A Method for Determining Small Anharmonicity Values from 2DIR Spectra Using Thermally Induced Shifts of Frequencies of High-Frequency Modes

Abstract

The off-diagonal anharmonicity for a pair of vibrational modes, determined as a shift of their combination level, Δ(12), can be linked to the molecular structure via modeling. The anharmonicity, Δ(12), also determines the amplitude and shape of the cross-peak between modes 1 and 2 measured using 2DIR spectroscopy. For large anharmonicities, the anharmonicity value can be readily obtained from the shape of the cross peak. In practice, however, the anharmonicities are often small (≪1 cm(-1)). In this case, the amplitude of the cross peak rather than its shape is sensitive to the anharmonicity value, and determination of the anharmonicity requires absolute cross-peak measurements. We proposed and tested a new approach of determining anharmonicities, which is based on sensitivity of high-frequency vibrational modes to temperature. The approach permits calibrating the cross-peak amplitude in terms of the effective anharmonicity resulting from the thermal excitation of lower-frequency vibrational modes. It relies on a series of relative 2DIR measurements. While the sensitivity of the method depends on various specific parameters of the molecular system, such as transition dipoles and temperature sensitivity of the high-frequency modes involved, we have estimated that the anharmonicities as small as 0.02 cm(-1) can be determined for the cross peaks between -N(3) and C═O stretching modes using this approach.