Crystals Manual

Chapter 6: Atomic And Structural Parameters

6.1: Scope of the atomic and structural parameters Section

6.2: Specifications of atoms and other parameters

6.3: Input of atoms and other parameters - LIST 5

6.4: Printing and punching list 5

6.5: Editing structural parameters - \EDIT

6.6: Reorganisation of lists 5 and 10 - \REGROUP

6.7: Repositioning of atoms - \COLLECT

6.8: Conversion of temperature factors - \CONVERT

6.9: Hydrogen placing - \HYDROGENS

6.10: Perhydrogenation - \PERHYDRO

6.11: Regularisation of atomic groups - \REGULARISE

The areas covered are:
 

 Specifications of atoms and other parameters
 Input of atoms and other parameters              - \LIST 5
 Modification of lists 5 and 10 on the disc       - \EDIT
 Conversion of temperature factors                - \CONVERT
 Hydrogen placing                                 - \HYDROGENS
 Per-hydrogenation                                - \PERHYDRO
 Regularisation of groups in LIST 5               - \REGULARISE

There is a consistent syntax thoughout CRYSTALS for refering to atoms and atomic parameters. This was refered to briefly in Chapter 1, and will be defined more fully here.
 

 
ATOM SPECIFICATION

There are three different but related ways of specifying an atom or a group of atoms.
 
TYPE(SERIAL,S,L,TX,TY,TZ)

This specification defines one atom. The various parts of the expression are :
TYPE The atom type, defined in Chapter 1 in the section on form-factors.
SERIAL The serial number, in the range 1-9999
Checking of serial numbers

Atoms of the same type are distinguished from one another by having different serial numbers. However, at no stage is a check made to ensure that there is not more than one atom in LIST 5 with the same type and serial number. If a routine is searching for an atom with a given type and serial number, the first atom found will always be taken, and any subsequent atoms with the same type and serial number will be ignored.

Serial numbers are considered to be different if they differ from each other by more than 0.0005.
S 'S' specifies a symmetry operator provided in the unit cell symmetry LIST (LIST 2). 'S' may take any value between '-NSYM' and '+NSYM', except zero, where 'NSYM' is the number of symmetry equivalent positions provided in LIST 2 (see the section of the user guide on 'initial data input'). if 'S' is less than zero, the coordinates of the atom in LIST 5 are negated (i.e. inverted through a centre of symmetry at the origin) and then multiplied by the operator specified by the absolute value of 'S' to generate the new atomic coordinates. 'S' may be less than zero even if the space group is non-centrosymmetric ( i.e. introduce a false centre), but must not be greater than 'NSYM'. The default value for 'S' is '1', specifying the first matrix in LIST 2, usually the unit matrix.
L 'L' specifies the non-primitive lattice translation that is to be added after the coordinates have been modified by the operations given by 'S'. 'L' must not be greater than the number of allowed non-primitive translations in the space group. The translations provided by 'L' depend on the lattice type and are given by :

          L=    1             2                3                4

      P       0,0,0
      I       0,0,0      1/2,1/2,1/2
      R       0,0,0      1/3,2/3,2/3      2/3,1/3,1/3
      F       0,0,0        0,1/2,1/2      1/2, 0 ,1/2      1/2,1/2,0
      A       0,0,0        0,1/2,1/2
      B       0,0,0      1/2, 0 ,1/2
      C       0,0,0      1/2,1/2, 0

      1.  Centre of symmetry if 'S' negative
      2.  Symmetry operator 'S'
      3.  Non-primitve lattice translation
      4.  Whole unit cell translations 'T(X)', 'T(Y)', 'T(Z)'.

    i.e.
           X'=  [R(s)](+X) + t(s) + L + T(X) + T(Y) + T(Z)
    or
           X'=  [R(s)](-X) + t(s) + L + T(X) + T(Y) + T(Z)

The format given above is a complete atom definition. For convenience the definition may sometimes be shortened. The obligatory parts are the TYPE and SERIAL. The remaining parameters, S, L, TX, TY, TZ, are optional.

An optional parameter taking its default value may be omitted, though its place must be marked by its associated comma. A series of trailing commas may be omitted.

The following are all equivalent :

      TYPE(SERIAL,1,1,0,0,0)
      TYPE(SERIAL,,,0,0,0)
      TYPE(SERIAL,1,,,,0)
      TYPE(SERIAL,,,,,)

The values of S , L , TX , TY and TZ are exactly those output and used by the distance angles routines under the headings S(I) , L , T(X) , T(Y) and T(Z) respectively. (See the section of the user guide on 'results of refinement').

When the symmetry operators are applied, the actual values of S and L are checked to see that they are reasonable. If the values found are not reasonable, an error message will be output and the job terminated.

In some cases, the symmetry operators are accepted on input, but not used by the routine. The description of the routine will state this.
 

 
UNTIL sequences When a group of atoms lie sequentially in the atom parameter list, there is an abbreviated way to refer to the group.

      TYPE1(SERIAL1,S,L,TX,TY,TZ)  UNTIL  TYPE2(SERIAL2)

This definition specifies all the atoms in the current list starting with the atom TYPE1(SERIAL1) The first atom in the specification must occur before the second atom in the current parameter list, otherwise an error message will be output and the task aborted. If symmetry operators are used, they must be given for the first atom of the sequence, and will be appied to all the atoms in the sequence.
 

