The fundamental vibrational interval of ${\mathrm{H}}_2^{+}$ has been determined to be $\mathrm{\Delta }{G}_{1/2}=2191.126614(17){\mathrm{cm}}^{-1}$ by continuous-wave laser spectroscopy of Stark manifolds of Rydberg states of ${\mathrm{H}}_2$ with the ${\mathrm{H}}_2^{+}$ ion core in the ground and first vibrationally excited states. Extrapolation of the Stark shifts to zero field yields the zero-quantum-defect positions $-R_{{\mathrm{H}}_2}/n^2$, from which ionization energies can be determined. Our new result represents a 4-order-of-magnitude improvement compared to earlier measurements. It agrees, within the experimental uncertainty, with the value of $2191.126626344(17)(100){\mathrm{cm}}^{-1}$ determined in nonrelativistic quantum electrodynamic calculations [V. Korobov, L. Hilico and J.-Ph. Karr, Phys. Rev. Lett. 118, 233001 (2017)].

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• Electronic structure of atoms & molecules
• Electronic transitions
• Molecular spectra
• Stark effect
• Atomic & molecular beams
• Ions
• Rydberg atoms & molecules
• Photoionization
• Precision measurements