The LVMs are given in the table. The 998 and 902 cm^{-1} modes are
localised on O_{c} and O_{a}. The 813 cm^{-1} is localised on
O_{b}. The 665 cm^{-1} and other modes are extended over all the O
atoms. Thus the effect of an additional O is to displace upwards the
mode due to VO_{2} by about 100 cm^{-1} and introduce an additional
mode 1000 cm^{-1}. This top mode is in good agreement with a
mode found at 1005 cm^{-1}, although the other modes are about
70-100 cm^{-1} too low. A similar error was found for VO_{2}, and
this error lies within the uncertainties of the method, and again, the
upward mode shift from VO_{2} VO_{3} is correctly
predicted. The prediction and observation of three O-related modes
supports the assignment of the modes at 1005, 976, 910 cm^{-1} to
VO_{3} and therefore indirectly the 889 cm^{-1} mode to VO_{2}.

Just as we had trouble finding the lowest energy structure for VO_{2},
we also found a low energy structure for VO_{3} consisting of an OV
centre with two O_{i} atoms in the dilated bonds neighbouring the
Si-O-Si of the OV. This is similar to the alternative VO_{2} model
described above but with an additional O_{s} sitting in the vacancy.
This proved to be lower energy than the VO_{3} model described above,
and also had good agreement with experimental LVMs. However since the
energies of VO_{2} have to be corrected in order to find the actual
lowest energy structure we have assumed this also applies to VO_{3},
and so exclude this model. Experimental stress induced alignment
experiments should be able to differentiate between these two centres,
since the VO_{3} presented above has C_{1h} symmetry, whereas this
low energy VO_{3} has C_{2v} symmetry. Work is currently underway
on the higher order VO_{n} complexes by Lindström and Hallberg, and
hopefully they should be able to check this.