Dialog Box: Transformation Parameters [ Control Window ]
The structure which is input and listed in the Control Window is referred to as the Old or original structure, and that derived from it is referred to as the New or transformed structure.
There are three options for the symmetry of the transformed crystal; your can use 1) no symmetry, that is space group P1; 2) you can specify the symmetry; or 3) you can use the program FINDSYM, by Harold T. Stokes and Dorian M. Hatch, to find the space group. [FINDSYM is not available for Macintosh]
If you want to specify the symmetry (option 2), click on the Transformed Cell Symmetry button if the symmetry of the New crystal is to be different from the Old symmetry. The default symmetry is the same as the Old. The symmetry specified here pertains to the New orientation, not the Old, i.e., CRYSCON does not transform symmetry, so you must supply the correct symbol or operations for the transformed unit cell. The symbols for different orientations are listed in the International Tables Vol. 1 (1952) Table 6.2, and in the file HALL.DAT - these symbols all appear in the list box in the Space Group Symmetry dialog.
The use FINDSYM option actually uses the program FINDSYM.EXE (Windows; or findsym [Linux]) exactly as provided by its authors - this program must be in the CRYSCON home directory [for Linux, the files data_space.bin and _wyckoff.bin must also be present]. FINDSYM writes its output to the file FINDSYM.LOG, and this output is copied line by line to the transformation results file output by CRYSCON. FINDSYM uses its own Tolerance, which is similar to that used by CRYSCON (below) in determining whether atoms lie on special positions.
FINDSYM always looks for lattice translations within the generated atoms and assigns new unit-cell parameters for the smallest conventional cell. Thus if your matrix specifies a doubling of the a-axis, for example, this option will not work - the final cell will just be the original one, with the a-axis at its original length. In such a case if you want to use the symmetry of the supercell you must determine what it is yourself and enter it with option 2). Otherwise, select option 1) no symmetry. Typically there are substitutions or other deviations from the original cell if you are going to use a supercell, so after making these modifications you can run the structure through CRYSCON again with a unit matrix and FINDSYM should find the symmetry, if any.
FINDSYM uses certain conventions and there are limitations to the output - the results will use the following settings.
Thus this option cannot be used to transform into a rhombohedral cell, for example. However, the symmetry of the transformed structure can be determined, then the Transformed to Input option in the Input menu can be used, then the structure can be transformed again to the desired setting of the space group using that specified symmetry.
The Numbers after decimal is applied to the fractional atomic coordinates. Atomic positions from X-ray diffraction typically are good to 5 or fewer decimal places, but some programs may require the positions of atoms which are in special positions containing coordinates of 1/3, 2/3 etc. to be specified more precisely. This should occur only in rhombohedral crystals using hexagonal axes (and even then atoms in the unit cell can be selected which do not contain the rhombohedral lattice translations), or in some hexagonal crystals.
Three types of transformation can be carried out.
1. Translation only simply adds the Pre-symmetry translations to the input atoms (Old or original atoms) and does nothing else.
2. Input atoms only applies pre- and post-matrix translations and the translation matrix, but does not try to fill out the unit cell for either the old or new setting. The number of New symmetry-unique atoms will be the same as that of the Old input atoms. This is the only option which will transform anisotropic temperature factors. This option may be used for simple reorientation involving interchange of axes, and other transformations which do not involve a change of symmetry or primitive unit-cell volume. It can be used for primitive to non-primitive transformations and vice-versa, and transformations among different non-primitive Bravais cells. Again, the correct symmetry for the New orientation must be supplied. Use this option when transforming from Cartesian coordinates, as in an imported PDB or mmCIF file, to crystal coordinates
3. Full unit cells will transform all atoms in the Old unit cell to those in the New unit cell, generating new atoms when necessary (supercell or decrease of symmetry) and averaging atomic position when that is necessary (subcell or increase of symmetry). Anisotropic temperature factors are not transformed - they are converted to isotropic. Vectors are transformed, although if the symmetry is changed the new vectors are not guaranteed to be consistent with the new symmetry.
