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Energy-level diagrams and their contribution to fifth-order Raman and second-order infrared responses: Distinction between relaxation mechanisms by two-dimensional spectroscopy

We develop a Feynman rule for energy-level diagrams emphasizing their connections to the double-sided Feynman diagrams and physical processes in the Liouville space. Thereby we completely identify such diagrams and processes contributing to the two-dimensional response function in the Brownian oscillator model. We classify such diagrams or processes in quartet and numerically present signals separately from each quartet of diagrams or Liouville-space processes. We find that the signal from each quartet is distinctly different from the others; we can identify each peaks in frequency domain with a certain quartet. This offers the basis for analyzing and assigning actual two-dimensional peaks and suggests the possibility of Liouville-space-path selective spectroscopy. As an application we demonstrate an example in which two familiar homogeneous mechanisms of relaxation are distinguished by existence or non-existence of certain peaks on the two-dimensional map; appearance or disappearance of certain peak is sensitive to the coupling mechanism. We also point out some confusion in the literature with regard to inclusion of relaxation effects.