(Color) Spectra of ice (left panels) and of liquid water (right panels). Color coding: black, IR; red, parallel-polarized Raman (the incoming polarization parallel to the outgoing polarization, spectrum averaged over all possible incoming polarizations); green, perpendicular-polarized Raman (the incoming polarization perpendicular to the outgoing polarization, averaged over all possible polarization directions); blue, density of bond frequencies; and cyan, density of states. Relative units; parallel and perpendicular-polarized Raman are on the same scale. (A) Computed spectra of top five bilayers of an ice slab at . (B) Experimental ice spectra, Raman spectra are averages over different polarizations of single crystal spectra given in Ref. 63. IR spectrum at from Ref. 46. (C) Calculated liquid spectra for top of a liquid slab at . (D) Experimental liquid spectra. Polarized Raman spectra derived from isotropic and anisotropic spectra of Ref. 64 at (solid) and (dashed). IR spectra at adopted from Ref. 65.
(Color online) Bottom: SFG- spectra of liquid surface, computed with different values of the damping constant . Solid lines, from top to bottom: , 30, 60, 80, and at . Above (dangling-OH region), was set to for all curves. Relative units. In all the calculations, was set to 0.1 units. Dot-dashed line: as a function of frequency. Five liquid layers (i.e., top ) were included in the calculation. Top panel: experimental spectrum from Ref. 54.
(Color) Distribution of bond frequencies for one of the proton-disordered ice models. Bottom panel: black, red, and green correspond to first, second, and third ice bilayers. The top panel shows the breakdown of all top layer bond frequencies (black) to contributions originating from different coordinations. Green, three-coordinated molecules and red, three-coordinated . Blue and brown: OH bonds of four-coordinated molecules which are H bonded to and molecules, respectively. Cyan: OH bonds connecting the top bilayer to the one below.
(Color) Panels (A) and (B): resonant contribution to elements for ice; same relative units are used for all elements. Black, green, and red correspond to calculated with one, two, and three top bilayers of ice, respectively. The results for five bilayers are very similar to those for three bilayers. Blue: , calculated with three bilayers, and reduced by a factor of 2 to ease the comparison with . (A) Decoupled OH bonds (“HDO isotopically isolated in ice”). (B) . Panels (C) and (D): computed SFG spectra; the same relative units are used for all spectra. Red, spectrum, which is determined by , and blue, spectrum, determined by a linear combination ; the relative contributions were derived for the experimental geometry employed in Fig. 6. (C) Hypothetical spectra with OH bonds assumed decoupled. Dashed line corresponds to the spectrum of 25% HDO isolated in ice (intermolecular coupling set to zero). (D) Fully coupled ; the peak of the dangling-OH feature is at .
(Color online) Distribution of , where denotes an angle of a OH bond with respect to the axis. was averaged over sections of classical trajectory; see Sec. II. Panel (A): distributions of for the first, second, and third bilayers of the crystal ice slab and for the reconstructed top bilayer, see end of Sec. III. Panel (B): distribution of for -oriented OH bonds connecting the bilayers for the crystal slab model. From bottom to top on the right and from top to bottom on the left, the five lines correspond to (1) top bilayer, OH pointing down into the surface; (2) second bilayer, up; (3) second bilayer, down; (4) third bilayer, up; and (5) third bilayer, down.
(Color online) Computed spectra of crystal ice surface [(A) and (C)] compared to experimental ones in the H-bonded region [(B) and (D)]. The computed spectra correspond to the experimental geometry. Since the model overestimates OH frequency shift due to H bonding, the scales of the top and the bottom spectra were displaced with respect to each other, so that the computed and the experimental spectral bands roughly overlap. Dot-dashed lines in panels (A) and (C) correspond to an ice model with a partially reconstructed top bilayer, see text. Three ice bilayers were included in the calculations. The same relative units are used for all computed spectra. Panels (A) and (C): computed spectra in the order of decreasing peak intensities correspond to (crystal surface), (crystal surface), and (reconstructed surface). Panels (B) and (D): experimental spectra in the order of decreasing peak intensities correspond to 128 and .
(Color online) A snapshot of a crystal top bilayer of ice and of a partially reconstructed top bilayer from a simulation.
