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Local rotation matrices

Local rotation matrices are used to rotate the global coordinate system (given by the definition of the Bravais matrix) to a local coordinate system for each atomic site. They are used in the program for two reasons:

It is of course possible to perform calculations without ``local rotation matrices``, but in such a case the LM combinations given in Table 7.2 (and by SYMMETRY) may not be correct. (A program SYM written by G. Vielsack determines the LM values for arbitrary orientations.)

Fortunately, the ``local rotation matrices`` are usually fairly simple and are now automatically inserted into your case.struct file. Nevertheless we recommend to check them in order to be sure.

The most common coordinate transformations are

Inspection of the output of SYMMETRY tells you if the local rotation matrix is the unit matrix or it gives you a clear indication how to find the proper matrix.

The local rotation matrix R , which transforms the global coordinates r to the rotated ones r', is defined by R r = r'.

There are two simple ways to check the local rotation matrixes together with the selected LM combinations:

A first example for ``local rotation matrices`` is given for the rutile TiO2, which has already been described as an example in section 10.3. Also two other examples will be given (see below).



 
next up previous contents
Next: Rutile (TiO) Up: Appendix Previous: Appendix

2000-04-11