A diatomic molecule doesn't have a perfectly quadratic potential energy. So the harmonic oscillator model needs some adjustment to describe real molecules.
Professor I have 3 questions regarding this topic- (1)If this rovibrational graph is different for the fundamental absorption( R branch first transition) from what we have expecting... then we must have to correct the rotational part also ..why only anharmonicity is introduced to Explain this change in absorption band ??? Rovibrational may be Nonrigid rotor+Anharmonic Oscillator.... isn't it??so we also have to correct the energy value for Rigid rotor by the Nonrigid term i.e, E(R)=BJ(J+1)-DJ²(J+1)² (2)Why Q branches are generally forbidden for heterodiatomic molecules? While it appears sometimes (weakly) for some molecules??? (3)Can we draw Rovibrational energy levels for Emissions also???why the emissions are not generally considered in the selection Rules for Rovibrational spectra???
These are good questions. (1) You're right, we do have to include rotational corrections. These are covered in the next few videos in the sequence (centrifugal distortion: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-w6DgknErjXI.html; rovibrational coupling: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-p6jYylRXhYo.html). Anharmonicity was considered first, in this video, because it is the most important of the various corrections to the idealized HO + RR model. (2) The Q branch is forbidden because of the harmonic oscillator selection rule (ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-slacvVeurvw.html). It does appear, weakly, though, because these selection are only rigorously obeyed for a true harmonic oscillator. For an *anharmonic* oscillator, they are mostly true, but occasionally violated. Some discussion of breaking the selection rules is here: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-kI52U241hHk.html (3) Yes, absolutely we can talk about rovibrational emission spectroscopy. The difference in energy between a pair of rovibrational states is the same when a photon is being absorbed to excite the molecule as when a photon is being emitted as the molecule relaxes.
Plotting infrared spectra in wavenumbers is very common. And the since the frequency is just the wavenumber multiplied by the speed of light (ν = c ṽ), the plot looks exactly the same, just in different units. In fact, spectra like this are are often described colloquially as being plotted against "frequency in wavenumbers". But if you want frequency in units of Hz, just multiply the numbers on the horizontal axis by 3⨉10¹⁰ cm/s.
Great question. All diatomic molecules are anharmonic -- they must be, because they will dissociate if you stretch the bond far enough. But it is true that some molecules are more anharmonic than others -- i.e. their anharmonicity constant xₑ is larger. In general, bonds containing an H atom will be considerably more anharmonic than those that do not. Beyond that, the anharmonicity depends in a fairly complicated way on the quantum mechanics of the molecular orbital(s), and is not easy to predict.
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