflections have different Fo values and mean path lengths. In this sort of case, the time for a structure factor calculation can be significantly reduced if reflections with symmetry related sets of indices are adjacent in LIST 6, when the conserved values of A and B can be used repeatedly.
In a similar way, during a structure factor calculation for a twinned crystal, the contribution and derivatives for each element are stored as they are calculated and then combined to produce /FCT/ when all the contributions have been accumulated. Between reflections this stored information is retained, so that if the next reflection contains contributions from elements with the same indices as the previous reflection, it is unnecessary to re-compute the A and B parts. Obviously, reflections with common contributors must again be adjacent in LIST 6, in which case a structure factor calculation, with or without least squares, takes only slightly longer than the corresponding normal calculation with the same number of observations.
The directives are carried out in the order in which they appear.
The directives REFINE, SCALE, and CALCULATE initiate cycles of S.F.L.S. calculations. If one of the directives SHIFT , MAXIMUM or FORCE is given following REFINE, a scaled shift will be applied to that cycle of refinement.
6 Default
7 Alternative reflection list
If CALCULATE is included with other commands within a single \SFLS block, it MUST BE the last command.
This directive indicates that structure factors should be calculated, but that no refinement of any type should be done. Structure factors are computed for every reflection and used to compute R and Rw for all data. R and Rw are also computed for reflections with I>threshold Sigma(I). The default value for the threshold is 4.
The directives SHIFT , MAXIMUM and FORCE may not be given before the next REFINE directive.
OFF - Default
MEDIUM
HIGH
The value OFF indicates that the
discrepancy for each reflection (/Fo-Fc/)/Fo is computed and if greater than
3*(overall R factor) from the previous cycle of structure factors, a warning
is printed. Only the first 25 such reflections are listed.
If the ENANTIOPOLE parameter is activated in LIST 23 (structure factor control, see section 7.7), sensitive reflections, for which /(F+)-(F-)/ .> .05 *((F+)+(F-)/2), are also listed.
If LIST is MEDIUM , the structure factors are listed as they are computed. The output contains h, k, l, Fo (on the scale of Fc), Fc, the phase and sin(theta)/lambda, the unweighted and weighted delta's. (Fo - Fc or Fo**2 - Fc**2, depending upon the type of refinement being done), and information which is useful when anomalous dispersion effects are present, and contains the real part of Fc (/Fc'/), the imaginary part of Fc (/Fc"/), the computed difference between /F(h,k,l)/**2 and /F(-h,-k,-l)/**2, and the calculated or theoretical Bijvoet ratio (t.b.r.).
When a twinned crystal structure is being refined, LIST = HIGH gives FoT and /FcT/ in place of Fo and Fc, respectively. Also, the contributions of each element to each reflection of a twinned crystal are listed. As well as /FcT/ and the indices, Fc, multiplied by the square root of the element scale factor, and the element number are also printed for each component under the column headed by /FC'/. This option is only obeyed if LIST 13 (section 4.13) indicates that a twinned crystal structure is being refined.
List MEDIUM and HIGH produces one line of output for each reflection.
NONE - Default value
PART
FULL
If MAP is PART , a list of core addresses is printed,
together with any unused locations. If MAP is FULL , the addresses and
contents of the areas of code claimed by each list as it is brought down
are printed on the line printer as the list is loaded.
This option produces reams of output and should never be used
except by programmers.
If MAP is NONE , its default value, a core map is
not printed.
FoT - Default value
Scaled-FoT
In the refinement of a twinned crystal, if /Fo/ = FoT , its
default value, the FoT is output as the data for the key /Fo/ , the
corresponding /FcT/ is output for Fc , and the phase is arbitrarily
set to zero. If /Fo/ is SCALED-FoT , the data for Fo , Fc
and PHASE contain an estimate of the required quantities for the
element in whose reference system the nominal indices are given, i.e.
estimates of the resolved data are produced.
