  Molecular magnets based on [Mo$_3$]$^{11+}$ units with one unpaired electron
per trimer have attracted recent interest due to the identification of quantum
spin liquid candidacy in some family members. Here, we present comprehensive
measurements on polycrystalline samples of ZnScMo$_3$O$_8$, MgScMo$_3$O$_8$,
and Na$_3$Sc$_2$Mo$_5$O$_{16}$ with the same Mo$_3$O$_{13}$ magnetic building
blocks. The crystal structures are characterized with x-ray or neutron powder
diffraction and the magnetic ground states are determined by performing ac and
dc susceptibility, specific heat, neutron powder diffraction, and $\mu$SR
measurements. Our work indicates that ZnScMo$_3$O$_8$ and MgScMo$_3$O$_8$ have
ferromagnetic Curie-Weiss temperatures of 18.5 K and 11.9 K, ordered ground
states with net moments (low-moment ferromagnetism or canted
antiferromagnetism), and zero field ordering temperatures of $T_c =$ 6 K and
$<$ 2 K respectively. On the other hand, Na$_3$Sc$_2$Mo$_5$O$_{16}$ hosts a
dynamical magnetic ground state with no evidence for magnetic ordering or spin
freezing down to 20 mK despite an antiferromagnetic Curie-Weiss temperature of
-36.2 K, and therefore is a candidate for quantum spin liquid behavior. By
comparing the present results to past work on the same family of materials, we
construct a phase diagram which illustrates that the magnetic ground states of
these Mo-based molecular magnets are very sensitive to small changes in the
nearest neighbor Mo-Mo distance.
