Towards the calculation of multidimensional vibrational spectra*

Great advances are being made in the experimental realization of multiphoton spectroscopy, such as the experimental confirmation of four- and five-photon absorption in the visible energy range as well as two-dimensional Raman spectra.

The complexity of these nonlinear processes means, however, that computational studies are important for unraveling the full information content of the experimentally recorded spectra. Furthermore, many of the unique responses that can be observed in multidimensional vibrational spectroscopies are directly related to electric and/or mechanical anharmonicities. These methods therefore provide a unique window into molecular vibrational responses that would otherwise be difficult to disentangle from the dominant harmonic contributions.

In this presentation, I will in particular focus on the evaluation of the vibrational response functions that determine a wide class of multidimensional vibrational spectroscopies. Our approach takes as its starting point the Liouville equation, from which a sum-over-states expression for the response function at the appropriate order for an in principle arbitrary number of incident laser pulses is derived. The vibrational contributions to these response functions are determined recursively and the results are evaluated for a general setup of polarization vectors and time-ordering of the incident lasers. For selected numbers of independent variables (i.e. frequencies or frequency differences/sums in the IR range), the program generates spectra of the appropriate dimensionality.

I will provide some illustrations of the code to different multidimensional vibrational spectra. I will also present a benchmark study of the accuracy of density functional theory for the calculation of harmonic and fundamental vibrational frequencies.