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Whenever we read rotational, vibrational and electronic spectroscopy, we find details on the interaction of the electric dipole moment of the molecule with the oscillating electric field of electromagnetic radiation. The selection rules are also derived on the basis of transition dipole moment operator on wavefunctions. I was talking to spectroscopists today and asked that why do spectroscopy textbooks (and authors) do not mention anything about oscillating magnetic field of light waves. The magnetic field also carries the same energy as the oscillating electric field. Doesn't that interact with electrons as well?* They said that interaction of the magnetic field with a molecule's electric dipole is very weak and hence nobody mentions about it. Does anyone have a good reference or an equation which shows that the oscillating magnetic field interacts very weakly with the molecule's electric dipole moment? They were mentioning Fermi's golden rule and at this stage I lost them.

__ * Electron spin resonance is an example.

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    $\begingroup$ One simple way to intuit the neglect of magnetic field interactions is to note that few molecules have significant magnetic fields to interact with. First order magnetic fields (which would generate a strong interaction with the magnetic field component) are a product are a product of unpaired electrons and these are not that common in stable species. The exceptions are some transition metal compounds and the dioxygen molecule which is a diradical. ESR is an example of a spectroscopic tool that exploits the effect but is often used for exploring short-lived radical intermediates. $\endgroup$
    – matt_black
    Commented Apr 11, 2019 at 9:09

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The magnetic dipole transition intensity is typically about $10^5$ times smaller than the allowed electric dipole but as this can vary by ten orders of magnitude, second order transitions (with terms $x^2,y^2$ etc ) as well as magnetic dipole transitions can occasionally be important. The electric dipole matrix element is $\langle a|\hat r|b\rangle$, where $\hat \mu =e\hat r$, the second order dipole $\langle a|\hat r \hat r|b\rangle$ and magnetic dipole $\langle a|\hat J|b\rangle$ where $\hat J$ is the angular momentum operator $\displaystyle \sim \langle a|z\frac{\partial}{\partial x} - x\frac{\partial}{\partial z} |b\rangle $.
The transition intensity is the square of these terms and the selection rules differ for each type of transition. A derivation is given over several pages by Steinfeld 'Molecules and Radiation' chapter 1, 2nd ed (publ MIT Press).

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  • $\begingroup$ Thanks for the reference. Can the electric dipole moment interact with an oscillating magnetic field of the light wave? $\endgroup$
    – ACR
    Commented Apr 11, 2019 at 11:02
  • $\begingroup$ Magnetic fields interact with particle spin, electron or nuclear, as in nmr spectroscopy (nuclear Zeeman efffect). I'm not aware of the type of interaction you mention, but that may well just be my ignorance. $\endgroup$
    – porphyrin
    Commented Apr 11, 2019 at 18:07
  • $\begingroup$ I got the book by Steinfeld now. It is pretty intensive. Will check if I can find a qualitative version. Thanks. $\endgroup$
    – ACR
    Commented Apr 11, 2019 at 21:17

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