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. 
Ko Okumura and Yoshitaka Tanimura