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Theory: Elimination of translations and rotations in the case of molecules

The method outlined in the previous Sections can be applied to molecules without hesitation. However, because molecules are free to displace and rotate in space as a whole, the first six (in the case of a linear molecule, five) frequencies will come out as zero. This can be dealt with exactly by eliminating translational and roatational degrees of freedom during the procedure of building the symmetry-adapted displacements. This is done by orthogonalising the displacements to six (five in the case of a linear molecule) special vectors: (i) three (two) vectors of the centre of mass representing the translation, and (ii) three vectors of the angular momentu, representing rotations. The orthogonalisation is performed using the standard Shmidt method. There will be six (five) linearly dependent vectors after this, which are discarded. Since the chosen six (five) vectors of translations and rotations are invariants, displacements remain symmetry-adapted after this procedure.


next up previous contents
Next: Vm - Vibrations of Up: Calculation of phonons (atomic Previous: Theory: use of symmetry   Contents
Lev Kantorovich 2006-05-08