Unveiling subsurface hydrogen-bond structure of hexagonal water ice

The phase-resolved sum-frequency-generation (SFG) spectrum for the basal face of hexagonal ice is reported and is interpreted by molecular dynamics simulations combined with ab initio quantum calculations. Here, we demonstrate that the line shape of the SFG spectra of isotope-diluted OH chromophores is a sensitive indicator of structural rumpling uniquely emerging at the subsurface of hexagonal ice. In the outermost subsurface between the first (B1) and second (B2) bilayer, the hydrogen bond of ${\mathrm{O}}_{\mathrm{B}1}-\mathrm{H}\cdots {\mathrm{O}}_{\mathrm{B}2}$ is weaker than that of ${\mathrm{O}}_{\mathrm{B}1}\cdots \mathrm{H}-{\mathrm{O}}_{\mathrm{B}2}$ . This implies that subsurface O-O distance is laterally altered, depending on the direction of O-H bond along the surface normal: H-up or H-down, which is in stark contrast to bulk hydrogen bonds. This new finding uncovers how water molecules undercoordinated at the topmost surface influence on the subsurface structural rumpling associated with orientational frustration inherent in water ice.

Figure 1

Schematic illustration of an ideal full-bilayer termination structure of ice Ih(0001) surface among one of the many possible random orientational alignments of water that satisfies the ice rules. Oxygen of four-coordinated water molecules is colored by red, while that of three-coordinated water molecules at the topmost bilayer is colored by blue. For SFG vibrational spectroscopy, infrared and visible laser pulses are coaxially irradiated onto the ice Ih(0001) surface. (Inset) Schematic illustration of a local tetrahedral hydrogen-bond network.

Figure 2

(a) Thickness dependence of SFG intensity and (inset) $|{\chi }^{\left(2\right)}{|}^2$ spectra of the hydrogen-bonded OH stretching band of isotope diluted HDO ice-Ih(0001) film on Rh(111) measured at 120 K with $\mathit{PPP}$ configuration. (b) ${\mathrm{D}}_2\mathrm{O}$-deposition-induced change of the $|{\chi }^{\left(2\right)}{|}^2$ spectra of the isotope diluted ice film with 140-bilayers thickness at 120 K. (c) Schematic illustration of increase of film thickness and the resultant conversion of surface region into bulk during the layer-by-layer growth mode.

Figure 3

The experimentally observed resonant $\mathrm{Im}{\chi }^{\left(2\right)}$ spectrum for the hydrogen-bonded OH-stretching band of isotope diluted ice Ih(0001) measured at 120 K with $\mathit{PPP}$ configuration. The spectrum is dominated by the $\mathit{ZZZ}$-component of ${\chi }^{\left(2\right)}$ (Appendix pp2).

Figure 4

(a) Classification of OH oscillators at the surface of ice Ih(0001). Only OH oscillators used for definition are shown here and oxygen atoms are colored by red. $\mathrm{B}n$ indicates the $n\mathrm{th}$ bilayer from the topmost surface ($n=1,2,3$), and $\mathrm{B}n$-up (green spheres) and $\mathrm{B}n$-down (blue spheres) are interbilayer OH bonds that orient parallel to the $c$ axis and point toward the surface and into the bulk, respectively. $Bn\mathrm{p}$-up (cyan spheres) and $\mathrm{B}n\mathrm{p}$-down (magenta spheres) are intrabilayer OH bonds that orient nearly perpendicular to the $c$ axis and lean toward the surface and into the bulk, respectively. [(b)–(d)] The $\mathit{ZZZ}$-component of resonant $\mathrm{Im}{\chi }^{\left(2\right)}$ spectra derived from the QM/MM calculation for the hydrogen-bonded OH-stretching mode of isotope-diluted ice Ih(0001). The spectra of $\mathrm{B}n$-down (blue), $\mathrm{B}\left(n+1\right)$-up (green) and their sum [red, $\mathrm{B}n$-down $+\mathrm{B}\left(n+1\right)$-up] for $n=1$ (b) and $n=2$ (c). The spectra of B1-down+B2-up (dashed), B2-down+B3-up (dotted), and their sum (solid) (d).

Figure 5

(a) Schematic illustration of the intermolecular hydrogen bond. $R_{\text{o-o}}$ is intermolecular distance and φ is $\mathrm{O}-\mathrm{H}\cdots \mathrm{O}$ angle. (b) Structural parameters $\mathrm{\Delta }{R}_{\text{o-o}}$ (filled square) and δφ (open circle) for interbilayer hydrogen bond calculated from the MD simulations. The black dashed line is guide to the eye. [(c) and (d)] Hydrogen-bond network at subsurface connected by water molecule with B1-down OH bond (c) and B2-up OH bond (d). Upper and lower halves of each bilayer are labelled with $a$ and $b$, respectively. Hydrogen atoms in the intrabilayer hydrogen-bond network (colored dashed lines) in the B1 and B2 bilayer are omitted. The first solvation shell for water molecules with B1-down and B2-up OH bonds is marked with blue and green shadow, respectively, where the values of $\mathrm{\Delta }{R}_{\text{o-o}}$ and δφ for the interbilayer hydrogen bond are also shown by colored characters. The white number written on the oxygen atom (red sphere) is coordination number of hydrogen bond for each molecule.

