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Rotating molecules have an associated magnetic moment that can couple with both nuclear and electronic spin magnetic moments, thereby impacting the hyperfine energies of rotating molecules.

Can one compute such rotational magnetic moments from ab initio calculations?

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The ab initio calculation of hyperfine properties of molecules has been done, for example by Jeremy Hutson's group in this work, this work, and this work. Table I in the last of those papers, and Tables I, II, III, and IV of the first of those papers, all show that high accuracy ab initio methods are not even necessary, as B3LYP/QZ4P level of theory reproduces experimental hyperfine properties almost exactly.

All calculations in those three papers use the ADF software the calculate all hyperfine properties, except for the rotational $g$ factor which is calculated using the DALTON software. The manuals for these programs, will say more about what precisely they are doing when you calculate these hyperfine properties.

One way that you can obtain the molecular magnetic moment of a molecule is by using this definition of the magnetic moment:

$$\tag{1} \mathbf{m} \equiv -\hat{\mathbf{x}}\frac{\partial E}{\partial B_x} -\hat{\mathbf{y}}\frac{\partial E}{\partial B_y} -\hat{\mathbf{z}}\frac{\partial E}{\partial B_z}. $$

So as long as you have a sub-routine that can calculate the energy of a molecule in the presence of a magnetic field (i.e. a typical ab initio calculation with the Hamiltonian containing the extra term $\hat{H}_B$), you can get the magnetic moment.

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