      Examples

                  C(1) until C(6)

      Six atoms lying around a centre of symmetry:

                  C(1) until C(3) C(1,-1) UNTIL C(3)

These specifications each define one atom. FIRST Refers to the first atom in LIST 5 or LIST 10, and LAST refers to the last atom in the list. If these are used as atom designators, no serial number may be given, but symmetry operators may be. They may be used in until sequences.

      examples
                  LAST
                  FIRST(x)
                  FIRST(-1) UNTIL C(16)  C(23) UNTIL LAST

This specifies all atoms in the list, can take symmetry operators or parameter names, but cannot be accompanied on the same line by any other atom specifiers.

      examples
                  ALL
                  ALL(x)
                  ALL(-1)

Atomic parameters have a NAME. Some instructions permit the use of the parameter name by itself, which implies that parameter for all atoms. The parameter name may be combined with an atom specifier, in which case only the parameter for that atom (or group in an UNTIL sequence) is referenced. Symmetry operators may be used. The normal drop-out rules apply.
 
Parameter NAMES

The following NAMES are recognised.

      X      Y      Z      OCC      U[ISO]    SPARE
      U[11]  U[22]  U[33]  U[23]    U[13]     U[12]
      X'S    U'S    UIJ'S  UII'S

      Examples
        X            The 'x' coordinate for all atoms
        C(9,X,Y)     The 'x' and 'y' coordinates for atom C(9)
        FIRST(X'S)   The 'x','y' and 'z' coordinates for the first atom
        FIRST(U'S) UNTIL C(23)
                     The anisotropic temperature factors for all atoms
                     up to C(23).

 The isotropic temperature factor is defined by:

       T = exp(-8*pi*pi*U[iso]*s**2)
                                       where s = sin(theta)/lambda

      The anisotropic temperature factor (adp) is defined by:

       T = exp(-2*pi*pi*(h*h*a'*a*u[11]
                        +k*k*b'*b'*u[22]
                        +l*l*c'*c'*u[33]
                    +2.0*k*l*b'*c'*u[23]
                    +2.0*h*l*a'*c'*u[13]
                    +2.0*h*k*a'*b'*u[12])).
                                       where x' are the reciprocal
                                       cell parameters and h, k and
                                       l are the Miller indices

CRYSTALS contains two definitions od Uequiv. Both definitions are acceptable to Acta. The arithmetic mean of the principle axes is often similar to the refined value of Uiso. The geometric mean is more sensitive to long or short axes, and so is more useful in publications. Ugeom is the sphere with the same volume as the ellipsoid.

      U(arith) = (U1+U2+U3)/3
      U(geom)  = (U1*U2*U3)**1/3
                                    Where Ui are the principal axes of
                                    the orthogonalised tensor.

It should be noted that if a set of anisotropic atoms are input with the FLAG key set to anything but 0, then the parameters will be interpreted as Isotropic atoms, or special shapes.
 

 
Uequiv Two expressions are available for the equivalent temperature factor (the geometric or arithmetric mean of the principal components). The Immediate Command 'SET UEQUIV' sets which definition will be used.

      Ugeom  = (Ui * Uj * Uk)**1/3

      Uarith = (Ui + Uj + Uk)/3
                                       Where Ui, Uj & Uk are the
                                       principal components of U

      Ugeom is the radius of the sphere with the same volume as the adp
      ellipsoid, and thus gives a good indication of the quality of the
      ellipsoid. Uarith is often closer to the value of Uiso, and so is
      useful for returning to an isotropic refinement.

The SPecial Shape keys are

      type serial occ FLAG x y z u[11]  u[22] u[33] u[23] u[13] u[12] spare
                                 U[ISO]                               spare
                                 U[ISO] SIZE                          spare
                                 U[ISO] SIZE  DECLINAT AZIMUTH        spare

FLAG  meaning    parameters
'old' types of atoms:

 0    Aniso ADP  u[11]  u[22] u[33] u[23] u[13] u[12] 
 1    Iso ADP    U[ISO]                               

New 'special' shapes:

 2    Sphere     U[ISO] SIZE                          
 3    Line       U[ISO] SIZE  DECLINAT AZIMUTH        
 4    Ring       U[ISO] SIZE  DECLINAT AZIMUTH        

The parameters have the following meaning for the new special shapes:
Special U[iso] U[iso] is related to the 'thickness' of the line, annulus or shell.
 
Special SIZE SIZE is the length of the line, or the radius of the annulus or shell.
Special DECLINAT DECLINAT is the declination angle between the line axis or annulus normal and the z axis of the usual CRYSTALS orthogonal coordinate system, in degrees/100.
Special AZIMUTH AZIMUTH is the azumuthal angle between the projection of the line axis or annulus normal onto the x - y plane and the x axis of the usual CRYSTALS orthogonal coordinate system, in degrees/100.

If either of these angles is input with a value greater than 5.0, it is assumed that the user has forgotten to divide by 100, which is thus done automatically.
 

 

 
OVERALL PARAMETER SPECIFICATION

Overall parameters are specified simply by their keys. The following overall parameter keys may be given :

      SCALE      OU[ISO]      DU[ISO]      POLARITY
      ENANTIO    EXTPARAM

The dummy overall temperature factor is in no way related to the overall temperature factor, and its use is explained in the input of LIST 12, which comes in the section of the user guide on 'structure factors'.
OU[ISO] This parameter is the overall isotropic temperature factor and has a default value of 0.05.
POLARITY This is the Rogers eta parameter, and is a multiplier for the imaginary part of the anomalous scattering factor. Setting the value to 1.0 (its default) has the effect of using the imaginary part of the anomalous scattering factor as given. Changing the value to -1.0 has the effect of changing the hand of the model. Setting the value at zero has the effect of removing the contribution of f". However, if contributions from f" are not required, IT IS MORE EFFICIENT to set ANOMALOUS = NO in LIST 23. If you need to use f", remember not to apply Friedels law (LIST 13) during data reduction, and to include anomalous scattering (LIST 3 and LIST 23). See D. Rogers, Acta Cryst (1981), A37,734-741. POLARITY and ENANTIO should not be used simultaniously.
ENANTIO This overall parameter is the fractional contribution of F(-h) to the observed structure amplitude, and like the POLARITY parameter is sensitive to the polarity of the structure. It is defined by

