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We consider the application of a basic principle of quantum theory, thetracelessness of a certain class of hamiltonians, to the precision spectroscopyof the molecular hydrogen ions. We show that it is possible to obtain thespin-averaged transition frequencies between states from a simple weighted sumof experimentally accessible spin-dependent transition frequencies. We discussthe cases ${\rm H}_{2}^{+}$ and ${\rm HD}^{+}$, which are distinct in themultipole character of their rovibrational transitions. Inclusion of additionalfrequencies permits canceling also the electric quadrupole shift, the Zeemanshift and partially the Stark shift. In this context, we find that measuringelectric quadrupole transitions in ${\rm HD}^{+}$ is advantageous. The requiredexperimental effort appears reasonable.

Canceling spin-dependent contributions and systematic shifts in precision spectroscopy of the molecular hydrogen ions