# Rotational magnetic moment and ab-initio calculations

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?

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