Magneto-optical trapping forces for molecules are far weaker than for alkali atoms because the
photon scattering rate is reduced when there are multiple ground states, and because of optical
pumping into dark states. The force is further reduced when the upper state has a much smaller
Zeeman splitting than the lower state. We use a rate model to estimate the strength of the trapping
and damping forces in a magneto-optical trap (MOT) of CaF molecules, using either the A2Π1/2
- X2Σ
+ transition or the B2Σ
+ - X2Σ
+ transition. We identify a new mechanism of magnetooptical
trapping that arises when, in each beam of the MOT, two laser components with opposite
polarizations and different detunings address the same transition. This mechanism produces a strong
trapping force even when the upper state has little or no Zeeman splitting. It is the main mechanism
responsible for the trapping force when the A2Π1/2 - X2Σ
+ transition is used.