Figure 6

(a) $\mathrm{Im}{\chi }_{\mathit{ZZZ}}^{\left(2\right)}, \mathrm{Re}{\chi }_{\mathit{ZZZ}}^{\left(2\right)}$ and (b) $|{\chi }_{\mathit{ZZZ}}^{\left(2\right)}|$ and $\mathrm{Arg}{\chi }_{\mathit{ZZZ}}^{\left(2\right)}$ spectra of the dangling OD-stretching band of HDO ice surface at 120 K. The HDO concentration in ${\mathrm{D}}_2\mathrm{O}$-rich water vapor was $\sim 32$ mol%, corresponding to an [OD]/[OH] ratio of $\sim 3.4$. A black dashed line is a result of curve fitting with a Lorentz function.

Figure 7

(a) $\mathrm{Im}{\chi }_{\mathit{ZZZ}}^{\left(2\right)}, \mathrm{Re}{\chi }_{\mathit{ZZZ}}^{\left(2\right)}$ and (b)$|{\chi }_{\mathit{ZZZ}}^{\left(2\right)}|$ and $\mathrm{Arg}{\chi }_{\mathit{ZZZ}}^{\left(2\right)}$ spectra of the hydrogen-bonded OH-stretch band of HDO ice surface at 120 K. The HDO concentration in ${\mathrm{D}}_2\mathrm{O}$-rich water vapor was $\sim 32$ mol%, corresponding to an [OD]/[OH] ratio of $\sim 3.4$.

Figure 8

Three-layer model under the infinite plane-wave approximation [108]. $n_m(m=0,1,2)$ are the refractive indices of vacuum, HDO crystalline ice, and Rh(111) substrate, $d$ is the thickness of HDO-ice layer. The direction of $P$-polarization vector of reflected light is the same as in Ref. [108]. The SFG process is assumed to take place at vacuum/ice interface.

Figure 9

IR wavenumber dependence of the transfer coefficients $|T_I^{\mathrm{SF}}{T}_I^{\mathrm{VIS}}{T}_Z^{\mathrm{IR}}|$ for $I=X,Y,Z$ simulated at $d=51.8\mathrm{nm}\left(\sim 140\mathrm{BL}\right)$ and ${\theta }_0^{\mathrm{SF}}={\theta }_0^{\mathrm{Vis}}={\theta }_0^{\mathrm{IR}}=61.5^{\circ }$.

Figure 10

IR wavenumber dependence of (a) amplitude and (b) phase of calculated transfer coefficients $T_Z^{\mathrm{IR}}$ and $T_Z^{\mathrm{SF}}$, and the experimentally observed ${\chi }_{\mathit{ZZZ}}^{\left(2\right)}$. The amplitude and phase of $T_Z^{\mathrm{IR}}$ and $T_Z^{\mathrm{SF}}$ are normalized and shifted to take the same value of ${\chi }_{\mathit{ZZZ}}^{\left(2\right)}$ at $3100{\mathrm{cm}}^{-1}$. The horizontal axis of $T_Z^{\mathrm{SF}}$ is derived from the frequency of sum-frequency light subtracted by the frequency of incident visible light.

Figure 11

[(a) and (b)] The half width at half maximum for the distribution of $\mathrm{O}-\mathrm{H}\cdots \mathrm{O}$ angle, δφ (open circle), and the deviations of $\langle R_{\text{O-O}}\rangle$ from the bulk value $\langle R_{\text{O-O}}^{\mathrm{bulk}}\rangle , \mathrm{\Delta }{R}_{\text{O-O}}\equiv \left(\langle R_{\text{O-O}}\rangle -\langle R_{\text{O-O}}^{\mathrm{bulk}}\rangle \right)/\langle R_{\text{O-O}}^{\mathrm{bulk}}\rangle$ (filled square) for various interbilayer (a) and intrabilayer (b) hydrogen bonds. [(c) and (d)] Probability distribution of $\mathrm{O}-\mathrm{H}\cdots \mathrm{O}$ angle φ for interbilayer (c) and intrabilayer (d) hydrogen bonds normalized by the value at $\phi ={180}^{\circ }$. The definitions of $\mathrm{B}n$-up, $\mathrm{B}n$-down, $\mathrm{B}n\mathrm{p}$-up, and $\mathrm{B}n\mathrm{p}$-down are given in Fig. 4.

Figure 12

(a) Density profile of the center of mass for water molecules ($\sim$ position of oxygen atoms). (b) Tetrahedrality at each bilayer. [(c) and (d)] Area normalized probability distribution of tilt angle θ with respect to the $c$ axis for interbilayer OH oscillators (c) and intrabilayer OH oscillators (d). Note that the B1-up OH oscillators do not form H-bond with other molecules and are freely dangling at the topmost surface.