Fundamental Vibration of Molecular Hydrogen

The fundamental ground tone vibration of ${\mathrm{H}}_2$, HD, and ${\mathrm{D}}_2$ is determined to an accuracy of $2\times {10}^{-4}{\mathrm{cm}}^{-1}$ from Doppler-free laser spectroscopy in the collisionless environment of a molecular beam. This rotationless vibrational splitting is derived from the combination difference between electronic excitation from the $X^1{\Sigma }_g^{+}$, $v=0$, and $v=1$ levels to a common $E{F}^1{\Sigma }_g^{+}$, $v=0$ level. Agreement within $1\sigma$ between the experimental result and a full ab initio calculation provides a stringent test of quantum electrodynamics in a chemically bound system.