Question

how does an extra neutron affect vibrational energy? which would be the case in -OH and -OD in terms of higher vibrational energy.

Answer 1

A higher mass leads to lower frequency (\(\nu\)) of oscillations, the energy is given by:

\(E_{n}=(n+1)h\nu\) \(\rightarrow E_{n}\propto \nu\)

From the equation you can observe that a higher frequency leads to a higher energy, thus a higher mass will have a lower vibrational energy.

You can google kinetic isotope effect for further information