Reinvestigation of the Infrared Spectrum of the Gas-Phase Protonated Water Tetramer Huan Wang and Noam Agmon* The Fritz Haber Research Center, Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel * S Supporting Information ABSTRACT: Gas-phase H 9 O 4 + has been considered an archetypal Eigen cation, H 3 O + (H 2 O) 3 . Yet ab initio molecular dynamics (AIMD) suggested that its infrared spectrum is explained by a linear-chain Zundel isomer, alone or in a mixture with the Eigen cation. Recently, hole-burning experiments suggested a single isomer, with a second-order vibrational perturbation theory (VPT2) spectrum agreeing with the Eigen cation. To resolve this discrepancy, we have extended both calculations to more advanced DFT functionals, better basis sets, and dispersion correction. For Zundel-isomers, we find VPT2 anharmonic frequencies for four low-frequency modes involving the excess proton unreliable, including the 1750 cm -1 band that is pivotal for differentiating between Zundel and Eigen isomers. Because the analogous bands of the H 5 O 2 + cation show little effect of anharmonicity, we utilize the harmonic frequencies for these modes. With this caveat, both AIMD and VPT2 agree on the spectrum as originating from a Zundel isomer. VPT2 also shows that both isomers have the same spectrum in the high frequency region, so that the hole burning experiments should be extended to lower frequencies. ■ INTRODUCTION The structure of aqueous acid solutions has been a subject of intense debates 1-7 on whether the dominant protonated water structure is H 3 O + ·(H 2 O) 3 (the “Eigen cation”) 3,6 or H 2 O··· H + ···OH 2 (the “Zundel cation”). 2,4,5,7 It therefore seemed reassuring that for gas-phase clusters there was a consensus, 8-12 the protonated water tetramer being an Eigen cation (Scheme 1 left), which is the most stable isomer. 13-15 Its measured infrared (IR) spectrum 8-12 showed several characteristic bands, of which four were reproduced theoretically [the water symmetric stretch (ss) and asymmetric stretch (as) modes near 3700 cm -1 , a strong hydrogen-bonded (HBed) OH band at 2665 cm -1 , and the free bend (b), 1615 cm -1 ]. This, however, left two prominent bands unassigned (at 1750 and 1050 cm -1 ), and a few smaller peaks (1847, 1904, 2307 and the “α band” at 2245 cm -1 ), which are thought to be combination bands. 16 The 1750 cm -1 band was noted to be “markedly similar to that displayed by the isolated Zudnel ion”, 9 but was nevertheless interpreted as originating from an Eigen isomer. Subsequently it was (erroneously 17 ) assigned to the bending mode of the hydronium core. 16 Kulig and Agmon 18 then performed ab initio molecular dynamics (AIMD) simulations using density functional theory (DFT) with the BLYP functional, Dunning’s double-ζ basis set, and no dispersion correction. [These simulations are quantum mechanical for the electrons, but classical for the nuclei.] The Fourier transform of the dipole moment autocorrelation function (DACF), as the computed IR spectrum, indeed showed the two low frequency features (at 1750 and 1050 cm -1 ) for the trans-Zundel isomer (Scheme 1, middle), but not for the Eigen isomer. [The cis- Zundel isomer could not be studied by AIMD because it rapidly converted to the trans form]. They consequently suggested that the observed cluster is a Zundel isomer, or at least a mixture of both isomers. This analysis has recently been contested by Fournier et al., 17 who have performed isomer selective photochemical hole burning IR-IR double resonance measurements on this cluster above 2000 cm -1 . Probing “either of the proposed Zundel specific transitions recovers the full suite of transitions, thus establishing that the observed spectrum is indeed homoge- neous”. 17 Logically, if the Zundel assignment of the probed transitions is beyond doubt, such a result implies that the single isomer is actually the Zundel isomer (cf. ref 19), rather than the Eigen isomer advocated by Fournier et al. However, the frequencies of these “Zundel specific transitions” were taken from the AIMD simulations. 18 These are not quantitative, because classical trajectories do not include nuclear quantum effects (NQE), 20 such as zero-point energy (ZPE) and tunneling. To get a spectrum with NQE included, Fournier et al. have conducted a single anharmonic second-order Vibrational Perturbation Theory (VPT2) 21 computation in Gaussian 09, 22 at the B3LYP/6-31+G(d) level of theory with no dispersion correction, as reported in the Supporting Informa- tion (SI) of ref 17. They concluded that the computed Eigen isomer spectrum agrees nicely with experiment, the 1750 cm -1 band being the combination of two H 3 O + rocking modes 17 and the 1050 cm -1 band assigned to the H 3 O + umbrella (U) mode. Received: February 25, 2017 Published: March 29, 2017 Article pubs.acs.org/JPCA © 2017 American Chemical Society 3056 DOI: 10.1021/acs.jpca.7b01856 J. Phys. Chem. A 2017, 121, 3056-3070