Experimental determination of structural motifs of interference-free water undecamer cluster (H_2O)_11

Domain: physics
Published: 2025-12-13
Editorial outcome: major_revision

Abstract
Structural characterization of archetypal water clusters is essential for exploring the nature of aqueous hydrogen-bonding interactions that are responsible for the properties of water. While spectroscopic measurement of interference-free neutral water clusters has been proven to be challenging due to the difficulty in size selection, recent studies have successfully measured the infrared spectra of small water clusters (H2O)n (n = 2−10). Thus far, experimental evidence for structural motifs of larger water clusters (H2O)n (n ≥ 11) without environmental perturbation such as an ultraviolet-chromophore label, a messenger tag, or a host matrix has been lacking. Here utilizing the recently-developed size-specific infrared spectroscopy apparatus with a tunable vacuum ultraviolet free electron laser (VUV-FEL) and quantum-chemical studies, we have provided experimental evidence to characterize the structure of interference-free neutral water undecamer (H2O)11. Distinct OH stretching bands provide the evidence for the three lowest-energy isomer families denoted as 515, 43′4, and 55′1 structural motifs. The 515 structure is found to be the dominant one, which features a “5+1+5” assembling of two stacked 5-membered rings with an additional H2O on the side. Formation mechanism of these three structural motifs is proposed based on calculated energetics. This work provides crucial insights into the microscopic development of hydrogen-bonding water networks and advances our capabilities toward size-dependence study of a diverse range of neutral hydrated clusters for exploring the stepwise mechanisms of solvation processes such as salt dissolution and acid dissociation.

Introduction
Water plays an important role in many fields, ranging from geology, environment, biology, to astronomy1–3. Water molecules undergo continuous vibration/rotation and hydrogen-bond (HB) rearrangement, forming various complex yet dynamic hydrogen-bonding networks. Structural characterization of liquid water has been proven to be a grand challenge because of its multifaceted, ever-changing patterns of HBs4. Inasmuch as the nature of the intermolecular forces between water molecules in water clusters bears resemblance to that in the bulk5,6, it is crucial to understand the growth patterns of water clusters. As illustrated recently, the studies on hydrated clusters can provide multifaced values to help understanding the bulk properties, e.g., the water coordination structure around hydroxide in the cluster and aqueous solution is similar7; kosmotropic and chaotropic anions change local water structures distinctively different, amplifying the ion-specific effect at the cluster scale8,9. Water clusters can be studied by adding one water molecule at a time, which helps to determine the size-dependent development of the structural motifs that are difficult to extract from the condensed-phase experiments10–17. Spectroscopic studies of archetypal water clusters thus provided central benchmarks for developing accurate potential functions and universal models of water18,19.

The structures of small neutral water clusters have been studied experimentally and theoretically. The first transition from two-dimensional (2D) to three-dimensional (3D) structure was experimentally verified at the (H2O)5-6 region20–26, the next transition from all-surface to one-water-centered structure was theoretically predicted to occur at (H2O)1727, and the third transition from one-water-centered to two-water-centered structure was expected at (H2O)3028. The largest neutral water cluster for which the precise structure has been experimentally determined without environmental perturbation (i.e., interference-free) is (H2O)10 thus far29–31. An undecamer water cluster, (H2O)11, has hence become the long-standing goal of structural characterization for unraveling the cooperative interactions driven by subtle changes in the hydrogen-bonding topology.

Theoretical studies of (H2O)11 predicted 15 different isomer families based on their oxygen framework and hydrogen-bonding topology32–44. Quantum-chemical calculations with different methods and basis sets may give different relative energy sequences, which makes it difficult to accurately determine the structures. Structural characterization of (H2O)11 without interference from, e.g., an ultraviolet-chromophore label, a messenger tag, or a host matrix is a cumbersome experimental target, because of difficult size-selection. Infrared-ultraviolet (IR-UV) double resonance spectra of phenol-tagged (H2O)11 suggested the presence of “fused-cube” structures45. However, it was unclear whether these structures resulted from the strong attachment of the phenol16,46.

So far, the structures of interference-free neutral (H2O)11 have not been characterized experimentally. Here, we report a size-specific infrared (IR) spectroscopic study of interference-free neutral (H2O)11 using a scheme based on threshold photoionization with a tunable vacuum ultraviolet free electron laser (VUV-FEL). The agreement between experiment and theory leads us to identify three lowest-energy isomer families that are denoted as 515, 43′4, and 55′1 structures, which feature “5+1+5”, “4+3+4”, and “5+5+1” assembling of water molecule/cluster pairs, respectively (vide infra). These results provide important insights into the formation and growth mechanism of diverse HB network structures that are responsible for the complex properties of water.

