Isotope Effects in the Zundel–Eigen Isomerization of H⁺(H₂O)₆

Abstract

The isomerization pathway between the energetically low-lying Zundel and Eigen isomers of the protonated water hexamer was investigated using high-level ab initio calculations including a treatment of zero-point corrections. On the basis of these calculations, the Zundel−Eigen isomerization was found to proceed through a stable intermediate isomer, which consists of a four-membered ring with two single acceptor water molecules. The inclusion of vibrational zero-point energy is shown to be important for accurately establishing the relative energies of the three relevant isomers involved in the Zundel−Eigen isomerization. Diffusion Monte Carlo calculations including anharmonic vibrational effects show that all three isomers of H + (H 2 O) 6 and D + (D 2 O) 6 have well-defined structures. The energetic ordering of the three isomers changes upon deuteration. The implications of these results for the vibrational spectra of H + (H 2 O) 6 and D + (D 2 O) 6 are also discussed.

Correlations between the Structures and Spectra of Protonated Water Clusters

“…These will be obtained using DMC. For the protonated water clusters with three or four water molecules, e.g., 3H , 3D , 4H-E , and 4D-E , we use the probability amplitudes obtained as part of a previous study, while for clusters containing five and six water molecules, we follow the protocol used in our recent study of the 6H clusters …”

“…The details of DMC and our implementation of guided DMC for water clusters can be found elsewhere. ,,− In this work, we use the potential energy surface that was developed by Yu and Bowman . At the end of the simulation, we obtain a distribution of structures of the ion of interest, which provides Monte Carlo sampling of the ground-state wave function.…”

“…As in perturbation theory, the corrections to the intensities of 1–0 transitions come in at second order; we have used the harmonic intensities in plots of the spectra. This approach is the same as what was used in a recent study of 6H . All of these calculations were performed by using the Gaussian 16 program package.…”

“…Assigning vibrational spectra of medium-sized clusters that are held together by hydrogen bonds has represented a long-standing challenge for theoretical and computational approaches. − Early studies focused on using scaled harmonic calculations to provide assignments. , The challenge in applying this approach to systems that include strong ionic hydrogen bonds comes from the large variability of the anharmonicities of the OH vibrations, depending on the strength of the hydrogen-bonding interaction. For example, if we consider the ratio of the harmonic frequencies to the fundamental frequencies obtained from the assignment of the spectrum of H + (H 2 O) 5 , we find that the ratios for the three vibrations that are assigned to the OH vibrations in the hydronium core range from 0.770 to 0.935. , …”

“…Second-order vibrational perturbation theory (VPT2) has evolved into a method of choice for including anharmonicity in semirigid systems. − While this approach is effective in reproducing the anharmonic frequencies and intensities for vibrations that are well-described as perturbed harmonic oscillators, the approximation breaks down for hydrogen-bonded systems. , This is particularly notable for ionic hydrogen bonds between a hydronium ion and water molecules where the large anharmonicity of the OH stretching vibrations and strong couplings of these vibrations to low-frequency motions that affect the strength of the hydrogen bonds can result in energies of vibrationally excited states being calculated to be lower than the calculated zero-point energy. , This is also illustrated by H + (H 2 O) 5 , where the reported differences between the VPT2 and measured values for the higher frequency OH stretching vibrations of the hydronium core near 2850 cm –1 are smaller than 20 cm –1 , while deviations larger than 250 cm –1 are found for the much more anharmonic lower frequency OH stretching vibration at 1890 cm –1 …”