Jake Tan's Project in Kuo's Group: Rg Solvated H3O+

Tuning the Vibrational Coupling of H3O+ by Changing its Solvation Environment

This study demonstrates how the intermode coupling in hydronium (H3O+) ion is modulated by the composition of the first solvation shell. A series of rare gas solvated hydronium ions (H3O+Rg3, where Rg=Ne, Ar, Kr, and Xe) is examined via reduced-dimensional anharmonic vibrational (RDAV) ab initio calculations. We considered six key vibrational normal modes, namely: the hindered rotation, the two H-O-H bends, and the three O-H stretches. Between the O-H stretches and the H-O-H bends, the first is more sensitive to solvation strength. Our calculations revealed that Fermi resonance between the first overtones of O-H bends and the fundamentals of O-H stretches led to complex spectral features from 3000 to 3500 cm-1. Such interaction is not only sensitive to the type of rare gas messengers surrounding the H3O+ ion; it also exhibits an anomalous HàD isotope effect. Although it is accepted that visible combination tones (~1900 cm-1) do arise from the complex coupling between the hindered rotation and the H-O-H bends, the origin of their intensities is not yet clearly understood. We found that the intensity of these combination tones could be much stronger than their fundamental H-O-H bends. Within our theoretical framework, we tracked the combination tone’s intensity back to the asymmetric O-H stretches. This simple notion of intensity borrowing is confirmed by examining eight complexes (H3O+•Rg3 and D3O+•Rg3) with spectral features waiting for experimental confirmations.

The C3v symmetry of H3O+•Rg3 and D3O+•Rg3 greatly simplifies the understanding of the anharmonic coupling. We will begin by examining the Fermi resonance between the overtones and combination tones of the H-O-H bends with the fundamentals of O-H stretches.

In all of the complexes considered in this study, the b1 and b2 modes belong to the E representation. Their first overtones (2b1, 2b2, b1+b2­) belongs to the A1+E representation. These excited states happened to be in the 3000-3500 cm-1 window, where the fundamental O-H stretches (s1, s2, and s3) are located. The s1 belongs to the A1 representation, while both s2 and s3 belong to the E representation. By vanishing integral arguments, the first overtones of the H-O-H bends having the E symmetry can only couple with s2 and s3, while that is having the A1 symmetry only couples with s­1. In D3O+•Rg3, the same symmetry label applies, but their peak positions are located in the range 2100-2600 cm-1. Figure 9 shows the schematic diagram of these couplings.

The simplified energy diagram in Figure 9 allows us to extract anharmonic coupling constant (J) and the differences in zero-order energy (Δε) not only from our reduced-dimensional results but also from experimental measurements. Two assumptions will be made to acquire such information. First, it will be assumed that a two-level system well describes the Fermi resonance between the two A1 states. Second, the effects of electronic anharmonicity are negligible. With these assumptions, only the peak positions and absorption intensities are needed to retrieve (J) and (Δε). The working equation is shown below. Figures 10 and 11 show the observables caused by the coupling.

Figure 9: A vibrational state interaction diagram that describes the coupling of the H-O-H bending overtones (|2,0> and |0,2>) and combination tones (|1,1>) with the fundamental stretching modes for H3O+•Rg3. (Reproduced from publication 4 with permission from the PCCP Owner Societies)