Etalon-Assisted Determination of the Complex Index of Refraction of a Solution for the Study of Strong Cavity-Vibrational Coupling of PF 6 - in Acetonitrile.

A new method is established using an etalon cavity to assist in the determination of the wavelength-dependent complex index of refraction of a solution throughout the mid-infrared range. The results are used to study the cavity-vibration polaritons of PF ₆ ^- in acetonitrile. Mixed states are formed by placing solution inside a pair of parallel plate mirrors with a wavelength-scale spacing, i.e ., within an etalon, such that there are cavity states that are angle-tuned into resonance with the strong P-F vibrations. The dominant ν ₃ vibrations of PF ₆ ^- consist of nearly triply degenerate oscillations of the partial-positively charged phosphorous against antisymmetric concerted motions of different sets of fluorine atoms with partial negative charges. These vibrations are dominant even though the solute is 29 times less concentrated than the solvent on a molar basis. The first part of the paper describes the method of determining the complex index of refraction of the solution from a combination of etalon transmission maxima and the attenuated total reflection (ATR) absorption spectrum of the solution. The results are presented as an analytical function including a sum of 37 vibrational contributions. Absolute integrated isolated band intensities were determined to be 463 ± 4, 462 ± 7, and 266 ± 4 km/mol for the three ν ₃ PF ₆ ^- vibrations at 841.4, 847.4, and 854.0 cm ^-1 , respectively, which sum to 1191 ± 9 km/mol for the ν ₃ band. Then, the results are used to simulate the measured etalon transmission using the transfer matrix (TM) method with and without the ν ₃ target vibrations. The etalon transmission simulations reconstruct the position of cavity modes in the absence of target vibrations. They provide input data for the testing of simple quantum mechanical models for the interaction of vibrations with cavity modes and the interactions of vibrations with other vibrations within the molecule and between solute and solvent. The model shows that the nearly degenerate ν ₃ vibrations interact with each other with a vibration-vibration coupling of 33 ± 5 cm ^-1 . This is comparable to the cavity-vibration coupling of 30.4 ± 2.9 cm ^-1 of the two strongest vibrations of PF ₆ ^- .