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Theory of sum frequency generation in a gas bordering a solid

We theoretically analyze infrared-visible sum-frequency generation (SFG) from gas molecules near a solid. The incident IR radiation is supposed to be in resonance with one of the normal intramolecular vibrations. We separate the evolution of the molecule's internal and external degrees of freedom using an adiabatic approximation. We solve the equation of translational motion containing the `integral of collisions' with phonons in the basis of ingoing and outgoing waves. The SFG spectrum is shown to be consisting of two lines, one at the sum frequency and a satellite arising from the desorbing molecules. The line shapes obtained are determined by the rate of `collisions with phonons' as well as molecule-surface distance dependence of the vibrational frequency and linewidth.