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We develop a Feynman rule for energy-level diagrams emphasizing theirconnections to the double-sided Feynman diagrams and physical processes in theLiouville space. Thereby we completely identify such diagrams and processescontributing to the two-dimensional response function in the Brownianoscillator model. We classify such diagrams or processes in quartet andnumerically present signals separately from each quartet of diagrams orLiouville-space processes. We find that the signal from each quartet isdistinctly different from the others; we can identify each peaks in frequencydomain with a certain quartet. This offers the basis for analyzing andassigning actual two-dimensional peaks and suggests the possibility ofLiouville-space-path selective spectroscopy. As an application we demonstratean example in which two familiar homogeneous mechanisms of relaxation aredistinguished by existence or non-existence of certain peaks on thetwo-dimensional map; appearance or disappearance of certain peak is sensitiveto the coupling mechanism. We also point out some confusion in the literaturewith regard to inclusion of relaxation effects

the journal of physical chemistry. a/the journal of physical chemistry. a.

Energy-Level Diagrams and Their Contribution to Fifth-Order Raman and Second-Order Infrared Responses: Distinction between Relaxation Models by Two-Dimensional Spectroscopy