Quantitative modeling of nonlinear processes in coherent two-dimensional vibrational spectroscopy

The line shapes and intensities in coherent multidimensional vibrational spectra are determined by amplitude level interference between different nonlinear processes. The relative amplitude and phase of each process is controlled by the transition moments and dephasing rates associated with each coherence in a nonlinear pathway. The important nonlinear pathways involve processes that are doubly vibrationally enhanced (DOVE) and nonresonant. The DOVE processes are sensitive to dephasing-induced resonances that change the appearance of two-dimensional spectral features. To understand how these contributions interfere to create a two-dimensional vibrational spectrum, line shapes were measured in the frequency domain for a set of model compounds over a range of vibrational frequencies. The amplitudes and dephasing rates for each pathway were determined by modeling spectra. By comparing the amplitudes with a deuteriobenzene internal standard, quantitative values were obtained for the DOVE processes. The results agree with recent ab initio calculations of the third-order DOVE susceptibilities, previous measurements of the concentration dependence, and estimates based on the absorption and Raman cross-sections of each resonance. The interference effects make the DOVE measurements sensitive to the sign of the transition moments.