Results
Assignment of IR spectra of the water undecamer
The experimental IR spectrum of (H2O)11 is shown in Fig. 1a. The corresponding band positions are listed in Table 1.

To assign the experimental spectrum and to identify the structures of existing isomers, theoretical studies were carried out to locate the global-minimum structure on the potential energy surfaces and the harmonic vibrational spectra for (H2O)11. The TGMincode with constrained basin-hopping Monte Carlo algorithm47–49 was used for the global-minimum isomer search, and ab initio MP2/aug-cc-pVDZ (AVDZ) and DLPNO-CCSD(T)/aug-cc-pVTZ (AVTZ) methods were used to calculate the energies and spectra. Our global-minimum structural search found 4521 independent structures for (H2O)11, which identified various low-lying isomers and also cover the previously-calculated isomers32–44. As shown in Fig. 2, the structures of the three lowest-energy isomer families for (H2O)11 (labeled 11A (515A-1), 11B (43′4A-1), and 11C (55′1A-1)) are predicted to be nearly isoenergetic within 0.3 kcal/mol at the MP2/AVDZ level, which are consistent with the previous calculations at the MP2/aug-cc-pVTZ and RI-MP2/complete basis set (CBS) levels40,43. The nomenclature for the structures of (H2O)11 follows the literature40,43, in which the individual digits signify the number of water monomers on a given horizontal plane, and the prime indicates that those monomers do not form a closed hydrogen-bond ring. The simulated IR spectra of the 11A, 11B, and 11C isomers are compared with the experimental spectrum in Fig. 1, and the corresponding harmonic vibrational frequencies in the OH stretching region are listed in Supplementary Tables 3−5, respectively. The three lowest-energy isomers of each family and their corresponding IR spectra are representatively illustrated in Supplementary Figs. 10 and 11, respectively.

In the simulated IR spectrum of isomer 11A (Fig. 1c), the four intense bands of single H-donor OH stretching modes (2960, 3116, 3305, and 3352 cm−1, Supplementary Table 3) are consistent with the experimental values (2965, 3117, 3289, and 3343 cm−1, Table 1); the calculated double H-donor OH stretching modes (3394−3583 cm−1) agree with the experimental bands in the spectra range of 3390−3600 cm−1; the predicted bands of H-donor-free OH stretching modes (3699, 3708, and 3716 cm−1) are in excellent agreement with the experimental bands (3701 and 3715 cm−1). Analogously, the simulated IR spectra of isomers 11B and 11C (Fig. 1d, e and Supplementary Tables 4 and 5) agree with the experimental one (Fig. 1a and Table 1).

The best agreement between the experimental and simulated IR spectra is obtained when assuming a ratio of a 1(11A): 0.8(11B): 0.5(11C) mixture of isomers (Fig. 1b), which is consistent with the calculated relative energies. Note that the estimated relative populations of isomers are slightly different from the Boltzmann distribution of an ideal gas (Supplementary Table 6). The simulated IR spectra of the structures of energetically higher isomer families (44′3′A-X) (Supplementary Fig. 11) exhibit some distinct bands that are not observed experimentally, indicative of trivial contribution to the experimental spectrum. Since the low-lying structures of the same isomer family have similar IR spectra due to similar geometries, unambiguous identification of all the other isomers of the 515A, 43′4A, and 55′1A families is cumbersome unless even higher experimental spectroscopic resolution becomes feasible. Thus, it is more rational to analyze the trend of structural motifs for large water clusters.

It can be concluded that the overall agreement of the calculated spectra of the 515A, 43′4A, and 55′1A isomer families with the experimental one is reasonable to confirm the assignment of these three structural motifs responsible for (H2O)11. Note that the simulated intensities of the 2960 cm−1 bands (single H-donor OH stretching modes) in the 11A and 11B isomers are much stronger than those in the experimental spectrum. It could be rationalized that the coupling between hydrogen-bond fluctuation and OH stretch broadens the OH stretching band. Furthermore, the fluctuation of single H-donor OH stretching mode is larger than that of double H-donor OH stretching mode. This makes it more difficult to directly compare the simulated and experimental intensities of vibrational bands of hydrogen-bonded molecular clusters, owing to the challenge of theory (anharmonicity, intermolecular zero-point motions, etc.) and the complexity of experiment (IR absorption combined with dissociation, intramolecular vibrational-energy redistribution (IVR), etc.), as reported previously29,50,51.