The Tolerance is used to decide if atoms are coincident, and their positions should be averaged (if the unit cell is decreased in volume, or the symmetry is increased). The tolerance in Angstroms is converted to fractional coordinates on x, y and z, and applied to each atomic coordinate in turn. That is, atoms are considered to be coincident if they fall within a unit-cell shaped box with edges of length equal to the tolerance.
The Numbers after decimal box specifies the number of figures after the decimal for fractional atomic coordinates. This also applies to CIF file export.
Use symmetry on vectors. If this box is checked, vectors (such as magnetic spin vectors) will be operated on by the symmetry elements. If not, the atoms generated from each input atom will all have the same vector as that input atom. Note that CRYSCON, unlike ATOMS, does not apply Shubnikov symmetry.
The Standard matrices combo box will supply matrices for some common unit-cell transformations. These matrices should all preserve the chirality or "hand" of the structure - other combinations of signs on the coefficients are possible, particularly for the last five matrices for simple interchange of axes.
The parameters specified on the left side of the Tranformation Parameters dialog, going downward in the dialog, correspond to the operations successively carried out by CRYSCON - see General Procedure for more detail. After setting and verifying all parameters, click on the Transform button, and the results appear in a new text window (see Types of Windows).
First, Pre-symmetry translations may be applied to the input atom coordinates. If the origin for your atomic coordinates does not correspond to that of the standard symmetry specified for the Old crystal, corrections must be made here.
If you have the inverse transformation matrix or that for going in the opposite direction to that desired - that is, you have the "new" to "old" matrix - you can enter the matrix and then use the Invert Matrix button.
---Translation only (origin shift) option
Nothing beyond Pre-symmetry translations is done the remainder of the parameters are ignored.
---Input atoms only option.
The Pre-matrix translations are applied to the Old input atoms, they are transformed with the matrix, and the Post-matrix translations are applied. (Pre-symmetry translations are not used).
Use this option if you want to convert a set of atoms in Cartesian coordinates to fractional crystal coordinates, as for a PDB file.
---Full unit cells option
CRYSCON now generates all the atoms in the Old unit cell. If the origin of the New unit cell differs from that of the Old, with respect to the common symmetry elements, you must make corrections in either the Pre-matrix translations or Post-matrix translations edit boxes. Such differences among sub/supergroups are common, and it may be necessary to study the diagrams and coordinates in the International Tables to get these translations. CRYSCON transforms the vectors on the input atoms with the symmetry matrices. In the case of special positions, the vector is taken from the first atom generated for that position. For subsequent atoms generated for that position, the new vector is compared and a warning message issued if the two vectors are not the same.
The transformation matrix is in the nine edit boxes. Some common standard transformation matrices may be selected in the Standard matrices combo box to the right. The upper three coefficients (first line) of the matrix give the New a-axis in terms of the old a, b and c axes. Likewise the second and third lines specify the new b- and c-axes.
CRYSCON now transforms the coordinates according to the matrix supplied, adding additional atoms by translation if necessary, or averaging atomic positions when necessary. The Tolerance is used to decide when atomic positions are "coincident", and must be averaged. The tolerance should be large enough to avoid having quasi-superimposed atoms in the result, but of course it must be less than the smallest bond length in the structure. Setting this may take some trial and error. A value of 0.4-0.5 seems to be large enough for even rather extreme cases of atomic shifts in sub/supercells and sub/supergroups.
CRYSCON does not attempt to average vectors on coincident atoms; it takes the vector from the first-generated atom and issues a warning message if vectors on subsequent coincident atoms are not the same.
Post-matrix translations may be applied here if the standard origin for the New space group is different from that of the Old space group. This is an alternative to the Pre-matrix translations - it should not be necessary to use both.
CRYSCON now applies the New symmetry to eliminate symmetry-equivalent atoms. Again a tolerance is applied to decide if atom positions are "coincident". This generates a standard set of symmetry-unique atoms, or the "asymmetric unit". However, in many cases when generating a subcell or increasing the symmetry the averaging process does not put the new atoms exactly on special symmetry positions and the calculation must be repeated in part - see General Procedure.
The Clear button resets the transformation matrix to the identity matrix, and it also resets the Symmetry to be the same as that of the Old structure.
The Transform HKL file button will read a file containing index data and transform the indices.