Modeling Carbon Dioxide Vibrational Frequencies in Ionic Liquids: II. Spectroscopic Map

The primary challenge for connecting molecular dynamics (MD) simulations to linear and two-dimensional infrared measurements is the calculation of the vibrational frequency for the chromophore of interest. Computing the vibrational frequency at each time step of the simulation with a quantum mechanical method like density functional theory (DFT) is generally prohibitively expensive. One approach to circumnavigate this problem is the use of spectroscopic maps. Spectroscopic maps are empirical relationships that correlate the frequency of interest to properties of the surrounding solvent that are readily accessible in the MD simulation. Here, we develop a spectroscopic map for the asymmetric stretch of CO₂ in the 1-butyl-3-methylimidazolium hexafluorophosphate ([C₄C₁im][PF₆]) ionic liquid (IL). DFT is used to compute the vibrational frequency of 500 statistically independent CO₂-[C₄C₁im][PF₆] clusters extracted from an MD simulation. When the map was tested on 500 different CO₂-[C₄C₁im][PF₆] clusters, the correlation coefficient between the benchmark frequencies and the predicted frequencies was R = 0.94, and the root-mean-square error was 2.7 cm^-1. The calculated distribution of frequencies also agrees well with experiment. The spectroscopic map required information about the CO₂ angle, the electrostatics of the surrounding solvent, and the Lennard-Jones interaction between the CO₂ and the IL. The contribution of each term in the map was investigated using symmetry-adapted perturbation theory calculations.