Supplementary Figures

Supplementary Figure 1 | STM/AFM Observation of H2O/Cu(110) with CO-terminal tips. a, STM image of Cu(110) after depositing water at 78 K and CO at 8 K (V = 30 mV, I = 20 pA). The image was obtained at 4.8 K with a Cu-terminal tip. b, STM image of the same area as in a but obtained with a CO-terminal tip. c, The same images as in Fig. 1d in the main text but without the schematic model. d–f, The same STM, AFM, and Laplacian-filtered AFM images as in Fig. 2j, k, and l in the main text, respectively, but with the yellow lines representing the lattice of surface Cu atoms (the unit cell is 2.56

One terminal of a short chain is imaged as a knob (the yellow arrows) whereas the other terminal has the same width as the chain. The former (latter) terminal is assigned to type iii (type i or ii), suggesting that the chains grew from a core like the "tetraphyllous cluster" to yield a terminal of type iii, and that types i and ii correspond to the "growth point" of the chain. Scale bars, 50 Å (a); 20 Å (b). For high-resolution STM/AFM images, a CO molecule was picked up from the surface to attach to the tip apex 3,4 . CO molecules on the surface are observed as round depressions by STM with a Cu-terminal tip (the yellow arrows in Supplementary Fig. 1a), whereas the STM images of CO turn into protrusions after picking up a CO molecule (the yellow arrows in Supplementary Fig. 1b). The zigzag shape of the STM image for the water chains is emphasized by using the CO-terminal tip ( Supplementary Fig. 1b,c).

Supplementary
Coadsorbed CO molecules are also helpful to determine the adsorption sites of water molecules. Supplementary Fig. 1d,e shows STM and AFM images, respectively, of the "tetraphyllows cluster" along with a CO molecule (see Fig. 2j Fig. 2c). Because vertical H2O is more protruded than horizontal H2O (see Fig. 1b), vertical H2O yields a larger attractive interaction with the tip at the tip height.
With decreasing tip height, the Pauli repulsion between vertical H2O and the tip becomes dominant whereas horizontal H2O is still attractive (Supplementary Fig. 2d). At Δz ≤ −1.70 Å, interaction forces over both the vertical and horizontal H2O molecules are repulsive, giving rise to oxygen-skeleton images ( Supplementary Fig. 2e,f). The shape of the force map in Supplementary Fig. 2f is similar to that of the Δf maps at the tip height ( Supplementary Fig. 2b). Note that dissipation signals even at the closest tip height (Δz = −2.00 Å) were below the noise level (~2 meV).  Supplementary Fig. 3), which is responsible for the symmetric pentagonal rings in the AFM image in Fig. 1e in the main text.

Supplementary
To confirm the contribution of H atoms to the AFM images, we conducted AFM simulations using the Probe Particle Model provided by . The surface Cu atoms were also considered in the simulations. Here the electrostatic field of the sample 8 was excluded. It is noteworthy that, in the simulations, the atomic positions of the sample were fixed (i.e., the relaxation of the adsorbate molecules was not considered). Supplementary Fig. 4a shows the structural model we used. The bottom (upper) part of the chain is comparable to a terminal of type i (type ii) as shown in Fig. 2a-c (2d-f) in the main text. Supplementary Fig. 4b-e shows the tip-height dependence of the simulated Δf images. The appearances of the images are quite similar to the experimental force maps in Supplementary Fig. 2c-f. In particular, the oxygen-skeleton images are successfully reproduced in Supplementary Fig. 4d,e. Remarkably, H atoms are not visualized clearly in the simulated images. To confirm that, we use another model in which all H atoms are removed ( Supplementary Fig. 4f). The simulated AFM images of this model  (Fig. 4d). Because the direction of H bonds (i.e., the locations of H atoms) in the water chain cannot be discriminated, two kinds of atomic structures are conceivable.