       Fo**2 =(1-x)* F(h)**2 + x*F(-h)**2

Note that many other programs use expression (4), which cannot cope with Neutron data, and gives a value for 'g' which is about 1,000,000 times smaller than 'r*'.

       g ~= [(e**2/mc**2)**2 . lambda**3/V**2 . Tbar ] . r*

 \LIST 5
 OVERALL SCALE= DU[ISO]= OU[ISO]= POLARITY= ENANTIO= EXTPARAM=
 READ NATOM= NLAYER= NELEMENT= NBATCH=
 either ATOM TYPE= SERIAL= OCC= FLAG= X= Y= Z= U[11]= ....U[12]=
 or     ATOM TYPE= SERIAL= OCC= FLAG= X= Y= Z= U[ISO]
 INDEX P= Q= R= S= ABSOLUTE=
 LAYERS SCALE=
 ELEMENTS SCALE=
 BATCH SCALE=

 \LIST 5
 OVERALL SCALE=0.123
 READ NATOM=2 NELEMENT=2
 ATOM PB 1 FLAG=0 .25 .25 .25 .03 .03 .03 .0 .0 .0
 ATOM C 2  X= .23 .13 .67
 ELEMENTS 0.8 0.2
 END

This directive specifies various parameters that refer to the structure as a whole.
SCALE= The overall scale factor, default = 1.0
DU[ISO]= The dummy overall isotropic temperature factor, default = 0.05.
OU[ISO]= The overall isotropic temperature factor, default = 0.05.
POLARITY= Rogers eta parameter (see above), default = 1.0.
ENANTIO= Flack enantiopole parameter (see above), default = 0.0.
EXTPARAM= Larson r* secondary extincion parameter, default = 0.0.
 
READ NATOM= NLAYER= NELEMENT= NBATCH=

This directive specifies the number of atoms, layer scale factors, element scale factors, and batch scale factors that are to follow.
NATOM= The number of atom cards to follow, default = 0.
NLAYER= The number of layer scale factors to follow, default = 0.
NELEMENT= The number of element scale factors to follow, default = 0.
NBATCH= The number of batch scale factors to follow, default = 0.
 
ATOM TYPE= SERIAL= OCC= FLAG= X= Y= Z= U[11]= ..

The parameters for an atom, repeated NATOM times.
TYPE= The atomic species, an entry for which should exist in LIST 3. There is no default value.
SERIAL= The atoms serial number. There is no default value.
OCC= This parameter defines the site occupancy EXCLUDING special position effects (i.e. is the 'chemical occupancy). The default is 1.0. Special position effects are computed by CRYSTALS and multiplied onto this parameter.
FLAG= This parameter specifies the type of temperature factor for the atom, and if it is omitted a default value of 1 is assumed. NOTE that it must be set to 0 for anisotropic atoms.
X= Y= Z= These parameters specify the atomic coordinates for the atom, for which there are no default values.
U[11]= U[22]= U[33]= U[23]= U[13]= U[12]= These parameters have different interpretations depending upon the value of FLAG

If FLAG=0

These parameters specify the anisotropic temperature factors for the atom and if they are omitted default values of zero are assumed. The order of the cross terms is obtained by dropping 1,2,3 sequentially from [123].

If FLAG=1

The first parameter specifies the isotropic temperature factor, which defaults to 0.05.

If FLAG=2,3 or 4, the six parameters represented by u[ij] have the following imterpretation:
 

KEY   shape      parameters  

 2    Sphere     U[ISO] SIZE                          
 3    Line       U[ISO] SIZE  DECLINAT AZIMUTH        
 4    Ring       U[ISO] SIZE  DECLINAT AZIMUTH        

The parameters have the following meaning for the new special shapes:
Special U[iso] U[iso] is related to the 'thickness' of the line, annulus or shell.
 
Special SIZE SIZE is the length of the line, or the radius of the annulus or shell.
Special DECLINAT DECLINAT is the declination angle between the line axis or annulus normal and the z axis of the usual CRYSTALS orthogonal coordinate system, in degrees/100.
Special AZIMUTH AZIMUTH is the azumuthal angle between the projection of the line axis or annulus normal onto the x - y plane and the x axis of the usual CRYSTALS orthogonal coordinate system, in degrees/100.

If either of these angles is input with a value greater than 5.0, it is assumed that the user has forgotten to divide by 100, which is thus done automatically.
 

 
INDEX P= Q= R= S= ABSOLUTE=

This directive is used to input the constants that define an index for layer scaling. The layer scale index for the reflection with indices HKL is computed from

      index = (h*p + k*q + l*r + s)

      NO
      YES  -  Default value

This directive defines the layer scale factors, starting with the scale for an index of 1.
SCALE= This parameter gives the layer scale, and has a default value of 1. It is repeated NLAYER times.
 
ELEMENTS SCALE=

This directive defines the scale factors for the elements of a twinned structure.
SCALE= This parameter gives the element scale factor, and has a default value of 1. It is repeated NELEMENT times - the number of components in the twin.
 
