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Laser cooling and magneto-optical trapping of molecules typically involvesmultiple transitions driven by several laser frequencies. We analyze howmagneto-optical trapping forces depend on the angular momenta, $F_l$ and $F_u$,and the g-factors, $g_l$ and $g_u$, of the lower and upper states. When $F_l >F_u$ the polarizations must be reversed relative to cases where $F_u \ge F_l$.The correct choice of circular polarization depends on the sign of $g_{u}$ butnot on the sign of $g_{l}$. If $g_{u}$ is zero there is no trapping force, andthe trapping force is very weak whenever $g_u$ is small compared to $g_l$,which it usually is when the cooling transition is the $^{2}\Sigma$ to$^{2}\Pi_{1/2}$ transition of a molecule. For some molecules, mixing of theexcited $^{2}\Pi_{1/2}$ state with a nearby $^{2}\Sigma$ excited state cangreatly increase $g_u$, leading to stronger trapping forces. A strong trappingforce can also be produced by rapidly and synchronously reversing both themagnetic field and the laser polarizations. We simulate a recent experiment onmagneto-optical trapping of SrF molecules, and suggest that an alternativechoice of laser beam polarizations will strengthen the trapping force.

Magneto-optical trapping forces for atoms and molecules with complex level structures