Variational studies of ro-vibrational spectra of DT${}^{+}$ and T${}_2^{+}$ ions

In this work we study the last two hydrogen molecular ion isotopologues: DT${}^{+}$ and T${}_2^{+}$, for which high-precision calculations have not yet been made. We obtain the nonrelativistic solutions of the Schrödinger equation for the wide range of vibrational states up to the highest possible vibrational $1s{\sigma }_g$ state which are of spectroscopic precision. Transition amplitudes for electric dipole transitions, leading-order relativistic corrections and coefficients of the effective hyperfine structure Hamiltonians for both DT${}^{+}$ and T${}_2^{+}$ are also calculated.