Surface vibrational energy relaxation by sum frequency generation: Five-wave mixing and coherent transients

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Abstract
Vibrational energy relaxation of molecular adsorbates at solid surfaces has been measured in several recent experiments by pumping vibrational transitions with resonant picosecond infrared laser pulses and probing the excited state vibrational populations with transient infrared–visible sum frequency generation (SFG). In this paper, we develop a description of the infrared‐pump, SFG‐probe experiment as a five‐wave mixing process in the perturbation limit. Five‐wave mixing describes the effect of finite vibrational coherent response times (T2) on the experimental time resolution and includes coherent interactions between the pump and probe infrared fields which contribute to transient coherent artifacts in the experimental signal. Neither of these effects is included in the previous steady state descriptions of the SFG vibrational probe. The five‐wave mixing expression is developed for a three‐vibrational‐level model of the adsorbate molecule and is integrated numerically for Gaussian pulse shapes to illustrate the effects of coherent artifacts and to compare these artifacts with those observed in pump–probe absorption experiments, which are described by four‐wave mixing. Numerical simulations of the three‐level response for a recent measurement of the surface vibrational energy relaxation of methyl thiolate/Ag(111) illustrate the use of the five‐wave mixing expression to distinguish unambiguously between rapid energy relaxation and coherent artifacts in the experiment.