Worked example—hydrogendifluoride bifluoride ion

The bifluoride ion (hydrogendifluoride, [HF2]), offers a simple example that permits the mathematics to be worked through in detail. 

using the hydrogen displacements in the x component of the bending vibration at 1235 cm , as an example, the displacement tensors and their trace values, see Eq. (2.38), are calculated. 

Readers may wish to convince themselves that they can obtain the remaining vibrational tensors in a similar manner. The trace values of the individual tensors are given in Table 2.3. From the individual tensors the 

The atom and mode specific tensor The trace value / 

The mode-independent total displacement tensor value for the hydrogen atom is  

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