BATCH SCALE=

This directive defines the batch scale factors.
SCALE= This parameter gives the batch scale factor, and has a default value of 1. It is repeated NBATCH times. Remember to set appropriate keys in LIST 6
 

 
Futher examples of parameter input

 ATOM TYPE=C,SERIAL=4,OCC=1,U[ISO]=0,X=0.027,Y=0.384,Z=0.725,
 CONT U[11]=0.075,U[22]=0.048,U[33]=.069
 CONT U[23]=-.007,U[13]=.043,U[12]=-.001
 ATOM C 5 U[ISO]=0.0 .108,.365,.815,.074
 CONT .051 .065 -.015 .048 -.014
 ATOM C 2 1 0.05 0.149 0.411 0.651 0 0 0 0 0 0
 ATOM C 1 X=0.094,Y=0.343,Z=0.890
 ATOM C 3 X=0.050 0.406 0.648

        -  Punches the atomic parameters in CRYSTALS format.
      A -  Punches the atomic parameters in CRYSTALS format.
      B -  Punches the atomic parameters in XRAY format.
      C -  Punches the atomic parameters in SHELX format.

 \DISPLAY LEVEL=
 END

 \DISP HIGH
 END

This allows the user to display a summary of the contents of list 5. The output is sent to both monitor and listing channels, so the contents of list 5 can be examined on-line during interactive work. The output produced is more compact than that from PRINT 5, and various levels of detail can be selected. The instruction required is :-
 
\DISPLAY LEVEL=

DISPLAY has one optional parameter.
LEVEL

      LOW
      MEDIUM
      HIGH

The effects of this parameter are :-

LOW The names of the atoms, overall parameters, and any layer, batch, and element scales in list 5 are displayed.

MEDIUM Each atom in list 5 is displayed with its type, serial, occupancy, isotropic temperature factor ( if any ), and positional parameters. The values of the overall parameters and of any layer, batch, and element scales are displayed.

HIGH All of the parameters of each atom in list 5 are displayed. The values of the overall parameters, and of any layer, batch, and element scale factors are displayed.
 

 

 \EDIT INPUTLIST= OUTPUTLIST=
 EXECUTE
 SAVE
 QUIT
 MONITOR LEVEL
 LIST LEVEL
 DELETE  ATOM SPECIFICATIONS  .  .
 ATOM TYPE= SERIAL= OCC= U[ISO]= X= Y= Z= U11= ..
 CREATE Z ATOM-SPECIFICATION  ...
 SPLIT Z ATOM-SPECIFICATION ...
 CENTROID Z ATOM-SPECIFICATION ...
 KEEP  Z ATOM-SPECIFICATIONS ...
 AFTER  ATOM-SPECIFICATION
 MOVE Z ATOM-SPECIFICATION  ...
 SELECT ATOM-PARAMETER  OPERATOR  VALUE, . .
 SORT TYPE1 TYPE2 ...
 SORT KEYWORD
 DSORT TYPE1 TYPE2 ...
 RENAME ATOM1  ATOM2  (, ATOM1  ATOM2) ...
 TYPECHANGE KEYWORD OPERATOR VALUE NEW-ATOM-TYPE
 RESET PARAMETER-NAME VALUE ATOM-NAMES
 CHANGE  PARAMETER-SPECIFICATION VALUE ...
 ADD  VALUE PARAMETERS  ...
 SUBTRACT  VALUE  PARAMETERS  ...
 MULTIPLY  VALUE  PARAMETERS  ...
 DIVIDE  VALUE  PARAMETERS  ...
 PERTURB VALUE PARAMETERS ...
 SHIFT  V1, V2, V3   ATOM-SPECIFICATION . .
 TRANSFORM  R11, R21, R31, . . . R33  ATOM-SPECIFICATION . .
 DEORTHOGINAL  ATOM-SPECIFICATION . .
 UEQUIV  ATOM-SPECIFICATIONS  .  .
 ANISO  ATOM-SPECIFICATIONS  .  .
 INSERT IDENTIFIER
 SPHERE NEWSERIAL ATOMLIST
 RING NEWSERIAL ATOMLIST
 LINE NEWSERIAL ATOMLIST
 REFORMAT
 END

 LIST LOW
 TYPECHANGE TYPE EQ Q C
 SELECT U[ISO] LT 0.1
 ADD  0.25 X
 RENAME C(1) S(1)
 CHANGE  S(1,OCC) UNTIL O(1) .5
 KEEP  1 FIRST UNTIL LAST
 L L
 SPLIT 100 C(45)
 DELETE  C(46) UNTIL LAST
 RESET OCC 1.0 ALL

This is a powerful crystallographic editor for modifying a LIST 5 or LIST 10. It offers the editing facilities frequently needed for the management of atom parameters, including conditional operations and arithmetic.
 

EDIT is a semi-interactive Instruction, in that each Directive is computed as soon as its input is complete. Since CONTINUE can be used to extend a directive over several lines, completion is indicated be the start of a new directive, or the special directive EXECUTE.

After the terminating END, the resulting list is output to the disc. However if the list has not been changed, a new list will be created only if the list type is being changed ( e.g. 10 to 5 ). The current edited version of the list can be saved at any time to protect against future editing mistakes ( the SAVE directive ). It is also possible to abandon editing without creating a new list ( the QUIT directive ).

When used in interactive mode, a new list is created even though errors may have occured during command input unless the QUIT directive is used. In online and batch modes no new list will be created if errors occured during the edit. In this case an error message in generated.

Take care to note that some directives refer to atom or group of atoms, others refer to one or more parameters, and two (CHANGE and SELECT)will refer to either an atom specification or a parameter specification. Although atom definitions can include a series of symmetry operators, the only directives that will use them are those for which the subsequent description explicitly states that the symmetry operators are used. In all other cases, the symmetry information will be read in without any error messages and ignored. Those operations which require a single parameter type as argument (ADD, MULTIPLY etc ) will fail if composite parameters ( "U'S", etc ) are given.

 
\EDIT INPUTLIST OUTPUTLIST

INPUTLIST

      5   -  Default value, the atomic coordinates
      10                    the Fourier peaks search

OUTPUTLIST

      5   -  Default value, the atomic coordinates
      10                    the Fourier peaks search

 
END This should be the last card in the set of modification directives.
 