The 11A, 11B, and 11C isomers lie within 0.3 kcal/mol of each other, indicating that they can possibly coexist at the finite temperature of experimental conditions. As shown in Fig. 3, our MP2/AVDZ calculation shows that the 11B → 11A isomerization needs going through several transition states and intermediates, with the largest barrier of elementary process of 3.22 kcal/mol. The largest barrier of elementary process for the 11C → 11A isomerization is calculated to be 2.67 kcal/mol at the same theoretical level (Fig. 3). Such barriers might be sufficiently large so that the 11B and 11C isomers could be kinetically trapped by quenching the nonequilibrium species in the soft expansion of cold molecular beam52, which is reminiscent of the observation of low-lying structures of (H2O)n (n = 5−10) at finite temperature5,25,26,30,53–55.

To assess the temperature effect on the isomer distribution, Gibbs free energies (ΔG) of isomers 11A, 11B, and 11C were calculated in the temperature range of 0−300 K and the results are shown in Supplementary Fig. 13. It turns out that the calculated free energy difference ΔG11B-11A and ΔG11C-11A does not vary noticeably below room temperature, indicating that the population of the 11A, 11B, and 11C isomers changes little at low temperature. Furthermore, the 11C isomer becomes the free-energy minimum above 500 K, which is consistent with the previous predictions43.

Analysis of the electronic structure
To elucidate the nature of the hydrogen-bonding interactions in the water undecamer, the electronic structures of the 11A, 11B, and 11C isomers were analyzed with adaptive natural density partitioning (AdNDP)56, principal interacting orbital (PIO)57, energy decomposition analysis-natural orbitals for chemical valence (EDA-NOCV)58, and natural bond orbital (NBO)59 methods, respectively. The AdNDP and PIO analyses of 11A, 11B and 11C are shown in Supplementary Figs. 14–16 and 17–19, respectively. As pointed out previously26,60, HB bonding in the water clusters may be described by a three-center two-electron (3c2e) interaction featuring the delocalization of an adjacent oxygen lone pair (LP(O)) donor to the antibonding σ*(OH) region. Indeed, for 11A, five 3c-2e HB LP(O)→σ*(OH) on the top face, six 3c-2e HB LP(O)→σ*(OH) on the side face, and five 3c-2e HB LP(O)→σ*(OH) on the bottom face are located, as shown in Supplementary Fig. 14.

The contribution of HB to the total bonding in the 11A, 11B, and 11C isomers is predicted to be 96.0%, 95.1%, and 95.1% (Supplementary Table 7), respectively. As shown in Supplementary Figs. 14–16, the AdNDP results reveal extensive delocalized HB interactions in (H2O)11. The total second-order perturbation interaction energy of the 11A, 11B, and 11C isomers is calculated to be 315.25, 312.13, and 304.21 kcal/mol (Supplementary Tables 8–10), respectively, which supports the trend of structural stability. The calculated Wiberg bond order (WBO) and natural hybrid orbitals (NHO) of these three isomers (Supplementary Tables 11–13) provided detailed bonding information that agrees well with the atomic distances listed in Supplementary Tables 8–10.

Methods
Experimental methods
The experimental IR spectra of (H2O)11 were measured using a VUV-FEL-based IR spectroscopy apparatus62. The water-argon-helium mixture was prepared by using the ultrapure water with resistivity > 18 megohm-centimeters (MΩ-cm). In order to avoid condensation, the operating temperature of the entire gas inlet and the pulsed valve was kept at 353 K. Neutral water clusters were generated by supersonic expansions of a water-argon-helium mixture using a high-pressure pulsed valve (Even-Lavie valve, EL-7-2011-HT-HRR) that is capable of producing very cold molecular beam conditions63. The stagnation pressure was approximately 50 bar. The molecular beam passed through a 4 mm diameter skimmer (Beam Dynamics, Model 50.8) and an aperture with 3 mm opening. The extraction plates of reflectron time-of-flight mass spectrometer (TOF-MS) were powered by a high-voltage direct current (DC) of 2950 V. Ionic water clusters were deflected out of the molecular beam by the DC electric field of the extraction plates.