Supplementary Note 5: Other kinds of defects in pentagonal water chains
We observed several kinds of defects in the water chains. Supplementary Fig. 7a shows STM images of a kink (represented by the red rectangle) and defects (the yellow and blue rectangles). With AFM, the kink is imaged as single-bonded pentagonal rings ( Supplementary Fig. 7b,c). This structure is presumed to originate from an accidental collision of two type-i terminals (see Fig. 2a-c) to yield a single H-bond between the pentagonal rings. As shown in Supplementary Fig. 7d,e, the defect represented by the yellow rectangle in Supplementary Fig. 7a is ascribed to fused hexagonal rings, substituting for a pentagonal unit. This structure is analogous to the kink with a hexagonal unit shown in Fig. 1d,e. The defect represented by the blue rectangle in Supplementary   Fig. 7a has a more complex structure; here, hexagonal rings and twin pentagonal rings are arranged alternately (Supplementary Fig. 7f). This network includes the structure of a "tetraphyllous cluster" (Supplementary Fig. 7g), suggesting two opposite chains grew from the core structure.
STM and AFM images of another characteristic defect are shown in Supplementary   Fig. 8a and d, respectively. The AFM image indicates that the defect consists of three fused hexagonal rings. It is noteworthy that the H-bonding arrangement of the fused hexagonal rings cannot be built only by horizontal H2O molecules. Thus some OH groups must be included in the structure, as shown schematically in the example in Supplementary Fig. 8e. However, we cannot identify the specific sites of the OH groups because the Δf intensity at each vertex of the hexagons is almost identical at several tip heights ( Supplementary Fig. 8b-d). This supports the idea that AFM does not image Hbonds themselves but predominantly reflects the O-atom positions. Such defects were probably formed by the existence of dissociative products of water and/or impurities.
Although water dissociation on the surface occurs above 150 K (ref. 15), the reaction may proceed even at 78 K in extremely low yield.
In addition, the upper parts in Supplementary Fig. 8b-d show the tip-height dependence of Δf images for an intact pentagonal chain. The Δz dependence of the appearances are quite similar to the force maps ( Supplementary Fig. 2c-f) and the simulated Δf images (Supplementary Fig. 4b-e).

Supplementary Note 6: Hexagonal water-hydroxyl islands on Cu(110)
The H2O-OH island in Fig. 3 in the main text was prepared by the following procedure. A clean Cu(110) surface was exposed to H2O gas at 78 K, so that pentagonal water chains were formed on the surface (Supplementary Fig. 9a). After that, the sample was annealed to 160 K for 15 min, followed by re-cooling to 78 K and measured with STM. Then protruded bands were observed (Supplementary Fig. 9b) We observed another island with AFM at 4.8 K. Although the CO-terminal tip which we used for Fig. 3 allows the honeycomb structure to be observed with STM, the inside structure is invisible in an STM image with another CO-terminal tip ( Supplementary Fig. 9c). Even with the tip, the oxygen skeleton is visualized with AFM ( Supplementary Fig. 9d). In this island, several pentagonal rings are located at the edge ( Supplementary Fig. 9e), suggesting that the pentagonal units, which are a dominant structure at 78 K, partially remain. Furthermore, the blue circle in Supplementary Fig. 9e indicates a vacancy within the hexagonal network. These local structures are hardly identified by the STM image ( Supplementary Fig. 9c), further evidencing the tremendous advantage of the AFM measurements.
Next, we consider the details of the assignment for the hexagonal network in Fig.   3c (shown again in Supplementary Fig. 10c). The superposed lines in Supplementary Fig.   10a show  Supplementary Fig. 10b), the dotted bonds are much longer than the other bonds, and therefore, they are assigned to Bjerrum defects (i.e., OH-OH pairs without H bonds between them).
Based on the arrangement of the p(2×6) structure 2, 17 , the inside structure of the islands is assigned in a reasonable manner as shown in Supplementary Fig. 10c. On the other hand, the edge bonds have relatively short O-O lengths (the bold solid lines at the island edges in Supplementary Fig. 10a), suggesting that the edges have different structures from the intact p(2×6) network in order to stabilize the abortive H-bonding network. Therefore, the edges were not considered here. To confirm the validity of the assignment, we show the relationship between the chemical species and the apparent lengths as a stacking histogram in Supplementary Fig. 10d. The bins are color-coded according to the assigned species: H2O-OH (blue), H2O-H2O (grey), and OH-OH (red). The histogram indicates that the distance between H2O molecules is basically longer than that between H2O and OH, in agreement with the property of H bonds; OH acts as a stronger H accepter than H2O and thus yields a stronger H bond (the blue lines in Supplementary Fig. 10c). The apparent length between OH and OH (4.0 ± 0.2 Å) is much longer than that in the p(2×6) model 2 (3.2 Å). This is probably because the finite network in the small islands allows the atomic positions to be easily modified. In AFM images with CO-terminal tips, the apparent bond lengths are magnified from the actual bond length due to the relaxation of CO (refs 9, 18), which also contributes to the difference of the lengths.