This directive indicates that structure factors should be calculated and the overall scale factor should be refined. The directives SHIFT , MAXIMUM and FORCE may not be given before the next REFINE directive.
This directive indicates a complete structure factor least squares calculation.
NO - Default value
YES
If PUNCH is YES, LIST 5 is punched after the current cycle of
refinement.
NEW - Default value
OLD
If MATRIX is NEW, a new matrix is computed for the current cycle.
If MATRIX is OLD , the left hand side of the normal matrix is not accumulated during the cycle of refinement. Instead, the version that already exists is used with the new right hand sides. This option is particularly useful at the end of a refinement of a large structure when the left hand side does not change appreciably from cycle to cycle. It greatly reduces the time for a cycle.
LOW - Default value
MEDIUM
The MEDIUM listing outputs details about all parameters refined, and lists
the values, shifts and e.s.d.s of all parameters in LIST 5. The LOW
listing outputs information only for those l.s. parameters for which the
SHIFT RATIO exceeds 3.0, and/or the SHIFT/ESD exceeds 1.0 . Only those
atoms in LIST 5 containing one or more refinable parameters are listed.
CHOLESKI - Default value
EIGENVALUE
The default Choleski invertor is suitable for most well conditioned problems.
The alternative Eigenvalue invertor is suitable for ill-conditioned cases,
such as those involving pseudo-symmetry. It is slower than the Choleski
method and cannot handle such large normal matrices. The memory
required is almost three times that used for each block in the Cholesky
method.
This directive sets the shift factor for the specified cycle of
refinement. (The shift factor is the amount by which the calculated
shift is multiplied before it is applied to generate the new parameters).
For each of the parameters given by the KEYS on the directive,
the shift factor is changed to the value given by VALUE.
The = sign is not optional.
If more
than one shift directive ( SHIFT , MAXIMUM or FORCE ) is given for
the same parameter, only the last is obeyed.
The following KEYS are recognized :
GENERAL This refers to all the variable parameters
OVERALL This refers to the overall parameters
OCC U[ISO] X Y Z
U[11] U[22] U[33] U[23] U[13] U[12]
SPISO SPSIZE LINISO LINSIZE LINDEC LINAZI
RINGISO RINGSIZ RINGDEC RINGAZI
This is the default for GENERAL, OVERALL and
SPECIAL parameters, with default shift factors 1.0.
This directive is similar to the directive SHIFT above, except that the
maximum shift that is applied for the given parameters cannot be
greater than VALUE. The units of VALUE are conventional,
WITH x, y, z measured in angstrom, and ADPs in Angstrom sq. If none of
the shifts exceend VALUE, then they are applied unmodified.
This provides a
method of automatically scaling down the applied shifts if the matrix
inversion has become unstable. Shift limiting restraints (LIST 16) are a
more controlled alternative
The KEYS are the same as in SHIFT above, and this is the default
action for Occ, adps and positions, with maximal values:
OCC 1.0
U* 0.05 (Angstrom sq)
X's 1.0 (Angstom)
This is similar to MAXIMUM above, except that the
maximum shift is scaled to VALUE even if it is less than VALUE.
The KEYS are the same as in SHIFT above. There is no default
shift.
This is an obsolete feature, and will be removed at a later date.
This directive indicates that structure factors are to be calculated and then the shift vector stored in LIST 24 (see 7.49) is to be applied. This is used to apply a shift vector calculated from one of the eigenvalues of the normal matrix. Although no new matrix is produced by this directive, sufficient space must be allocated for the normal matrix, since it is loaded when the new coordinates are calculated.
[Top] [Index] Manuals generated on Wednesday 8 November 2006
7.46: Processing of the refinement directives
The program expands the CALCULATE, SCALE or REFINE directives into sub-directives. These sub-directives MUST NOT be given by a user:
1. \REFINE
Compute structure factors and
derivatives. No refinement is
actually done.
2. \SCALE
Calculate structure factors and
refine the overall scale factor.
3. \CALCULATE
Calculate structure factors.