For the vibrational excitation of (H2O)11, we used a tunable IR laser. Subsequent photoionization of (H2O)11 was carried out with ~50 ns delay with a VUV-FEL light at 115.00 nm, forming (H2O)11+. When the resonant vibrational transition was evoked by the IR laser light and caused vibrational predissociation, a depletion of the selected neutral cluster mass signal can be detected. The IR spectrum of size-selected neutral water cluster (H2O)11 was obtained as a depletion spectrum of the ion signal intensity of (H2O)11+ as a function of IR wavelength. The VUV-FEL in the present experiment was operated at 20 Hz and IR laser was operated at 10 Hz. IR spectra were recorded in the difference mode of operation (IR laser on − IR laser off). IR and VUV power dependence of the signal was measured to avoid the saturation of vibrational excitation and photoionization. IR spectra were normalized with IR power.

As shown in Supplementary Figs. 1–2 and Supplementary Table 1, the rearrangement of (H2O)11+ (labeled 11A+) into [(H2O)(OH)(H2O)9]+ (iso 2) need go through several transition states and intermediates, with the largest barrier of elementary process of 4.03 kcal/mol at the MP2/aug-cc-pVDZ (MP2/AVDZ) level of theory. The largest barrier of elementary process for the [(H2O)(OH)(H2O)9]+ (iso 2) → [(H2O)(H2O)9(OH)]+ (iso 1) isomerization is calculated to be 7.37 kcal/mol at the same theoretical level. The calculated rate constant of unimolecular conversion and half-life time of reactant by using reaction path-variational transition state theory (RP-VTST) (Supplementary Table 2) indicate that when the temperature is lower than 80 K, there is a pretty large window of temperature for which the half-life time of the (H2O)11+ (11A+) → [(H2O)(OH)(H2O)9]+ (iso 2) and [(H2O)(OH)(H2O)9]+ (iso 2) → [(H2O)(H2O)9(OH)]+ (iso 1) isomerization is longer than the millisecond time scale. The conditions with such temperature are available in the supersonic expansions, because the rotational temperature of clusters should be less than 10 K and the vibrational temperature could be higher (i.e., a finite temperature)26,63. Accordingly, it is reasonable to conclude that the (H2O)11+ (11A+) cluster can reach the time-of-flight mass spectrometer (TOF-MS) detector. These results are consistent with previous observation of the (H2O)n+ clusters via the VUV near-threshold photoionization64–66.

Mass spectra obtained with different VUV wavelengths and beam conditions for neutral water clusters (H2O)n (n = 2−11) are shown in Supplementary Fig. 3. The assignment of chemical formula of clusters are discussed in Supplementary Information (Supplementary Figs. 4–7). It can be seen from Supplementary Fig. 8 that the intensity of the (H2O)11+ peak remarkably depletes with IR laser ON (e.g., at 3557 cm−1), whereas that of the H+(H2O)11 peak does not significantly change. As shown in Supplementary Fig. 9, the IR spectra of each individual cluster (H2O)n (n = 2−11) are all different from each other, indicating that these IR spectra are free from spectral contamination of larger water clusters, as demonstrated in our previous structural characterization of (H2O)n (n = 2−10)26,31,53–55,62.

The tunable VUV-FEL light was generated by the Dalian Coherent Light Source (DCLS) facility. With proper optimization of the LINAC (linear accelerator), a high-quality beam with the emittance down to ~1.5 mm milli-radians, a projected energy spread of ~1%, and a pulse duration of ~1.5 ps can be obtained. An online VUV spectrometer was used to record the spectral characteristics (wavelength, energy, time profile) of every VUV-FEL pulse. The tunable IR laser beam was generated by a Potassium Titanyl Phosphate (KTP)/Potassium Titanyl Arsenate (KTA) optical parametric oscillator/amplifier system (OPO/OPA, LaserVision) pumped by an injection-seeded Nd:YAG laser (Continuum Surelite EX). This system is tunable from 700 to 7000 cm−1 with a linewidth of 1 cm−1. The wavelength of the OPO laser output was calibrated using a commercial wavelength meter (High Finesse GmbH, WS6-200 VISIR).