(Color) Resonant contribution to elements for liquid water; the same relative units are used for all elements. (AA): decoupled OH bonds (“HDO isotopically isolated in ”). Solid line corresponds to calculated with three-top layers of water. Other lines show contributions of of different hydrogen-bond coordinations to . Diamonds, OOHH molecules (“two bonds via O, two bonds via H,” 61%); triangles, OOH (19%); circles, OHH (7%); and dot dashed, OH (11%). The numbers in parentheses denote integrated percent contributions to in the range within the negative H-bonded band. (A) decoupled OH bonds. Solid black, green, and red lines correspond to calculated with one, two, and three top layers of water, respectively. The results for five layers are very similar to those for 3. Blue: , calculated with three layers, and reduced by a factor of 2 to ease the comparison with . Dashed line: density of (decoupled) states of the liquid [blue curve of Fig. 1(C)] multiplied by to ease the comparison with elements. (B) Fully coupled . Color coding as in (A), except black and blue correspond to five liquid layers. Dashed and dot-dashed lines: calculated IR and parallel-polarized Raman spectra of liquid [black and red curves of Fig. 1(C)] multiplied by to ease the comparison with the elements.
(Color online) Excited state properties for the OH Hamiltonian corresponding to five layers of liquid . An excited state is expanded in the exciton basis localized on the different OH bonds . (A) Solid: , average number of bonds contributing to an excited state in a liquid. was calculated by (i) sorting bond expansion coefficients according to their absolute value and (b) adding in decreasing order until the sum exceeded 0.6. is the number of terms contributing to the sum. Dashed: Average number of OH for which both OH bonds of a molecule contribute to the sum. Dot-dashed: density of states. (B) Solid: average ratio of coefficients for pairs of bonds belonging to the same molecule; measures local molecular symmetry of the states. Dot-dashed: global symmetry parameter defined as ; the sum is over most-significantly contributing states. for a globally symmetric state with all having the same sign. corresponds to an equal number of positive and negative contributions. Dashed: fractional contribution of the top layer to an excited state. The averages are over excited states within wide frequency bands.
Bond-frequency properties for one of the liquid configurations contributing to the spectra; five liquid layers were included. (A) Difference between two bond frequencies of a molecule vs the average bond frequency. (B) Distribution of differences between two bond frequencies of a molecule.
(Color online) Left two columns: computed SFG spectra for liquid surface; same relative units are used for all the spectra. Five liquid layers were included in the calculation. Right two columns: experimental spectra of Gan et al. (Ref. 10) for different incident angles of visible radiation. values, from top to bottom, for both the experimental and the computed spectra: 39°, 45°, 48°, and 63°. Each pair of and spectra was multiplied by the same -dependent factor to eliminate the dependence of spectra on incident angle. SFG- spectrum is determined by and spectrum is determined by a linear combination of ; the relative contributions depend on the outgoing angle of the SFG beam , to a good approximation (Ref. 29) used in this computation, .
(Color online) (A) Computed squared resonant contribution to the liquid spectrum . Five liquid layers were included in the calculation. Dot-dashed, OH bonds assumed decoupled and solid, fully coupled model. (B) , derived from experiment, adopted from Figs. 2 and 4 of Ref. 54. Solid, and dot-dashed, 25% HDO isolated in . In both panels, in order to compare HDO and line shapes in the H-bonded region, both line shapes were renormalized to correspond to the same integrated intensity in this region (to the red from the feature). The spectra in the top and bottom panels are given in (different) relative units.
(Color online) Bottom: computed SFG- spectra for neat and for an acid solution model with a single ion at the liquid surface. Same relative units are used for both spectra. Five liquid layers were included in the calculation. Top: experimental spectra of the neat vapor/water interface and the vapor/ HCl solution interface at 0.27 and ( 0.5 and 0.1), respectively, from Ref. 21.
(Color online) [(A) and (B)] Molecular angular distributions corresponding to the top five liquid water layers with (squares) and without (circles) at the surface. (A) Distribution of cosines of angles between normals to molecular planes and the axis. (B) Distribution of cosines of angles between the water bisector and the axis. (C) Diamonds: the difference between the two curves in (B)—the curve demonstrates excess molecules with bisectors pointing “into the surface.” Triangles: the difference between the two curves in (A).
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