4. \RESTRAIN
Apply the restraints stored in
the current lists 16 and 17.
5. \INVERT
Invert the current normal matrix
and store a shift list as list 24.
6. \SOLVE
Take the current list 5 (the model parameters)
and apply the shifts given in the current
list 24.
7. \NEWSHIFTS
Allocate space for list 24.
8. \CYCLENDS
CRYSTALS will warn you that LIST 11, the normal matrix, cannot be loaded. To 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
[Top] [Index] Manuals generated on Wednesday 8 November 2006
7.47: Analysis of residuals - \ANALYSE
\ANALYSE INPUT= FO INTERVAL= TYPE= SCALE= THETA INTERVAL= LIST LEVEL= LAYERSCALE AXIS= APPLY= ANALYSE= END
\ANALYSE LIST HIGH END
ANALYSE provides a comparison between Fo and Fc as a function of the indices, various parity groups, ranges of F and ranges of sin(theta)/lambda. For a well refined structure with suitable weights, <Fo>/<Fc> should be about unity for all ranges, and <wdeltasq> should also be about unity for all ranges. A serious imbalance in Fo/Fc may mean the structure is incomplete, or unsuitable data reduction (section 5.14). A systemstic trend in <wdeltasw> may mean unsuitable weights are being used.
The monitor listing is always just as a funtion of F. The output to the listing file is user controlled.
This routine will also compute approximate layer scale factors for data which has been collected by layers. These can be refined in the least squares to complete a refinement.
6 Default
7 Alternative reflection list
sqrt(Fc) - Default value
Fc
sqrt(Fo)
Fo
If TYPE is sqrt(Fc),
(its default value), the interval between successive F ranges is based
on 'the square root of Fc' Values of Fc in the interval
'0 to INTERVAL**2' will be analysed in the first range, Fc values that lie
in the range INTERVAL**2 to 4*INTERVAL**2 in the second and so on).
INTERVAL is thus the increment in the square root of Fc between
successive ranges and, in this case, has a default value of 1.
If TYPE is Fc , the interval between successive Fc ranges is
based on the value of Fc. In this case INTERVAL is the increment
in Fc and has a default value of 2.5.
Fo - Default value
Fc
If SCALE is Fo, the reflection information
is printed on the scale of Fo.
(This is useful as the weighting parameters in LIST 4 (section 7.28)
must be provided on the scale of Fo).
If SCALE is Fc, the reflection information is printed on the scale
of Fc.
This directive determines the interval between successive sin(theta)/lambda squared ranges.
This directive allows the results of layer scaling to be investigated.
NONE - Default value
H
K
L
The default value of NONE indicates that no layer scaling is to be
done. H, K and L indicate the axes up which layer scaling
is to be done.
NO - Default value
YES
When layer scaling has been completed and the results printed,
the calculated scale factors will be applied to the stored Fo data
if APPLY is YES . If APPLY is NO , its default setting,
then the new scales will not be applied to the data.
If AXIS is NONE , then APPLY is ignored.
NO
YES - Default value
If ANALYSE is YES, a second agreement analysis
will be performed after the layer scaling so that the results of the
new scales can be seen. (This is true whether the new scales are
applied or not, i.e. independent of the value of APPLY ).
In this way the effects of layer scaling can be seen without damaging
the data. If ANALYSE is NO , the second agreement analysis is
suppressed.
[Top] [Index] Manuals generated on Wednesday 8 November 2006
7.48: Least squares absorption correction - \DIFABS
\DIFABS ACTION= MODE= INPUT= CORRECTION THETA= DIFFRACTION GEOMETRY= MODE= END \DIFABS ACTION=NEW MODE=FC END
Although this is a least squares fitting technique for an arbitary model, it does not form part of the main refinement module. The DIFABS parameters cannot be refined simultaneously with the atomic parameters.
