Crystals User Guide

Chapter 3: Atoms And Peaks, Parameters, And Parameter Values.

3.1: ATOMS and PEAKS

3.2: Parameters

3.3: IMPLICIT parameters

3.4: EXAMPLE 1

3.5: EXPLICIT parameters

3.6: Parameter values

3.7: CAUTION

3.8: EXAMPLE 2

3.9: LIST 5

3.10: EXAMPLE 3

3.11: EXAMPLE 4

3.12: Modifying LIST 5

For the user, it is probably the highly stylised and powerful methods for refering to atoms and structural parameters which provide the greatest conveniences in CRYSTALS. Atoms can be refered to either by a simple symbolic string, or by a more complex string which includes symmetry information. Parameters can be refered to either explicitly or implicitly.

Atoms are identified by their TYPE (up to four alphanumeric characters beginning with a letter) and their SERIAL number. Atoms with 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 so specified will always be taken, and any subsequent atoms with the same type and serial number will be ignored.

The atom TYPE is used as the key when looking for scattering factors in LIST 3. The atom type PEAK is used by the system to identify peaks taken from a map peak search. Users wishing to compute structure factors on peaks lists must either have a scattering factor for an atom type PEAK in their LIST 3, or use \EDIT to change PEAKS into some other atom type.

 EXAMPLES
        C(14)   PB(2)    PEAK(64)   Ca(12)

Sometimes it is necessary to inform CRYSTALS that it must use an atom equivalent by space group symmetry to one actually occuring in LIST 5 (for example, in defining a constraint), or CRYSTALS may wish inform the user that an output atom is an equivalent (for example, in the distance angles output). On these occasions, the extended atom definition (which conveys the symmetry information) is used. The specification is

TYPE(SERIAL,S,L,TX,TY,TZ)

TYPE and SERIAL were defined above, and have no default values. The other terms are optional, taking default values if omitted. Terms that are omitted must be indicated by their delimiting ",", except that the last given term may be delimited by a right parenthesis and the other default term delimiters be omitted. Default values are given after the examples.

 EXAMPLES
 C(14,-1,2,1,0,1)
 ZN(1,-2,,1,,1)   equivalent to       ZN(1,-2,1,1,0,1)
 CU(3,-1)         equivalent to	     CU(3,-1,1,0,0,0)

S specifies the symmetry matrix from LIST 2 which should be used. If S is negative, the atom coordinates from LIST 5 are negated before the operator is applied. The default value for S is one corresponding to the first symmetry operator given in LIST 2. THIS NEED NOT BE THE UNIT MATRIX, though it will be if the user takes care to make his first operator in LIST 2 the identity matrix.

L specifies the non-primative lattice translation to be applied AFTER the S operation. The translations for the various centrings are listed in VOL4. The default value for L is 1, corresponding to no translation.

TX, TY, and TZ are whole cell translation parallel to the cell edges, and are applied after S and L. Their default values are zero

Thus if the user makes the unit matrix his first operator in LIST 2, atom specifications of the form

C(2) FE(16)

will refer to the atoms at the actual positions given in LIST 5. Two special 'atoms' are permitted in CRYSTALS to enable users to handle LIST 5s in which they are not sure of the atom order. These are FIRST and LAST, refering to the first and last atoms in the list. A SERIAL cannot be given for these atoms, but S, L and the Ts can.

Groups of atoms can be referenced by a composite atom specification, the UNTIL sequence.

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

In this definition, all atoms between and including TYPE1(SERIAL1) and TYPE2(SERIAL2) in LIST 5 are referenced. Clearly, a sensibly ordered LIST 5 will enable the user to profit from this construction. If any operators are specified for the first atom, these operators are applied to all the atoms in the sequence. The atoms FIRST and LAST may be used in an UNTIL sequence.

Parameters may be given either implicitly or explicitly.

In an implicit reference, all parameters of a given type are invoked merely by giving the parameter name.

 \LIST 12
 FULL X Y Z U'S
 END

This instruction, which will be discussed more fully under Least-Squares, causes full matrix refinement to be carried out on the x, y, z and all the anisotropic temperature factors of all the atoms.

In an explicit reference to atomic or overall parameters, the individual parameters must be individually defined, though the UNTIL sequence, discussed above, provides a method for referencing groups of atoms.

The CRYSTALS system allows the user to associate parameter names with parameter values. These names are used in symbolic references to the parameter itself. Thus, to refer to the X coordinate of carbon(1), the user would type

C(1,X)

Multiple parameter references are permitted in some instances, for example in defining matrix blocks for least-squares. e.g.

CL(17,X,Z) indicating that the operation will be applied to both X and Z of the Cl atom with serial number 17.

Values corresponding to parameters are stored either in LIST 5 or in LIST 10. LIST 5 is either input by the user, or may be generated by system operations on an existing LIST 5 or LIST 10. LIST 10 has a similar format to LIST 5 and is produced either by a peak search on a Fourier map or by an operation on an existing LIST 10. Default values are provided by the system for some parameters.

The parameters stored for an atom are:

 TYPE - Described above under ATOMS and PEAKS.
 SERIAL - Described above under ATOMS and PEAKS
 OCC - The chemical site occupation factor, defaults to 1.0 
      (excluding symmetry effects).
 U[ISO]  - The isotropic temperature factor, defaults to 0.05.
 X -  The fractional x coordinate.
 Y -  The fractional y coordinate.
 Z -  The fractional z coordinate.
 U[11] | 
 U[22] |
 U[33] | The components of the atomic displacement parameters.
 U[23] |
 U[13] |
 U[12] |

The temperature factors are defined by:

 T[ISO] = EXP(-8*PI*PI*U[ISO]*S**2) 
 where S = sin(theta)/lambda

and

 T[ANISO] = EXP(-2*PI*PI*(h*h*as*as*U[11]
             +k*k*bs*bs*U[22]+l*l*cs*cs*U[33]
             +2.0*k*l*bs*cs*U[23]+2.0*h*l*as*cs*U[13]
             +2.0*h*k*as*bs*U[12])).

where 'xs' are the reciprocal cell parameters and h, k and l are the Miller indices of the current reflection.

