Crystal-Cartesian conversion. For crystals the mutual orientation of the crystal axes with the Cartesian axes used in the calculation must be specified. The c crystallographic axis is parallel to z, and the b crystallographic axis is in the y-z plane (a* = x). If non-Cartesian axes are used for molecules (which may be convenient for trigonal and hexagonal symmetry), the conversion is the same.
Symmetry elements. The basis functions used for symmetry analysis in VIBRATZ require that symmetry elements have a standard orientation as follows. Any unique axis is parallel to z. Note that this includes the two-fold axis in monoclinic. If a group contains mirror planes parallel to the unique axis and does not contain perpendicular 2-fold axes, one mirror plane is perpendicular to x. If perpendicular 2-fold axes are present, one of them is parallel to x and other mirror planes and 2-fold axes are disposed accordingly. Cubic groups have 3-fold axes on the cube body diagonal. Icosahedral groups have one 5-fold axis parallel to z and an adjacent 3-fold axis in the x-z plane.
The standard symmetry orientation may affect input in three ways.
First, for point groups, input atom coordinates may not be consistent with the orientation of the symmetry matrices. Usually this is a matter of rotation about the z axis, and there is an option to rotate the input atoms about z in the Input Atoms dialog (Input menu).
Second, some space groups in standard settings do not have the orientation specified above. The atom coordinates may be entered for the standard space-group settings, but for proper symmetry analysis it is then necessary to rotate both the symmetry matrices and the atoms to attain the VIBRATZ orientation. The particular space-groups affected are given in the Space-Group Symmetry dialog. When Space-Group Symmetry is selected, usually VIBRATZ automatically supplies the appropriate rotations to the Pre-Calculation Rotations dialog, but it may sometimes be necessary to specify these rotations, for example if the Custom Symmetry option is used. All calculated Output, such as atomic displacements and spectral intensities, assumes the orientation after the Pre-Calculation Rotations.
Third, if a special symmetry file is provided for a point group which is not one of those provided in the Point-Group Symmetry dialog, the basis functions given in that file must be consistent with the symmetry matrices and the polarization components also in that file, but the orientation does not have to be the VIBRATZ standard (see Making Symmetry Files).
Orientation in Atoms graphics window. The orientation of reference Cartesian axes in this window is x pointing directly out of the screen or paper, towards the observer; y horizontal to the observer's right; and z vertical. In the dialog bar of the Atoms Windows itself, and in the Rotation menu which is present when this window is active, there are options to rotate the image of the structure and the atomic displacement vectors. The original or base orientation for this image is that attained after the Pre-Calculation Rotations. Any rotations of this image have no effect on the calculations; they are all erased every time a calculation is made.