Weakly perturbative imaging of interfacial water with submolecular resolution by atomic force microscopy

Scanning probe microscopy has been extensively applied to probe interfacial water in many interdisciplinary fields but the disturbance of the probes on the hydrogen-bonding structure of water has remained an intractable problem. Here, we report submolecular-resolution imaging of the water clusters on a NaCl(001) surface within the nearly noninvasive region by a qPlus-based noncontact atomic force microscopy. Comparison with theoretical simulations reveals that the key lies in probing the weak high-order electrostatic force between the quadrupole-like CO-terminated tip and the polar water molecules at large tip–water distances. This interaction allows the imaging and structural determination of the weakly bonded water clusters and even of their metastable states with negligible disturbance. This work may open an avenue for studying the intrinsic structure and dynamics of ice or water on surfaces, ion hydration, and biological water with atomic precision.

The sharp lines in the ∆f images emerge from branching of probe-particle trajectories over saddle points of the total tip-sample interaction potential at small tip-water separations as discussed in Supplementary ref. 1. In the case of non-planar and strongly polarized system, such as water clusters, it leads to even more intriguing and unintuitive results, which deserve detailed discussion. The total interaction potential between the functionalized tip and the water molecules adsorbed on surface consists of Pauli repulsion, London dispersion and electrostatic interaction.
In the case of CO-tip, the image contrast can be fully understood by simulations ( Supplementary Fig. 2a-f) that consider just the former two components of the potential (Pauli repulsion and London dispersion). This assumption can be justified by a small charge presented on the CO-tip (see Supplementary Fig. 6). Characteristic sharp square lines appear between the upward H atoms as a result of the saddles in the Pauli repulsion, which are visible also in a contour of the total electron density of the cluster (see Supplementary Fig. 2c and f). Due to the finite van der Waals radius of the probe particle (see Supplementary Fig. 6), it moves around on slightly larger surface as described by the concept of "solvent excluded volume" introduced in biochemistry 2 . The potential saddles lead to branching of the probe particle trajectories (Supplementary Fig. 1b and e), which gives rise to the sharp square in the ∆f images ( Supplementary Fig. 2a and d). The center of the sharp square exhibits contrast inversion at very close tip-sample distance (see Supplementary Fig. 1h and m) as the probe particle is locked in the center of the square and further relaxation is prevented.
On the contrary, the image contrast acquired with the Cl-tip is strongly affected by the electrostatic field of the water cluster, leading to very different features at small tip-sample distance, which can be also reproduced by our simulations using a monopole tip (see Supplementary Fig. 2g and j, Fig. 3e and j). Based on these simulations, we can rationalize the origin of two main differences compared with the CO-tip case: (i) the shrinking of central square and (ii) appearance of additional fork-like features at the periphery (large amplitude, Fig. 3c and h) and chiral ear-like rings (small amplitude, Fig. 3d and i). All these features can be ultimately tracked down to a map of electrostatic potential (Supplementary Fig. 2i and l) overlaid on top of a contour of total electron density (or Pauli repulsion) along which the probe particle slides upon tip approaching. In the case of Cl-tip, the presence of the electrostatic field above the water tetramer makes the relaxation of probe particle more complicated. The probe particle (Cl ion) is repelled from negatively charged center toward positively charged H atoms, but then it suddenly slips off due to the Pauli repulsion over protruding H atoms and the restoring spring force of the tip. This sudden slip-off leads to additional branching of the probe particle trajectories ultimately manifested as discontinuity of ∆f signal measured on different sides of branching line. Thus, it gives rise to the sharp fork-like features and the chiral ear-like rings in the ∆f images. The exact position of branching lines is very sensitive to the detailed force balance between electrostatic and other forces (Pauli repulsion, restoring spring force). Therefore, the ∆f images obtained with Cl-tip at small tip heights contain some information of the electrostatic field, which is strongly entangled with other force fields. Here, we give specific formulas that define charge distribution on the tip for the multipole tip models. We have discussed three different models in our present paper: monopole (s), dipole (p z ) and quadrupole (d ) (see Supplementary Fig. 3a). A general formula for the spatial distribution of charge density corresponding to a multipolar tip can be This choice gives a straightforward interpretation of the factor Q. For a monopole, it is simply the total charge. For a dipole and quadrupole, and , respectively, give its magnitude.
From the definition of charged tip models, the charge density of a quadrupole is Equivalently, it can be written as Thus, it can be considered as a linear combination of the 1D Laplace filter in the z direction and the 2D Laplace filter in the xy plane. Since the Laplace filter tends to emphasize the local changes of the electrostatic potential, enhanced spatial resolution is expected with a d tip.
Such an effect can be seen very clearly in electrostatic force (F z ) between a point charge (as a test) and different tips ( Supplementary Fig. 3b). From the x-profile of F z ( Supplementary   Fig. 3c), it is obvious that the peak width at half height with a d tip is much smaller than that with an s tip or a p z tip. Besides, a "Mexican hat" shape can be seen at close distance (z=3 Å), which is also consistent with the DFT calculations in Supplementary Fig. 6. Therefore, the d tip does show higher spatial resolution compared with the s tip and p z tip.
In the simulations of the CO-tip, we adopted σ = 0.7 Å and Q = -0.2 e, which means the To extract the contribution of electrostatic force, we plotted the calculated force curves with s, p z and d tips after subtraction of the force with a neutral tip ( Supplementary Fig. 5a).

