Table 2 Error budget of the overtone (v = 1, N = 0) → (v′ = 3, N′ = 2) transition frequency of \({{\bf{H}}}_{{\bf{2}}}^{{\boldsymbol{+}}}\)

	Component a₁		Component b₁		Component b₂
Effect	\({{\boldsymbol{f}}}_{{{\boldsymbol{a}}}_{{\bf{1}}},{\bf{nom}}}^{({\boldsymbol{\mbox{--}}})}{\boldsymbol{\mbox{--}}}{{\boldsymbol{f}}}_{{\boldsymbol{a}}}^{({\bf{expt}})}\) (kHz)	Uncertainty (kHz)	\({{\boldsymbol{f}}}_{{{\boldsymbol{b}}}_{{\bf{1}}},{\bf{nom}}}^{({\boldsymbol{\mbox{--}}})}{\boldsymbol{\mbox{--}}}{{\boldsymbol{f}}}_{{\boldsymbol{b}}}^{({\bf{expt}})}\) (kHz)	Uncertainty (kHz)	\({{\boldsymbol{f}}}_{{{\boldsymbol{b}}}_{{\bf{2}}},{\bf{nom}}}^{({\boldsymbol{\mbox{--}}})}{\boldsymbol{\mbox{--}}}{{\boldsymbol{f}}}_{{\boldsymbol{b}}}^{({\bf{expt}})}\) (kHz)	Uncertainty (kHz)
Zeeman shift	80.2	0.46	120.02	0.68	39.87	0.23
a.c. Stark (2.4 μm)	−0.33	0.38	−0.35	0.41	−0.72	0.84
a.c. Stark (313 nm)	0.29	0.08	0.31	0.08	0.52	0.13
RF trap shift	0.05	0.06	0.05	0.07	0.11	0.14
AT splitting	−0.1	0.01	0	0.1	0	0.1
Recoil	17.07	0	17.07	0	17.07	0
Total	97.19	0.6	137.1	0.81	56.86	0.89

\({f}_{a}^{({\rm{e}}{\rm{x}}{\rm{p}}{\rm{t}})}\) and \({f}_{b}^{({\rm{e}}{\rm{x}}{\rm{p}}{\rm{t}})}\) are the two deperturbed spin component frequencies given in the text and \({f}_{{a}_{1},{\rm{nom}}}^{(-)}\), \({f}_{{b}_{1},{\rm{nom}}}\) and \({f}_{{b}_{2},{\rm{nom}}}\) are the Zeeman components measured under nominal conditions shown in Figs. 1 and 2. \({f}_{{a}_{1},{\rm{nom}}}^{(-)}\) denotes the lower frequency component of the Autler–Townes (AT) doublet. See Methods, section ‘Systematics of the \({{\rm{H}}}_{2}^{+}\) E2 transition’, for a detailed discussion of these effects.

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