Simplest Molecules as Candidates for Precise Optical Clocks

The precise measurement of transition frequencies in cold, trapped molecules has applications in fundamental physics, and extremely high accuracies are desirable. We determine suitable candidates by considering the simplest molecules with a single electron, for which the external-field shift corrections can be calculated theoretically with high precision. Our calculations show that ${{\mathrm{H}}_2}^{+}$ exhibits particular transitions whose fractional systematic uncertainties may be reduced to $5\times {10}^{-17}$ at room temperature. We also generalize the method of composite frequencies, introducing tailored linear combinations of individual transition frequencies that are free of the major systematic shifts, independent of the strength of the external perturbing fields. By applying this technique, the uncertainty of the composite frequency is reduced compared to what is achievable with a single transition, e.g., to the ${10}^{-18}$ range for ${\text{HD}}^{+}$. Thus, these molecules are of metrological relevance for future studies.