  We propose that a half semiconducting state can exist in trigonal-prismatic
transition metal dichalcogenide (TMDC) monolayers of d$^{1}$ configuration. In
that state both electrons and holes are spin polarized and share the same spin
channel. On the basis of hybrid density functional theory, we predict in
particular that VS$_2$ monolayers are half semiconductors with a direct band
gap. Moreover, we find that the conduction electron spin orientation of VS$_2$
switches under moderate strain. Our predictions thus open up intriguing
possibilities for applications of VS$_2$ in spintronics and optoelectronics.
Our analysis of trigonal-prismatic group-V MX$_2$ (M=V, Nb, Ta; X=S, Se, Te)
monolayers reveals a broad diversity of electronic states that can be
understood qualitatively in terms of localization of $d$ electrons.
