We have, in total-energy calculations and electron-energy-loss measurements
, identified a molecular adsorption state of hydrogen residing above a step
atom on a stepped copper surface. Rotational and vibrational properties of
the molecular motion in the bound adsorption state have been determined fr
om an effective three-dimensional potential-energy surface, derived from de
nsity-functional calculations. Our calculations reveal that the axially sym
metric orientational barrier confines the molecule to rotate in a two-dimen
sional (2D) manner, and corroborate the spectral assignment of our electron
-energy-loss measurements in terms of 2D quantum rotor states. Further supp
ort for the existence of this exotic hydrogen adsorption state comes from t
he good agreement between calculated and measured values of the adsorption
energy, the internal vibrational energy, and the dipole activity of the int
ernal vibration. The calculated adsorption energy is small, and in the rang
e for physical adsorption, whereas the strongly perturbed molecular bond an
d the short hydrogen-copper distance suggest the formation of a surface che
mical bond.