Nonlinear response from linear oscillators: Gas phase 2D action spectroscopy

There have been rapid developments in new spectroscopic methods to collect coherent multidimensional optical spectra using incoherent action-detection schemes such as fluorescence or photocurrents. Recently, we demonstrated the acquisition of two-dimensional infrared (2D IR) spectra of molecular ions cryogenically cooled in the gas phase measured from photodissociation of a weakly bound N2 "tag" molecule. Important differences exist between traditional multidimensional spectra and their action-based counterparts, which are now just being fully realized. Here, we apply standard nonlinear response theory in the pure-dephasing limit to model the cryogenic ion 2D IR spectra of the complex fac-Re(CO)3(CH3CN)3+ in the carbonyl stretch region. The simulated spectra show overall good agreement with the experiment and provide key insights into some of the unique characteristics of action-based 2D spectra. Notably, cryogenic ion 2D IR spectra only display bleaching features and inherent cross peaks between all excited vibrational modes. Action-based 2D IR spectra, therefore, can be measured even in the absence of anharmonicity and anharmonic coupling between modes. While the response from any single mode can be fully modeled from parameters measured in the linear spectrum, under multi-mode excitation both diagonal and cross-peak intensities also depend on the relative dipole moment orientations of other vibrational modes on the same molecule, a quantity not available from linear spectra and often not easily obtained in traditional nonlinear spectroscopy.