An atom is considered to be isotropic when abs(U[ISO])>0.00005. If an atom is isotropic and one or more of the anisotropic temperature factors is to be refined, the anisotropic terms are calculated from U[ISO] and then U[ISO] is set to zero. The conversion in the other direction is also made, except that U[ISO] assumes its default setting. \EDIT can be used to generate U[EQUIV] from U[ANISO]. The minimum (most negative) permitted value for U[ISO] or U[ii] is set in LIST 23.

Beware the U[ISO] default when inputting a LIST 5! It should be noted that if a set of anisotropic atoms are input with no U[ISO] key or U[ISO] data, then the default value of 0.05 will be inserted. This implies that all such atoms are isotropic, so that the anisotropic temperature factors will be treated as zero, and the calculation will proceed for isotropic atoms.

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. In fact, 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.

The dummy overall temperature factor is in no way related to the overall temperature factor, and its use is explained in the section on refinement.

 \LIST 5
 READ NATOM=2
 ATOM  PB 1 U[ISO]=0 X=.89 .78 .97 .11 .22 .33 .23 .13 .12
 ATOM  C  2          X=.45 .56 .46

The overall structural parameters are:

 SCALE    - The overall scale factor. Defaults to 1.0
 DU[ISO]  - The dummy overall temperature factor. 
           See the section on L.S.
 OU[ISO]  - The overall isotropic temperature factor. 
           Default is .05
 POLARITY - The Rogers polarity parameter. Default is 1.
 ENANTIO  - The Flack polarity parameter. Default is zero.
 EXTPARAM - The Larson extinction parameter. Default is zero.

The remaining parameters are:

 LAYERS - The layer scale factors.
 BATCH - The batch scale factors.

LIST 5 holds the parameter values, and the user should go to the Manual to find the full specifications. It can best be regarded as a table in which the column headings define the types of parameter, and the row labels the types of entity to which the paramertes belong. Certain entries in the table are mandatory, e.g. parameter type SERIAL for entity type ATOM, and others are optional, e.g. U[ISO], for which there is already a default value entered.
As an aid to beginners, some examples are given here.

 \LIST 5\
 \ no overall parameters. DU[ISO],OU[ISO] and SCALE 
 \ all have default values
 \ 5 atoms
 READ NATOM = 5
 ATOM C 1 X=0.094,Y=0.343,Z=0.890
 ATOM C 2 1 0.05 0.149 0.411 0.651 0 0 0 0 0 0
 ATOM C 3 X=0.050 0.406 0.648
 ATOM TYPE=C,SERIAL=4,OCC=1,U[ISO]=0,
 CONT 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
 END

 \LIST 5
 READ NATOM = 2, NLAYER =   6
 \ the zone axis is (H00)
 INDEX 1 0 0 1
 \ there are 6 layers, 0 to MOD(5)
 \ layer 3 (H=2) had the X-rays turned down!
 LAYERS 1 1 1.3 1 1 1
 OVERALL     20.821314   EXTPARAM=21.2
 ATOM C 1  U[ISO]=0. X=-0.231   0.085   0.066 
 CONT .038 .043 .041 .001 -.006 .003
 ATOM H 73           X=-0.443   0.231   0.219
 END
 \LIST 23
 \ note that layer scales are not applied unless
 \ set in LIST 23
 MODIFY EXTINCTION=YES LAYERSCALES=YES ANOMALOUS=YES
 \LIST 12
 \ remember that 'FULL' implies the overall scale factor.
 FULL LAYER(3)
 END
 \SFLS
 REFINE
 END

In this example we have some parameters defined by position, (SCALE, TYPE, SERIAL, Y, Z, and the temperature factors), and some by keyword (U[ISO], EXTPARAM and X). Although only layer 3, h=2, is anomalous, layer scales must be given for all layers. The layer scale factors and the extinction parameter are not applied during the computation of structure factors unless LIST 23 requests them.

Batch scale factors are handled in the same way as layer scales, except that the BATCH parameter must be set for each reflection in LIST 6. Remember that the BATCH parameter will be undefined if reflections from different BATCHES have been merged together.

As mentioned elsewhere, LIST 5 can be output from the binary database as a character file. The instruction \PUNCH 5 produces a file in a form suitable for re-input to CRYSTALS. '\PUNCH 5 D' produces a file in the SHELX format. These files can be edited using the manufacturer's editor, and such a procedure might be appropriate in an environment where interactive processing is restricted. In general however, the user is advised to use the \EDIT instruction in CRYSTALS. This is a purpose-built editor for manipulating parameters. Like all editors, it seems to get better as the user becomes more familiar with the facilities. Before editing a LIST 5, the user will usually wish to know something about its contents. Information can be extracted in several ways.

   \SUMMARY LIST 5 LOW
   END

   \MOLAX
   ATOM FIRST UNTIL LAST
   END

   \DISPLAY HIGH
   END

   \EDIT
   LIST HIGH
   END

    \PRINT 5
    END

   \DISTANCE
   OUTPUT MONITOR=DISTANCE
   END

    \MOLAX
    ATOM FIRST UNTIL LAST
    PLOT
    END