Search for variation of fundamental constants: Strong enhancements in $X^2\mathrm{\Pi }$ cations of dihalogens and hydrogen halides

We propose to use diatomic molecular ions to search for strongly enhanced effects of variation of fundamental constants. The relative enhancement occurs in transitions between nearly degenerate levels of different nature. Since the trapping techniques for molecular ions have already been developed, the molecules HBr${}^{+}$, HI${}^{+}$, Br${}_2^{+}$, I${}_2^{+}$, IBr${}^{+}$, ICl${}^{+}$, and IF${}^{+}$ are very promising candidates for such future studies.