Changing Vibration Coupling Strengths of Liquid Acetonitrile with an Angle-Tuned Etalon

Etalon-Assisted Study of the Strong CO Ligand Vibrations of the fac-[Re(CO)3(bpy)(CH3CN)]+ Octahedral Complex

The strong CO ligand vibrations of an octahedral complex, fac-[Re (CO)₃(bpy)(CH₃CN)]⁺, in acetonitrile are observed at 2040 and 1932 cm^-1. Facial rhenium tricarbonyl systems offer very strong and isolated CO vibrations with the potential for interactions between these vibrations. This work first identifies the dominant ion-pair species using attenuated total reflection infrared (ATR-IR) absorption spectra on a dilution series and then determines the strength of these CO ligand vibrations (as isolated vibrations) with a combination of ATR-IR and etalon-based measurements that determine the absolute complex index of refraction of the solution. Finally, the etalon experiments are modeled to study the interaction between vibrations, which is a property not embedded in the solution's complex index of refraction. The ATR-IR spectra are accomplished on a dilution series as well as a larger set of spectra as these solutions evaporated. The A'(1) CO ligand band at 2040 cm^-1 is fit with a sum of three Lorentzian functions characterizing the distribution of free, solvent-separated, and contact ion pairs of this octahedral complex vs concentration. The other CO ligand band at 1932 cm^-1 is broader and complicated by the dynamics of vibrational interactions, the unresolved splitting of the A'(2) and A″ CO vibrations, and ion-pair speciation. The etalon transmission measurements vs angle were on a 0.029 M solution, and Rabi splittings of 19 and 38 cm^-1 were observed for the A'(1) CO vibration and the unresolved A'(2) + A″ CO vibrations, respectively. The great strength of the CO ligand vibrations is evident despite the use of a dilute solution. Integrated band intensities are reported in comparison to hybrid density functional calculations for isolated vibrations. Then, the observed Rabi splittings are modeled to obtain the coupling strength of the CO ligand vibration with etalon cavity modes and with each other. In summary, this work develops a method to determine the concentration of these solutions from the ATR-IR spectrum, characterizes the ion-pairing, shows that the index of refraction is not constant in the IR spectral region of interest, and develops an interaction Hamiltonian that characterizes cavity-vibration and vibration-vibration coupling.

Etalon-Assisted Determination of the Complex Index of Refraction of a Solution for the Study of Strong Cavity-Vibrational Coupling of PF6- 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 PF₆^- 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 ν₃ vibrations of PF₆^- 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 ν₃ PF₆^- vibrations at 841.4, 847.4, and 854.0 cm^-1, respectively, which sum to 1191 ± 9 km/mol for the ν₃ band. Then, the results are used to simulate the measured etalon transmission using the transfer matrix (TM) method with and without the ν₃ 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 ν₃ 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 PF₆^-.

Shining light on the microscopic resonant mechanism responsible for cavity-mediated chemical reactivity

Strong light-matter interaction in cavity environments is emerging as a promising approach to control chemical reactions in a non-intrusive and efficient manner. The underlying mechanism that distinguishes between steering, accelerating, or decelerating a chemical reaction has, however, remained unclear, hampering progress in this frontier area of research. We leverage quantum-electrodynamical density-functional theory to unveil the microscopic mechanism behind the experimentally observed reduced reaction rate under cavity induced resonant vibrational strong light-matter coupling. We observe multiple resonances and obtain the thus far theoretically elusive but experimentally critical resonant feature for a single strongly coupled molecule undergoing the reaction. While we describe only a single mode and do not explicitly account for collective coupling or intermolecular interactions, the qualitative agreement with experimental measurements suggests that our conclusions can be largely abstracted towards the experimental realization. Specifically, we find that the cavity mode acts as mediator between different vibrational modes. In effect, vibrational energy localized in single bonds that are critical for the reaction is redistributed differently which ultimately inhibits the reaction.

Generalization of the Tavis-Cummings model for multi-level anharmonic systems: Insights on the second excitation manifold

Confined electromagnetic modes strongly couple to collective excitations in ensembles of quantum emitters, producing light-matter hybrid states known as polaritons. Under such conditions, the discrete multilevel spectrum of molecular systems offers an appealing playground for exploring multiphoton processes. This work contrasts predictions from the Tavis-Cummings model in which the material is a collection of two-level systems, with the implications of considering additional energy levels with harmonic and anharmonic structures. We discuss the exact eigenspectrum, up to the second excitation manifold, of an arbitrary number N of oscillators collectively coupled to a single cavity mode in the rotating-wave approximation. Elaborating on our group-theoretic approach [New J. Phys. 23, 063081 (2021)], we simplify the brute-force diagonalization of N² × N² Hamiltonians to the eigendecomposition of, at most, 4 × 4 matrices for arbitrary N. We thoroughly discuss the eigenstates and the consequences of weak and strong anharmonicities. Furthermore, we find resonant conditions between bipolaritons and anharmonic transitions where two-photon absorption can be enhanced. Finally, we conclude that energy shifts in the polaritonic states induced by anharmonicities become negligible for large N. Thus, calculations with a single or few quantum emitters qualitatively fail to represent the nonlinear optical response of the collective strong coupling regime. Our work highlights the rich physics of multilevel anharmonic systems coupled to cavities absent in standard models of quantum optics. We also provide concise tabulated expressions for eigenfrequencies and transition amplitudes, which should serve as a reference for future spectroscopic studies of molecular polaritons.