The vibrational properties of carbon monoxide adsorbed to the copper (100) surface are explored within density functional theory. Atoms of the substrate and adsorbate are treated on an equal footing in order to examine the effect of substrate-adsorbate coupling. This coupling is found to have a significant effect on the vibrational modes, particularly the in-plane frustrated translation, which mixes strongly with substrate phonons and broadens into a resonance. The predicted lifetime due to this harmonic decay mechanism is in excellent quantitative agreement with experiment.An important consequence of molecular adsorption to a metal surface is the emergence of new, low-frequency vibrations associated with fluctuations of the chemisorption bond. These "external modes" correspond to translations and rotations of the free molecule which become frustrated upon adsorption to a substrate. They play an instrumental role in many fundamental processes at surfaces, including chemical reactivity, desorption, and surface diffusion [1][2][3], and are, therefore, of intense scientific interest.In this letter, we theoretically investigate the vibrational dynamics of in-plane frustrated translational (FT) motion for a prototypical adsorbed system: carbon monoxide on the (100) surface of copper at halfmonolayer coverage. Frustrated translational vibrations are considered particularly important in surface chemistry because they are typically very low in energy (a few meV) and are thus thermally activated. This mode has been found to be extremely short-lived for CO on copper, with a lifetime in the few picosecond range [4][5][6]. The mechanisms governing the relaxation of this mode are of considerable interest.The present study focuses on the role of the substrate lattice in FT decay. Vibrational states for the combined substrate-adsorbate system are computed from first principles, with all atoms treated on an equal footing. These investigations reveal that the dominant contribution to FT relaxation comes from resonant mixing of frustrated translations with long-wavelength bulk copper phonons. This is a purely harmonic mechanism, and it gives rise to a computed lifetime in good quantitative agreement with experiment [4]. To our knowledge, this is the first detailed, quantum-mechanical investigation for an adsorbed metal system that demonstrates the strong interaction between adsorbate motion and long-wavelength bulk phonons. An earlier classical model of FT damping [7] considered this type of coupling for the case of an isolated FT oscillator attached to a semi-infinite, elastic medium. The damping was expressed as a macroscopic frictional force. Other microscopic theoretical studies have primarily considered only anharmonic effects in addressing adsorbate-lattice vibrational coupling, and have failed to identify this resonance because they have not modeled a large enough portion of the substrate to accommodate the long-wavelength phonons involved in resonant harmonic mixing.Carbon monoxide on the (100) surface of copper has been ...