  Predicting a new Dirac semimetal (DSM), as well as other topological
materials, is quite challenging, since the relationship between crystal
structure, composing atoms and the band topology is complex and elusive. Here,
we demonstrate an approach to design DSMs via exploring the chemical degree of
freedom. Based on the understanding of the well-known DSM Na$_3$Bi, three
compounds in one family, namely Na$_2$MgSn, Na$_2$MgPb and Na$_2$CdSn, have
been exactly located. Further hybrid-functional calculations with improved
estimation of band inversion show that two of them, Na$_2$MgPb and Na$_2$CdSn,
have band topology of DSMs. The nontrivial surface states with Fermi arcs on
the (010) and (100) side surfaces are shown to connect the projection of bulk
Dirac nodes. Most importantly, the candidate compounds are dynamically stable
and have been experimentally synthesized. The ideas in this work would
stimulate more designs on locating topological materials based on the
understanding of existing ones.