EXECUTE This directive which has no parameters does nothing to the edited list. It is provided to allow the user to see the results of one operation ( initiated by the directive whose input is terminated by EXECUTE ) before attempting the next.
 
SAVE Forces the current atom list to be writen to disk.
 
QUIT This directive will cause the edit to be abandoned without the creation of a new list if it is followed by END . If it is followed by any other directive it is ignored.

 
MONITOR LEVEL This directive controls the level of monitoring of editing operations. When each operation is performed, the results can be monitored in the monitor channel and in the listing file. Four levels of monitoring are provided. The inital level and the default level used when no value is specified is 'MEDIUM'. The possible values of the parameter 'level' are :-

      OFF          No monitoring occurs
      LOW          Type and serial only are displayed
      MEDIUM       Program selects level of display   (default)
      HIGH         At least the level represented by
                   'MEDIUM' listing is displayed

When the program selects a monitor level account is taken of the amount of relevant information for the particular directive. Thus for DELETE only 'type' and 'serial' need be displayed whereas for CHANGE all parameter values are displayed.
 
LIST LEVEL This directive produces a list of the current edited list in the monitor output stream and in the listing file. If KEEP has been used, the atoms which will be kept are indicated. The possible values for 'level' are :-

      OFF               No listing produced
      LOW               Type and serial listed
      MEDIUM            Type , serial , occ , u[iso] ,
                        x , y , z listed
      HIGH              All atomic parameters listed

 ATOM O 1 X = 0.3427 .89004 .09181

      NEWSERIAL = Z + OLDSERIAL

      CREATE 30 MO(1,-1) UNTIL C(15)

      Creates atoms MO(31) until C(45)

The original atoms are not deleted. The sequence Z ATOM-SPECIFICAIONS can be repeated. The new serial numbers are given by

      NEWSERIAL(1) = Z* OLDSERIAL and
      NEWSERIAL(2) = Z* OLDSERIAL +1

Only the atoms referenced in this directive will be kept in the list, all the others will be lost, even though they can be referenced right up until the final END card. The sequence Z ATOM-SPECIFICAIONS can be repeated.
 
Atoms that are KEPT are moved to the top of the list, and stored in the order in which they are specified on the KEEP card. Only one KEEP card may be given. Use CONTINUE if one line isn't long enough for the atom sequence.

The atom specifications may contain symmetry operators, which are used to generate the coordinates of the atoms that are to be retained. 'Z' Is an optional parameter which defines the serial number of the first atom in the specification immediately following it. For each atom thereafter in the current atom specification, the serial number is incremented by one to generate the output serial number. Atoms whose serial numbers are changed in this way must be referred to in subsequent instructions by their new serial numbers. If 'Z' is not given, the atoms retain their old serial numbers.

If an UNTIL sequence is used after a KEEP instructions has been given, it should be used with care, since the order of the new parameter list is different from the input list.
 
AFTER ATOM-SPECIFICATION ...

This defines the atom in the list after which atoms that are MOVEd should be placed. (See MOVE below). If this instruction is omitted, the default option places the first MOVED atom at the head of the list, and successive atoms after it. Once one AFTER directive has been given, atoms are placed behind the given atom in the order in which they are presented on MOVE cards. If no atom specification is given on this card, subsequent MOVEs will move the atoms to the head of the list.
 
MOVE Z ATOM-SPECIFICATION ...

This instruction moves atoms about in the list and places them in the position defined by the latest AFTER directive. (See the previous directive). This instruction does not remove atoms from the list, but simply reorders the list. The sequence Z ATOM-SPECIFICAIONS can be repeated.

The atom specifications may contain symmetry operators, which are used to generate the coordinates of the atoms that are to be moved. 'Z' is an optional parameter which defines the serial number of the first atom in the specification immediately following it. For each atom thereafter in the current atom specification, the serial number is incremented by one to generate the output serial number. Atoms whose serial numbers are changed in this way must be referred to in subsequent instructions by their new serial numbers. If no 'Z' is given, the atoms retain their old serial numbers.

If an UNTIL sequence is used after one or more MOVE instructions have been given, it should be used with care, since the order of the new parameter list is different from the input list.
 
SELECT ATOM-PARAMETER OPERATOR VALUE, . .

This instruction selects and retains atoms with parameters satisfying the specified conditions. Only atoms that satisfy ALL the selection criteria, whether these are in the same or different directives, will be kept. All other atoms will be deleted from the list.

The operators allowed are :

            EQ            equal
            NE            not equal
            GT            greater than
            GE            greater than or equal to
            LT            less than
            LE            less than or equal to

      SELECT SERIAL LT 50
      SELECT OCC GT 0.5, OCC LT 1.5
      SELECT C(1,X) LT 1., C(1,X) GT 0.
      SELECT TYPE NE Q

In the second format, a keyword corresponding to an atom parameter name (as defined in LIST 5) is given, and the whole list sorted on increasing value of the specified parameter. Note that sorting on TYPE will give results depending on the 'collating sequence' of the computer. Fortunately, this generally leads to alphabetic sorting.

SORT sorts the whole list 5, and cancels any existing KEEP instructions.
 

 
DSORT TYPE1 TYPE2 ...
 
DSORT KEYWORD This directive is exactly analagous to SORT, above, except that it sorts into descending order.
 

 
RENAME ATOM1 ATOM2 (, ATOM1 ATOM2) ... This directive requires pairs of atom specifications (optionally separated by a comma). The TYPE and SERIAL of 'atom1' are changed to those of 'atom2'. Atom1 must exist in LIST 5, atom2 must NOT exist in LIST 5. An atom can be renamed repeatedly. If atom1 contains symmetry operators, these are applied to the coordinates of the renamed atom. An atom cannot be renamed to itself in a single step.
 

