Vibrational Sum-Frequency Generation Spectroscopy in the Energy Representation from Dual-Level Molecular Dynamics Simulations.

We report a cost-effective molecular dynamics approach to calculate sum-frequency generation (SFG) vibrational spectra of molecular species at liquid interfaces in the energy representation formalism that brings together the instantaneous normal mode (INM) analysis at free-energy minima (FEM) and the dual-level free-energy perturbation (FEP) methods. This combined FEP-INM-FEM approach allows analyzing SFG spectra in terms of normal mode contributions at very-high ab initio levels, in contrast to standard time-correlation function (TCF)-based methods, from which it can be considered complementary. It is applied here to the study of the CH3-stretching band of methanol at the air-water interface, which has been thoroughly studied in the literature. The SFG band of acetonitrile in the same conditions has also been calculated with the aim of testing the capability of the method to reproduce small chemical shifts. The suitability of the proposed model is demonstrated by comparing the results with TCF data from QM/MM simulations and with experiments. Analysis of these results provides new insights into the strength and orientational dependence of the SFG signal of symmetric and asymmetric stretching vibrations of CH3 groups, which can be of paramount importance to analyze the spectra of more complex systems.