Complementary Eigen-Zundel Interpretation Reconciles Thermodynamics and Spectroscopy of Excess Protons in Aqueous HF Solutions

Abstract

Aqueous solutions of HF and HCl behave very differently at intermediate concentrations: HCl dissociates completely, whereas HF remains only partially dissociated and forms bifluoride (HF$_2^-$). This should lead to different excess-proton spectra in HF and HCl solutions, in contrast to experimental reports. Using ab initio molecular dynamics, we show that in HF the proton is not firmly bound to F$^-$, as suggested by textbook chemistry, but dynamically shared with a hydrating water molecule. This is rationalized by a modified Eigen-state description which also explains the formation of HF$_2^-$. The similar vibrational spectra of HF and HCl solutions are explained by a complementary Zundel picture in terms of almost identical excess proton transfer free-energy profiles for HF and HCl. These results reconcile thermodynamic and spectroscopic observations and provide a unified microscopic picture of excess protons in aqueous solution.

Figures (2)

• Figure 1: Analysis of excess-proton solvation, and IR spectra of 7.5 mol/kg HF and HCl solutions. (a) Simulation snapshots of systems containing 224 water molecules and 30 acid molecules, with HF shown on the left and HCl on the right, each including a zoomed view on representative Eigen structures. (b) Chemical structures and probability distribution of excess proton solvation configurations in the Zundel-picture and Eigen-picture for the two acid solutions. (c) Probability of finding an excess proton (H$^+$) and its conjugate base (A$^-$) in HF and HCl separated by a minimal number of hydrogen bonds, as indicated by the circled numbers in the sketch above the panel. (d) Simulated absorption coefficients $\tilde{\alpha}(\omega)$ of pure water, and HF and HCl solutions. The experimental absorption coefficient of pure water haleOpticalConstantsWater1973b is shown for comparison. (e) Difference spectra, as defined in Eq. \ref{['eq:difference_absorb']}, for the simulated acid solutions compared with experimental spectra reported in the literature: HF (6.5 mol/kg) khoramiEtudeMelangesEau1987, HCl (4.5 m) thamerUltrafast2DIR2015, HCl (15.5 m) and HF (17.5 m) giguereH3OIonsAqueous1976. The colored frequency ranges correspond to the transfer-waiting (TW, gray), transfer-path (TP, magenta), and normal-mode (NM, cyan) regions. In the legends concentrations are given in units of molality m$=$mol/kg.
• Figure 2: Analysis of the excess-proton free-energy landscapes in terms of the proton-transfer coordinate $d$ and the heavy atom distance $R$, as schematically illustrated in (a): the coordinate $d$ is the projection of the excess-proton position onto the heavy atoms connecting vector axis (O--O, F--O, or Cl--O) of length $R$. The excess proton is colored in dark turquoise and in all cases, negative $d$ correspond to the proton being closer to the left heavy atom. (b--f) Two-dimensional free-energy surfaces of the excess proton for Zundel configurations: H$_5$O$_2^+$ in HF, H$_5$O$_2^+$ in HCl, H$_3$OF in HF, H$_3$OF in dilute HF, and H$_3$OCl in HCl, respectively. (g) One-dimensional free-energy profiles along the proton-transfer coordinate $d$, for Zundel configurations in concentrated HF and HCl solutions. (h) Same as in (g), but only for H$_3$OF in concentrated and in dilute HF to highlight the effect of screening stabilization of the ion pair F$^- \cdots$H$_3$O$^+$ in HF. The free-energy shift of the ion pair F$^- \cdots$H$_3$O$^+$ between the two concentrations is indicated by the horizontal line. The mechanism underlying the energetic similarity between H$_5$O$_2^+$ and H$_3$OF in HF is illustrated schematically by the chemical structures and surrounding ions shown in the insets of (h). To facilitate comparison with H$_5$O$_2^+$, the $d$ coordinate of H$_3$OF is shifted by $\Delta = 0.04\,\text{\AA}$ in (g) and (h).