Sets of Atoms Differing in Mass or Chemical Bond Strength

1 Sets of Atoms Differing in Mass or Chemical Bond Strength 

The sets of inequivalent C—H bonds in the above example are of very similar chemical character, and so it is a good approximation to renormalize the bond vibrations to give 

The symmetry operations of the 2 point group link the two H atoms, but the O atom is clearly always distinct for a complete picture we need to add in the O atom motion. Each of the SALCs constructed for the H atoms has been given a symmetry label, and so in each case the O atom must move in a way that conforms to the symmetry of the H atom movement. In Section 5.2 it was shown that the O atom can only move along the direction defined by principal axis in an Aj mode and only in the in-plane T-direction in a 

For the Ai case there are only two possibilities for the O atom either it moves in phase with the H atoms or out of phase with them in the direction defined by b. So, there are two SALCs for the system as a whole that conform to the Ai irreducible representation  

the eoeffleients Ci,o and C2,o are used to emphasize that the magnitude of the movement of the O atom will not be the same as for the H atoms. The absolute amplitude of the H and O atom displacements will not be determined here, so we have also abandoned the normalization factors from Equation (6.56). In fact, in a vibration, the O atom will move to ensure that the centre of mass of the molecule remains static as the atoms oscillate. The O atom is more massive that the H atoms, so its amplitude of oscillation will be smaller than that of its H neighbours. 

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