 
TYPECHANGE KEYWORD OPERATOR VALUE NEW-ATOM-TYPE

This directive conditionally changes the TYPES of atoms. If an atomic parameter selected by the keyword (see sort above) satisfies the conditions defined by the 'operator' and 'value' (see SELECT above), then the TYPE of the atom is changed to 'new-atom-type'.

      TYPECHANGE OCC GT 1.2 O
                              If Occ large, convert to oxygen
      TYPECHANGE U[ISO] LE 0.03 N
                              If Uiso small, convert to nitrogen
      TYPECHANGE TYPE EQ Q C
                              Convert peaks (type Q) to carbon

This directive assigns the given value to the named parameter for all the atoms in the atom list

      RESET OCC 1.0 ALL
      RESET OCC .5 O(1) O(2) O(3)
      RESET U[11] .05 C(27) UNTIL C(50)

 PARAMETER(I)  VALUE(I)

The second form of ARG(I) on this card is :

 ATOM SPECIFICATION

The two different types of argument on this card may be used interchangeably :

      CHANGE  S(1,OCC) UNTIL O(1) .5
      CONT    C(1,-2,1) UNTIL C(12)
      CONT    C(13,X) .0179

Note that the anisotropic temperature factor produced by this operation is in fact still spherically symmetrical, and that the s.f.l.s. routines automatically ensure that when the temperature factor of an atom is to be refined, it is in the correct form.
 
INSERT IDENTIFIER=NAME This instruction inserts the value of the named identifier into the parameter 'SPARE' in the atom list, replacing any previous value. SPARE is normally used to hold rho after Fourier maps.

Currently available values for NAME are

      ELECTRON        This inserts the atomic electron count calculated
                      from the form factor
      WEIGHT          This inserts the atomic weight from LIST 29.

 \REGROUP INPUTLIST= OUTPUTLIST=
 SELECT MOVE= KEEP= MONITOR= SEQUENCE= SYMMETRY= TRANSLATION=
 END

 \REGROUP
 SELECT MOVE=1.6,MONITOR=HIGH
 END

This routine offers a way of re-ordering the atoms in LIST 5 or LIST 10, so that related atoms or peaks form a sequential group in the list, and the coordinates put the atoms as close together as possible.

THIS ROUTINE DOES NOT USE LIST 29 to get bonding distances.

In this routine, a set of distances is calculated about each atom or peak in the list in turn. For each atom or peak in the list below the current pivot, the minimum contact distance is chosen, and if this is less than a user specified maximum, the atom or peak is moved up the list to a position directly below the pivot. ( The MOVE parameter). When more than one atom or peak is moved, their relative order is preserved as they are inserted behind the current pivot atom. As well as reordering the list, the necessary symmetry operators are applied to the positional and thermal parameters to bring the atom or peak into the same part of the unit cell as the current pivot atom. The result of this process is to bring related atoms together in the list, and to place all the atoms in the same part of the unit cell.
 
\REGROUP INPUTLIST= OUTPUTLIST=

INPUTLIST=

      5   -  Default value, the atomic coordinates
      10                    the Fourier peaks search

      5   -  Default value, the atomic coordinates
      10                    the Fourier peaks search

      LOW   -  Default value
      HIGH

      NO   -  Default value
      YES

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

This routine changes the atom coordinates so as to form a 'molecule' using the covalent radii given in LIST 29. The atom TYPE, SERIAL and order in LIST 5 is not changed.
 

 
\COLLECT INPUTLIST= OUTPUTLIST=

INPUTLIST=

      5   -  Default value, the atomic coordinates
      10                    the Fourier peaks search

      5   -  Default value, the atomic coordinates
      10                    the Fourier peaks search

      LOW   -  Default value
      HIGH

      ALL
      PEAKS

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

 \CONVERT INPUTLIST= OUTPUTLIST= CROSSTERMS=
 END

 \CONVERT
 END

This routine will convert the temperature factors of a set of atoms into the correct form when their temperature factor, t, is given by :

       T = exp(-B[iso]*S**2)     where s = sin(theta)/lambda.

 or for an anisotropic atom :

       T = exp(-(h*h*b[11] + k*k*b[22] + l*l*b[33]
           + k*l*2*b[23] + h*l*2*b[13] + h*k*2*b[12]))

This is the instruction which initiates the routine to convert the temperature factors.
INPUTLIST=

      5   -  Default value, the atomic coordinates
      10                    the Fourier peaks search

      5   -  Default value, the atomic coordinates
      10                    the Fourier peaks search

      B[IJ]   -  Default value.
      2B[IJ]

 \HYDROGENS INPUTLIST= OUTPUTLIST=
 DISTANCE  D
 SERIAL    N
 U[ISO]    U
 U[ISO]    NEXT   MULT
 AFTER     TYPE(SERIAL)
 PHENYL    X R(1) R(2) R(3) R(4) R(5)
 H33       X R(1) R(2)
 H23       X R(1) R(2)
 H13       X R(1) R(2) R(3)
 H22       X R(1) R(2)
 H12       X R(1) R(2)
 H11       X R(1)
 END

 \HYDROGENS
 DISTANCE  1.09
 U[ISO]    NEXT   1.2
 H33     C(7) C(6) R(5)
 H22     C(14) C(15) C(13)
 END

      5   -  Default value, the atomic coordinates
      10                    the Fourier peaks search

      5   -  Default value, the atomic coordinates
      10                    the Fourier peaks search

      H
       \
      H-X-R(1)-R(2)
       /
      H

      H   R(1)
       \ /
        X
       / \
      H   R(2)

