Suppose we Have an atom $A$ that can emit light with frequency $mu_1,mu_2,…$ and an atom $B$ that can emit light with frequency $nu_1,nu_2,…$.

Now suppose that we have a molecule $AB$ formed from these two atoms.

Does this molecule emit light with frequency $mu_1,mu_2,… nu_1,nu_2,…$ or can we have extra frequency?

The frequencies of atoms in a molecule will be different. First of all, the binding will results in splitting of frequencies in proportion to the rate with which electrons hop between the two atoms. Secondly, the electron-electron interaction between the electrons of different atoms will introduce corrections. Finally, there will be vibrational modes due to the oscillations of the interatomic distance, which will produces satellites to the main absorption lines: $$omega_n = omega_0pm nOmega.$$

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