In this work we study the last two hydrogen molecular ion isotopologues, ${\mathrm{DT}}^{+}$ and ${\mathrm{T}}_2^{+}$, 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 ${\mathrm{DT}}^{+}$ and ${\mathrm{T}}_2^{+}$ are also calculated.

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• Electronic structure of atoms & molecules
• Fine & hyperfine structure
• Relativistic & quantum electrodynamic effects in atoms, molecules,& ions