Supplementary Note 4. Effect of the stiffness (k) and charge (Q) on the simulated
Approximatively, we used an exponential fitting to obtain the decay length of the electrostatic force between the tetramer and different tips. To avoid the effect of tip relaxation at short tip-water separation, only the data points at large tip heights were fitted. The decay length of the d tip is the smallest, as shown in Supplementary Table 1. Similarly, we exponentially fitted the experimental ∆f curves with CO-and Cl-tips after removing the contribution from the NaCl substrate ( Supplementary Fig. 5b). We found that the decay length with the Cl-tip is more than two times larger than that with the CO-tip (Supplementary   Table 1 For comparison, we mapped the electrostatic field distribution of Cl-tip and CO-tip by DFT calculations (Supplementary Fig. 6a, b and c). As shown in Supplementary Fig. 6d, although the Cl-tip (upper half) has much stronger electrostatic field, the quadrupole-like CO-tip (lower half) has a highly localized negative potential at the CO apex showing a "Mexican hat" wavelet-like profile, which is quite similar to the Laplacian of Gaussian function. Thus, the CO-tip indeed behaves as a high-pass filter which can further enhance the spatial resolution by removing the slowly changed background. All these features agree quite well with that of the d tip model (see Supplementary Fig. 3). and large (blue) oscillation amplitude 4 . The kink of the force curve is due to sudden lateral relaxation of the probe particle when lateral component of Pauli repulsion overcomes restoring spring force.

Supplementary Note 7. Effect of the oscillation amplitude on ∆f images
From the comparison of AFM images acquired with the Cl-tip using large (Supplementary Fig. 7a and b) and small amplitude ( Supplementary Fig. 7c and d), it is evident that the small-amplitude regime is much more sensitive to the chiral shape of the electrostatic potential. In general, the ∆f signal results from a weighted convolution of the force over a range of the oscillation amplitude 4 . In the case of large oscillation amplitude, the probe spends large part of the oscillation period at tip-sample distances, where the chirality of the electrostatic potential is almost negligible (Supplementary Fig. 7e, blue curve). In addition, the electrostatic potential changes significantly at the very close distance, having a non-trivial 3D chiral character. In the limit of the small amplitude, the frequency shift is proportional to derivative of force along z-distance ( Supplementary Fig. 7e, red curve).
Therefore, the non-trivial 3D character of the electrostatic potential induces a significant impact on the frequency shift when small amplitude is used. This chirality is further enhanced by a contrast inversion of the sharp features in AFM images ( Supplementary Fig.   7a-d), which is caused by a sudden lowering of the slope of the force curve when the probe particle is deflected laterally (Supplementary Fig. 7e).  Fig. 8b). In contrast, at the large tip height where the chiral electrostatic potential of tetramer is resolved with the d tip, the lateral relaxation of the tip apex is negligible ( Supplementary Fig. 8c, z=6.8 Å). The adsorption inhomogeneity mainly arises from the herringbone reconstruction of the underlying Au(111) substrate, which breaks the energetic degeneracy and inhibits the switching.

Supplementary
Instead, we found that the water dimer and trimer can be switched through a H-bond donoracceptor exchanging process ( Supplementary Fig. 10). Such a switching can be easily induced by CO-tips at small tip heights, but we were able to achieve submolecular-resolution AFM imaging at relatively large tip heights, thus allowing the accurate assignment of those weakly bonded clusters before and after the switching. With Cl-tips, it is very difficult to maintain stable STM/AFM imaging even at large tip heights due to the strong electrostatic interaction between the Cl-tip and the water molecules ( Supplementary Fig. 12). The switching of the dimer and trimer recorded with the same CO-tips at the same adsorption sites indicates that the contrast observed in AFM images does not arise from the asymmetry/scanning directions of the tip nor the different adsorption sites, but depends on the orientation of the water molecules. In In order to be more quantitative on how "weak" the perturbation of AFM imaging can be, we performed systematic AFM measurements to estimate the minimum forces needed to achieve the submolecular resolution, following the method described in Supplementary ref. 5.
We can get F z and the interaction energy U from the frequency shift ∆f at different tip heights according to Supplementary ref. 6 ( Supplementary Fig. 11). The lateral force F x (F y ) can be then obtained from the partial differentiation of the interaction energy U along x (y) direction. It can be seen that the minimum vertical (z) force which yields the submolecular resolution of the water dimer is only about 70.9 pN. The minimum lateral force along x (y) direction is 7.9 (10.5) pN. The corresponding tip-water interaction energy is as small as 40-50 meV, which allows the imaging of metastable water structures with very small transition barrier ( Supplementary Fig.   10).