  We present a theoretical study of magneto-optical trapping (MOT) force
exerted on magnesium monofluoride (MgF) with 3D rate equations, in which we
have considered the complex vibrational and rotational levels and the effects
of small internal splittings and degeneracies,including fine and hyperfine
structures and the magnetic quantum numbers. We investigate the feasibility of
MOT for MgF with a very small excited state g-factor ($g_{e} = -0.0002$) and a
large radiative decay reate (${\Gamma} = 2{\pi}\times22$MHz) for the electronic
transition of X$^2{\Sigma}^{+}$ to A$^2\Pi_{1/2}$ states. We also optimize the
MOT with reference to the three-, four- and more-frequency component models
with various polarization configurations and detunings. By applying the dual
frequency arrangement to more than one hyperfine level, we suggest a
configuration of the 3+1 frequency components for achieving the MOT of MgF.