          R(1)
         /
     H- X-R(2)
         \
          R(3)

      H        R(2)
       \      /
        X=R(1)
       /
      H

        H
         \
          X=R(1)
         /
      R(2)

 Place Hydrogen atoms on the following fragment:

      C(1)          C(5)
          \        /
           C(2)=C(3)
                   \
                    C(4)-Br(1)

     \HYDROGENS
      DISTANCE 0.99
      U[ISO]   0.06
      H33 C(1) C(2) C(3)
      AFTER C(1)
      H12 C(2) C(1) C(3)
      AFTER C(2)
      H23 C(4) Br(1) C(3)
      AFTER C(4)
      H33 C(5) C(3) C(4)
      END

 \PERHYDRO INPUTLIST= OUTPUTLIST=
 DISTANCE  D
 SERIAL    N
 U[ISO]    U
 U[ISO]    NEXT   MULT
 ACTION    MODE
 END

 \PERHYDRO
 U[ISO] NEXT 1.0
 END

The generated commands may be processed internally by CRYSTALS without the user needing to see them, or they may be sent to the PUNCH file for manual editing and then be USEd by CRYSTALS.
 
\PERHYDRO INPUTLIST= OUTPUTLIST=

INPUTLIST=

      5   -  Default value, the atomic coordinates
      10                    the Fourier peaks search

      5   -  Default value, the atomic coordinates
      10                    the Fourier peaks search

      NORMAL   -  Default value.
      PUNCH
      BOTH

 \REGULARISE    MODE
 COMPARE
 KEEP
 REPLACE
 AUGMENT
 METHOD NUMBER
 GROUP NUMBER
 TARGET Atom Specifications
 IDEAL  Atom Specifications
 SYSTEM a b c alpha beta gamma
 ATOM    x    y    z
 CP-RING x
 HEXAGON x
 OCTAHEDRON x y z
 PHENYL
 SQP x y z
 SQUARE x y
 TBP x z
 TETRAHEDRON x
 END

 \REGULARISE REPLACE
 GROUP 6
 TARGET C(1) UNTIL C(6)
 PHENYL
 END

This routine calculates a fit between the coordinates of a group of atoms in LIST 5 and another group. The calculated fitting matrix may be used to compare the geometry of two groups, or it may be applied to transform the new coordinates which will then replace the existing group in LIST 5 (D. J. Watkin, Act Cryst (1980). A36,975).

In this section, the group of atoms in LIST 5 to whose coordinates the fit is made is referred to as the 'TARGET atoms', and the group to be fitted onto that group is referred to as the 'IDEAL atoms'.

The source of the 'IDEAL atoms' can be the LIST 5, a pre-stored idealised geometry, or values read in from the directives. Those directives that refer to LIST 5 use the usual CRYSTALS formats for atom specifications.
 
Input for REGULARISE

The input to REGULARISE must define the groups to be fitted together, the method used for fitting , and the use to be made of the results. The user must ensure that corresponding atoms are specified in the same positions of the 'TARGET' and 'IDEAL' group definitions, so the program knows which pairs of atoms are to be matched. It is not necessary to have co-ordinates of every atom in the TARGET fragment. The inclusion of atom specifications for which coordinates do not exist in the parameter list indicates that the procedure must generate coordinates for these atoms. This allows the user to give a type and serial to new atoms created by the procedure. Any 'atoms' without coordinates are not included in the fitting process.

The maximum number of atom IDENTIFIERS permitted on an TARGET or IDEAL card is about 250. Note that an UNTIL sequence only counts as two identifiers. The number of implied atoms permitted is very large.

The 'IDEAL' group may be given in various ways. For calculations on a single structure, it may be extracted from the stored data in the same way as the 'TARGET' group. In this case however, all the atoms must previously exist. Alternatively, explicit co-ordinates may be given in a system defined by the user, or a predefined group may be used. In any case all the positional parameters of the atoms in the 'IDEAL' group will be known before the calculation begins.
 
Output from REGULARISE

The output from REGULARISE includes the fragment centroids, their sums and differences and the transformation fitting the IDEAL onto the TARGET.
 
Method of calculation

The centroid of each fragment is moved to the origin. The atomic coordinates are converted to an orthogonal system and rotated to an 'inertial tensor' system (to help condition the L.S. matrix).

The fitting calculation is either constrained to be a pure rotation- inversion, or is a free linear transformation (rotation-diltion). If requested, the pure rotation component of the calculated rotation-dilation matrix is extracted. The calculated matrix is applied to the co-ordinated of the 'IDEAL' group, which is then converted back to crystal fractions, for comparison with the TARGET.
 
WARNING

The 3 by 3 transformation matrices generated at various stages may well be singular, especially if no rotation is defined about one of the axes. To combat possible problems with matrix inversion, a Moore-Penrose type matrix inverter is used. Even so, the user should be aware the there may be no unique solution to his problem. For example, when a planar fragment is fitted to an almost planar fragment one fit may involve inversion of the non-planar fragment. Inversion can be prevented by using Method 3. Note also that if almost planar groups are being fitted, the dilation factor perpendicular to the plane may be very large, and thus have an undesirable effect if applied to atoms far from the plane.
 

 
\REGULARISE MODE
MODE is an optional parameter.
MODE

      COMPARE      -      Default value
      KEEP
      REPLACE
      AUGMENT

The effects are :-

COMPARE The specified groups are only compared. The translations and rotations necessary to match the groups will be calculated but not applied.

KEEP The specified groups will be compared and the calculated transformations applied. The TARGET atoms are kept, and atoms whose parameters have been calculated will be placed at the end of the new LIST 5.

REPLACE The specified groups will be compared and the calculated transformations applied. The new atoms whose parameters have been calculated will be placed at the end of LIST 5 and the old atoms deleted form the list.