A low order term Fourier series is used to model an absorption surface for differences between the observed structure factors and those obtained from a structure factor calculation after isotropic least squares refinement. Spherical polar angles are used to define the incident and diffracted beam path directions so that each reflection is characterised by four angles - viz. PHI(p), MU(p), PHI(s), and MU(s). A theta-dependent correction is evaluated to allow for diffracted beams with different path lengths occurring at the same polar angles. A low order term Fourier series is used in Bragg angle THETA, but is highly correlated with the temperature factors, and not normally recommended. This version is general for any 4-circle diffractometer data collection geometry.
The quantity minimised is the sum of the squares of the residuals, Rj, where
Rj = ( //Fc/-/Fo//)wj
The weighting function, wj, used is derived from the overall scale factor, the counting statistics standard deviation, and the Lorentz-polarisation factor.
In the original implementation, the correction factor was applied to
Fo. This lead to criticism in the literature that the observations were
being tampered with. In the current implementaion in CRYSTALS, the
correction can be applied to Fo or Fc.
References:
N. Walker and D. Stuart, 1983, Acta Cryst., A39, 158 - 166.
The code is incorporated with the permission of Dr N. Walker
Implementation
The correction is evaluated using observed structure factors, /Fo/, corrected for Lorentz-polarisation effects and any decay in intensity standards during data collection, with systematically absent reflections removed. Since equivalent reflections will be measured at different diffractometer settings, the correction should be calculated and applied to the data set without any transformation of the reflection indices, and without symmetry- equivalent or Friedel-pair reflections being averaged. Calculated amplitudes must be obtained from the isotropic refinement of an as-complete a model as practical from the unique (merged) data set. Such a LIST 6 (reflections, section 5.3) will probably be unsuitable for Fourier or difference maps (since these expect a unique segment of data only) unless you then remerge the data. The best maps must be computed with the correction applied to Fo before the data is merged. In addition, the most reliable merging R factor (Rint) must be computed from corrected Fos.
In favourable cases, when the observed data is the unique segment plus a small redundant volume (e.g. often the -1 layers at Oxford), you may get away with applying the correction to normally (merged) processed data during structure development.
Once the structure is fully developed (ie all atoms found and partially refined with an extinction correction if necessary), data reduction should be repeated inhibiting all index transformations. New values of Fc must be computed from isotropic atoms (Use UEQUIV in \EDIT to recover equivalent isotropic temperature factors, and then do a few cylces of isotropic refinement) and the DIFABS correction applied to Fc. Anisotropic refinement can be computed to completion (including optimisation of weights) using unmerged data. If you wish to see an absorption correctd Rint and compute a final difference map, the data must be re-merged. Use DIFABS with MODE = TRANSFER to move the correction onto Fo before transforming indices, sorting and merging the data.
6 Default
7 Alternative reflection list
TEST - Computes the correction, but does not apply it
UPDATE - Tries to update LIST 6
NEW - DEFAULT. Creates new LIST 6
If UPDATE is specified, the stored values of Fo are over written. If NEW is specified, a new LIST 6 is written to disc. The disc will be extended sufficiently to accommodate the new list.
FO - Applies the correction to Fo
FC - Applies the correction to Fc
TRANSFER - Applies the inverse of the Fc correction to Fo
Controls whether a theta-dependent correction is to be applied. - NOT RECOMMENDED.
NO - Default value
YES
Controls the geometry used for data collection to be input.
CAD4 - Default value
SYNTEX-P1
SYNTEX-P21
PICKER - Picker FACS-I
PW1100 - Philips PW1100
BISECTING - Default value
PARALLEL
GENERAL
This example assumes that there are no equivalent reflections.
\DIFABS
DIFFRACTION GEOMETRY=SYNTEX-P1
END
This example demonstrates a total re-processing of the data, including converting atoms to isotropic if they have previously been refined anisotropically. Note that a theta dependent correction from International Tables is applied during data reduction (see also section
5.14). The theta
dependant correction in DIFABS is ill-conditioned and unstable.
