  We screened six cobalt-based 18-VEC systems CoVSi, CoNbSi, CoTaSi (Si-group)
and CoVGe, CoNbGe, CoTaGe (Ge-group) by the first-principles approach, with the
motivation of stabilizing these orthorhombic phases into the cubic symmetry --
favorable for thermoelectrics. Remarkably, it was found that the Ge-group is
energetically more favorable in the cubic symmetry than the hitherto
orthorhombic phase. We account the cubic ground state of the Si-group to the
interplay of internal pressure and covalent interactions. The principle of
covalent interactions will provide an insight and could be vital in speeding
the search of missing cubic half-Heusler alloys. Meanwhile, the calculated
transport properties of all the systems on \textit{p}-type doping, except
CoVSi, are more promising than the well-known CoTiSb. We also provide
conservative estimates of the figure of merit, exceeding the CoTiSb. Based on
our findings, we suggest possible new phases of ternary compounds for
thermoelectric applications.
