  The fundamental vibrational interval of H$_{2}^+$ has been determined to be
$\Delta G _{1/2} = 2191.126\,614(17)$ cm$^{-1}$ by continuous-wave laser
spectroscopy of Stark manifolds of Rydberg states of H$_2$ with the 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
$-R_{\textrm{H}_2}$/$n^2$, from which ionization energies can be determined.
Our new result represents a four-order-of-magnitude improvement compared to
earlier measurements. It agrees, within the experimental uncertainty, with the
value of 2191.126\,626\,344(17)(100) cm$^{-1}$ determined in non-relativistic
quantum electrodynamic calculations V. Korobov, L. Hilico and J.-Ph. Karr,
Phys. Rev. Lett. 118, 233001 (2017)
http://doi.org/10.1103/PhysRevLett.118.233001.