\ save the contents of the old dsc file
\PURGE NEW
END
\ Connect the reflection file to HKLI
\OPEN HKLI ZNCPD.HKL
\ Use an \HKLI command to apply the tabulated theta correction
\HKLI
READ NCOEF=12 FORMAT=FIXED UNIT=HKLI F'S=FSQ CHECK=NO
INPUT H K L /FO/ SIGMA(/FO/) JCODE SERIAL BATCH THETA PHI OMEGA KAPPA
FORMAT (5X,3F4.0,F9.0,F7.0,F4.0,F9.0,F4.0,4F7.2)
STORE NCOEF=6
OUTPUT INDICES /FO/ BATCH RATIO/JCODE SIGMA(/FO/) CORRECTIONS SERIAL
ABSORPTION PHI=NO THETA=YES PRINT=NONE
THETA 16
THETAVALUES
CONT 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75
THETACURVE
CONT 3.61 3.60 3.58 3.54 3.50 3.44 3.37 3.30
CONT 3.23 3.16 3.09 3.02 2.96 2.91 2.86 2.82
END
\LP
END
\SYSTEMATIC
\ preserve the original indices
STORE NEWINDICES=NO
END
\SORT
END
\ copy from workfile to disk
\LIST 6
READ TYPE=COPY
END
\ unit weights
\LIST 4
END
\WEIGHT
END
\EDIT
UEQUIV FIRST UNTIL LAST
END
\LIST 28
MINIMA RATIO = 3.0
END
\SFLS
SCALE
END
\ assume there are no H atoms
\LIST 12
FULL FIRST(U[ISO]) UNTIL LAST
END
\SFLS
REFINE
REFINE
CALC
END
\LIST 28
\ remove all restrictions to get Fcs.
END
\DIFABS UPDATE FC
END
\ Complete anisotropic refinement, produce publication tables etc
\LIST 12
FULL X'S U'S
END
\LIST 28
MINIMA RATIO=3
END
\SFLS
REFINE
.....
\CIF
END
\ reprocess data so that it can be merged for the final
\ difference map
\DIFABS UPDATE TRANSFER
END
\SYST
END
\MERGE
END
\FOURIER
\ etc etc etc ---
[Top] [Index] Manuals generated on Wednesday 8 November 2006
7.49: Internal workings
SOme understanding of the internal data management in CRYSTALS may
help the user to sort out unexplained failures.
This list contains the refinement directives in internal format and it can only be generated by the computer. After the refinement directives have been read in, they are stored on the disc in binary format ready for processing. Before the structure factor least squares routines can use the information in LIST 12, it is necessary to convert them to a LIST 22.
If the conversion fails, or the input of LIST 5 or LIST 12 is in error, LIST 22 will be marked as an error list, and any job that attempts to reference LIST 22 will terminate in error.
For complex LIST 12s, i.e. those
containing EQUIVALENCE, LINK, RIDE, GROUP, WEIGHT or COMBINE, the user is
strongly advised to issue \LIST 22 and then \PRINT 22, and look at the
LIST 22
generated. The ouput, which is set out like a LIST 5, shows the
relationship between the physical and the least squares parameters.
The matrix that is produced by the structure factor least squares process is stored on the disc as a LIST 11. This list may be massive, so it is wise to purge the disk regularly with large structures. To recover the maximum space, delete the LIST 11 before purging.
\DISK
DELETE 11
END
\PURGE
END
LIST 11 is printed by :
When the normal matrix produced by the least squares process has been inverted, a set of shifts is calculated, suitably scaled if necessary, to apply to the atomic parameters. These shifts are output to the disc as a LIST 24, and then applied by the routines that compute the new parameters. List 24 can only be generated in the machine.
This list contains the restraints in internal format. Before the structure factor least squares routines can use the information in LIST 16 and 17, it is necessary to convert it to an internal format held in LIST 26.
If this operation fails, or the input of LIST 12 or LIST 16
goes wrong, LIST 26 will be marked as an error list, and any job
that attempts to reference LIST 26 will terminate in error.
[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 ]