AUGMENT The specified groups will be compared and the calculated transformations applied. The TARGET atoms which actually exist in LIST 5 are retained unaltered. Parameters that have been calculated for dummy atoms (represented by a name only in the TARGET list) will be placed at the end of the new LIST 5.

For REPLACE and KEEP the 'IDEAL' coordinates define the geometry to be preserved, i.e. the model, and the 'TARGET' coordinates specify where, in what orientation and with what atom identifiers the model is to be placed. That is, the TARGET structure is replaced by the IDEAL.
 

 
COMPARE
 
KEEP
 
REPLACE
 
AUGMENT

These 4 directives override the option specified by the MODE parameter of the REGULARISE command. The next group calculated will be treated in the specified mode. See the description of MODE for details. There are no parameters
 
METHOD NUMBER

This directive selects the method for matching the groups by giving its number from the following list:-

      Number     Method
      ------     ------
       1        Rotation  component of  rotation-dilation
                matrix applied. ( default )
       2        Rotation-dilation  matrix  calculated and
                applied.
       3        Pure  rotation matrix  calculated  by the
                Kabsch method and applied. This algorithm
                preserves chirality.

This directive specifies the number of atoms in the groups to be matched. It should be the first directive for each group of atoms. The appearance of a second or subsequent GROUP directive in the instruction stream initiates the calculation for the previous group.
 
TARGET Atom Specifications

This directive is used to specify the 'TARGET' group of atoms. The directive will carry a series of atom specifications which will define the positions of the 'TARGET' atoms and the names of any atoms to be created by the routine. Atoms which exist in LIST 5 and atoms to be created can appear in any order in the TARGET group , although the order should be such that corresponding pairs of atoms appear at the same relative positions in the 'TARGET' and 'IDEAL' groups.
 
IDEAL Atom Specifications

This directive is used to specify a group of 'IDEAL' atoms to be taken from the stored LIST 5. Every atom on this directive must exist.
 
SYSTEM a b c alpha beta gamma

This directive is will change the co-ordinate system used to interpret any subsequent ATOM directives.

The initial co-ordinate system has orthogonal axes of unit length and is equivalent to :-

 SYSTEM  1.0  1.0  1.0  90.0  90.0  90.0

Values must be given for a', b', and c', the angles default to 90.0.
 
ATOM x y z This directive allows the cordinates of a single atom to be specified, in fractional co-ordinates in the current co-ordintate system. It must be followed by three decimal numbers which will be the X, Y, and Z coordinates of the atom.
 
HEXAGON X The 'IDEAL' group is a regular hexagon with a side of length 'X'. The default for x is 1.0.
 
PHENYL The same as HEXAGON with a fixed side of 1.39.
 
CP-RING X The 'IDEAL' group is a regular pentagon with a side of length 'X'. The default for x is 1.4.
 
SQUARE X Y The 'IDEAL' group is a rectangle with atoms at (x,0,0) , (0,y,0) , (-x,0,0) , (0,-y,0) . The parameters X and Y specify the size of the group to be used.
 
OCTAHEDRON X Y Z The 'IDEAL' group is an octahedron with atoms at (0,0,0) , (-x,0,0) , (0,y,0) , (x,0,0) , (0,-y,0) , (0,0,z) , (0,0,-z). The parameters X, Y and Z specify the size of the octahedron. 'z' defaults to 'y' defaults to 'x' defaults to '1.0'
 
SQP X Y Z The 'IDEAL' group is a square pyramid with atoms at (0,0,0) , (x,0,0) , (0,y,0) , (-x,0,0) , (0,-y,0) , (0,0,z). The parameters X, Y and Z specify the size of the octahedron. 'z' defaults to 'y' defaults to 'x' defaults to '1.0'
 
TBP X Z The 'IDEAL' group is a trigonal bipyramid with atoms at (0,0,0) , (x,0,0) , (-x/2,0.86603x,0), (-x/2,-0.86603x,0) , (0,0,z) , (0,0,-z) . The parameters X and Z specify the scale in the xy plane and z directions.
 
TETRAHEDRON X The 'IDEAL' group is a regular tetrahedron with an atom at the centre. 'x' is the distance in Angstrom from the centre to an apex and defaults to '1.0'
 
ORIGIN

This directive is not yet implemented.
 

 
Uses of \REGULARISE

 

 
1 - Extending a fragment to a complete molecule
 

Three atoms of a phenyl group ( C(1), C(2) C((6)) have been located. Fill in the missing atoms from a non-dilated idealised phenyl group.

      \REGULARISE AUGMENT
      GROUP 6
      METHOD 1
      \ C(3), C(4), and C(5) do not yet exist.
      TARGET C(1) C(2) C(3) C(4) C(5) C(6)
      PHENYL
      END

A group of atoms is approximately octahedral. Replace them by a (posibly dilated) regular octahedron.

      \REGULARISE REPLACE
      GROUP 7
      METHOD 2
      TARGET CO(1) N(1) N(2) N(3) N(4) N(5) N(6)
      OCTAHEDRON
      END

Determine whether the two molecules in an asymmetric unit are related by a symmetry operation not expected for the space group. The matrix relating the molecules and the translation required to make their centroids coincide should display any additional (approximate) symmetry present. Remember that if one molecule is the enantiomer of the other, Method 3 will lead to an unsatisfactory fitting unless one molecule is inverted, (by using the operator -1 in the atom specifications e.g. FIRST(-1) UNTIL C(23). This can be done even if the space group is non-centrosymmetric ).
 

      \REGULARISE COMPARE
      GROUP 16
      TARGET C(101) UNTIL N(102)
      IDEAL  C(201) UNTIL N(202)
      END