Supplementary Note 7: AFM simulations of the hexagonal network
We also conducted AFM simulations for the hexagonal network shown in Fig. 3, using the Probe Particle Model provided by  in the same manner as described in Supplementary Fig. 4. Supplementary Fig. 11b-d shows simulated AFM images of the p(2×6) structure with Bjerrum defects 2,17 (Supplementary Fig. 11a). At a shorter tip height, the image appears as a honeycomb network where all of the oxygen sites have almost the same intensity ( Supplementary Fig. 11d) because the image predominantly reflects the repulsive interaction from the O atoms. In Supplementary Fig.   11b,c, on the other hand, the Bjerrum defects (the blue ellipse in Supplementary Fig. 11a) are slightly more protruded than the other oxygen sites. In the model, the H atoms of OH groups are the most protruded, whereas the geometric heights of all O atoms are almost the same 2 . Therefore, the protrusions at the defects originate from the top-most H atoms.
These results disagree with the experimental images, in which the OH groups are not protruded (see Fig. 3b). To investigate the disparity, we simulated another model in which H atoms are removed from the p(2×6) arrangement ( Supplementary Fig. 11e). In this model, the intensities of each oxygen seemed almost the same, in good agreement with the experimental images. The apparent bonds at Bjerrum defects (i.e., bonds with the longest O-O distance) have slightly weaker intensities than the other bonds ( Supplementary Fig. 11f-h), giving rise to a similar appearance as in Fig. 3c. We assume that the top-most H atoms of OH groups are relaxed and tilted by the approaching tip, accounting for the absence of a significant effect of the H atoms on the AFM images.
We also simulated another hexagonal network model of the "H-down" structure 2 ( Supplementary Fig. 11i). This network consists of a pair of a vertical H2O and horizontal H2O (the blue ellipse in Supplementary Fig. 11i). The vertical H2O molecules, which are located near the Cu atomic row, are ~0.5 Å more protruded than the horizontal H2O.
Owing to the atomic corrugations, the simulated AFM images do not appear as hexagonal rings ( Supplementary Fig. 11j-l), and these images are very different in appearance from their experimental counterparts.

Supplementary Note 8: Pentagonal water chains with additional water monomers
Water molecules form pentagonal chains on Cu(110) at 78-140 K (refs 1, 19), whereas the molecules are adsorbed as monomers under the extremely low coverage at ~6 K (refs 14, 20). Figure 12a shows an STM image of the same sample as Fig. 4 in the main text. The additional H2O molecules are mainly observed as isolated monomers (the solid red arrows). Sample biases of more than ~40 mV induce isolated monomers on the surface to diffuse along the atomic Cu row (the [11 ̅ 0] direction) 20 . At V = 200 mV, the additional H2O molecules in Supplementary Fig. 12a diffuse along the Cu row, but the hopping motion is restricted by the chains (Supplementary Fig. 12b). Even after the diffusion, the isolated monomers are not attached to the chains ( Supplementary Fig. 12c), suggesting a repulsive interaction between the isolated monomers and the chains.
On the other hand, a few water molecules are attached to the water chain (the dotted orange arrows in Supplementary Fig. 12a). At V = 200 mV ( Supplementary Fig. 12b), an attached molecule moved to the next site (near vertical H2O) along the [001] direction ( Supplementary Fig. 12c), in analogy with the hopping motion observed by AFM (see Fig. 4b,c). The difference of the hopping direction between the isolated and attached monomers implies that the adsorption structures are different.