  We perform density functional theory calculation to investigate the
structural and electronic properties of various two-dimensional transition
metal dichalcogenides, MX$_2$ (M$=$Ti, V, Cr, Zr, Nb, Mo, Hf, Ta, or W, and
X$=$S or Se), and their strain-induced phase transitions. We evaluate the
relative stability and the activation barrier between the octahedral-$T$ and
the trigonal-$H$ phases of each MX$_2$. It is found that the equilibrium and
phase transition characteristics of MX$_2$ can be classified by the group to
which its metal element M belongs in the periodic table. MX$_2$ with M in the
group 4 (Ti, Zr, or Hf), forms an octahedral-$T$ phase, while that with an M in
the group 6 (Cr, Mo, or W) does a trigonal-\textit{H} phase. On the other hand,
MX$_2$ with M in the group 5 (V, Nb, Ta), which is in-between the groups 4 and
6, may form either phase with a similar stability. It is also found that their
electronic structures are strongly correlated to the structural configurations:
mostly metallic in the $T$ phase, while semiconducting in the $H$ phase,
although there are some exceptions. We also explore the effects of an applied
stress and find for some MX$_2$ materials that the resultant strain, either
tensile or compressive, may induce a structural phase transition by reducing
the transition energy barrier, which is, in some cases, accompanied by its
metal-insulator transition.
