In this chapter we apply the mathematical methodology that we have developed in the preceding chapters to predict what the 1D and 2D IR spectra will look like for some generic systems. It turns out that 2D IR line shape and cross-peak patterns depend upon the experimental setup chosen to measure the 2D IR spectra, and some are better than others. Thus, this chapter is organized according to the common ways of collecting 2D IR spectra.

Linear spectroscopy

Before discussing 2D IR spectra, we illustrate the concepts of the preceding chapters by applying the methodology to linear infrared spectroscopy. For linear spectra measured using weak infrared light, and assuming that all the molecules are in their ground vibrational state before the laser pulse interacts with the sample, we only need to consider two vibrational levels and one Feynman diagram (Fig. 4.1a, b). Using this Feynman diagram, we develop the response function step by step:

• At negative times, the system is in the ground state, described by the density matrix ρ =|0〈 〉0|.

• At time t = 0, we generate a ρ10 off-diagonal matrix element of the density matrix (we also generate ρ01 element from the corresponding complex conjugate Feynman diagram, which is not necessary to consider because it is redundant). The probability that this happens is proportional to the transition dipole moment μ10.

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