Adiabatic theory of symmetry breaking and dipole moments of isotopic molecules. Correct dissociation of their electronic and muonic ions

To calculate the nonzero dipole moment of isotopic molecules such as HD or the correct dissociation limit of ions such as ${\mathrm{HD}}^{+}$ via the usual approach requires cumbersome, expansive nonadiabatic corrections to the Born-Oppenheimer approximation. Such a complication is herein shown unnecessary; the ‘‘best adiabatic’’ approximation of Pack and Hirschfelder [J. Chem. Phys. 52, 521 (1970)] provides a single straightforward formalism which gives such effects correctly and yet retains the potential energy curve concept. Simple example calculations show the size of these symmetry-breaking effects to be at the level of high-resolution spectroscopy for ${\mathrm{HD}}^{+}$ but very large in ions such as dtμ, which contains a deuteron, a triton, and a negative muon.