Theoretical methods
Global-minimum structural search based on constrained basin-hopping Monte Carlo algorithm together with quantum-mechanical energies calculated with density functional theory (DFT) was performed for (H2O)11 using TGMincode47–49. Quantum chemical calculations with wavefunction theory (WFT) were carried out to refine the energies of the low-lying isomers (within 5 kcal/mol) at the ab initio MP2/aug-cc-pVDZ (abbreviated as MP2/AVDZ throughout) level using the Gaussian 16 package67. Harmonic vibrational frequencies were calculated with analytical second derivatives of the total energy. A scaled factor of 0.956 was used for harmonic vibrational frequencies to account for the systematic errors in the calculations68. The resulting stick spectra were convoluted by a Gaussian lineshape function with a 6 cm−1 full width at half-maximum (FWHM). The MP2/AVDZ relative energies were calculated at 0 K with corrections of zero-point vibrational energies. The single-point ab initio DLPNO-CCSD(T)/aug-cc-pVTZ (AVTZ) relative energies were calculated on the MP2/AVDZ optimized geometries with the ORCA program69–71, which included the MP2/AVDZ zero-point vibrational energy corrections. Gibbs free energies G(T) = U(T) + PV – TS were calculated with statistical mechanics approach, where U, S, P, V, and T stand for the internal energy, entropy, pressure, volume, and temperature, respectively. Rate constant of unimolecular conversion and half-life time of reactant were calculated by using reaction path-variational transition state theory (RP-VTST) at the MP2/AVDZ level of theory with the GAUSSRATE and POLYRATE programs72,73.

The nature of the hydrogen bonding interaction in (H2O)11 was analyzed with the natural bond orbital (NBO)59, adaptive natural density partitioning (AdNDP)56 and principal interacting orbital (PIO)57 methods at the MP2/AVDZ level, and the energy decomposition analysis–natural orbitals for chemical valence (EDA-NOCV)58 method at the DFT level with GGA PBE-D4/TZ2P approach, respectively. The EDA-NOCV scheme provides both qualitative density (Δρorb) and quantitative energy (ΔEorb) information about the strength and contribution of orbital interactions in chemical bonding, as demonstrated in the study of water clusters (H2O)n (n = 2−10)26,31,53–55. We used the unrelaxed water fragments from the optimized structures to derive the intrinsic binding energies of water clusters.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The manuscript by Wang et al. reports an IR spectrum of (H2O)11 clusters, measured by a combination of IRMPD and VUV photoionization. Quantum chemical calculations indicate that three of the calculated structures can explain most of the features in the spectrum. The three structures are basically isoenergetic, with energy differences well below 1 kcal/mol. Many more structures are close in energy, see Figure S1, and almost equally populated. The authors single out the three low-lying isomers in Figure 2, but it would be relevant to know if any, and if yes, which isomers shown in Figure S1 would not be compatible with the experimental spectrum.\n\nThe authors seem to imply, at least as far as I understand, that they photoionize (H2O)11 cluster and observe (H2O)11(+) in their TOF mass spectrum. This does not make sense to me. It is well established that these clusters rearrange to (H3O+)(OH)(H2O)9 after photoionization. The hydration energy of H3O+ is then released in the cluster, which is very high, and will lead to immediate loss of water molecules. I have thus severe doubts that the IR spectrum of neutral (H2O)11 can be inferred from the ion iontensity of (H2O)11(+), or rather (H3O+)(OH)(H2O)9. The intensity of this peak will rather reflect the ion spectroscopy of a larger cluster. The authors have to discuss this issue and clearly justify how they can be sure that the measured ion intensity is representative of the abundance of the neutral cluster, without loss of water molecules. In this respect, I expect to see a few mass spectra obtained with IR laser on/off and different wavelengths. In addition, some information on the performance parameters of the TOF (resolution, mass accuracy) must be given.\n\nMinor issues:\nL24: I do not understand what the authors mean with \"hydrogen-bonding motions\" and \"unusual properties\" of water.\nL28/29: I would not call an UV chromophore \"confinement\". For a host matrix, this is appropriate, but not for a chromophore or a messanger tag.\nL35: \"5+1+5 assembling of two water pentamer cluster pairs with one connecting water molecule.\" This sounds like to separate rings, connected by one H2O molecule. In reality, it is two stacked rings, heavily hydrogen bonded with each other, and an addditional H2O on the side. This must become clear from the wording in the abstract, in a less ambiguous way.\nL41: \"essential sources of life\" is somewhat unscientific, water is a source of life only in poems.\nL59: \"fine structure\" is a technical term from atomic physics, misplaced here.\nL85: \"water-argon-helium mixture\" why argon? can argon tagging be ruled out?\nLine 154 and following: barriers heights must be referenced to the starting point, not to a neighboring local minimum. The way the authors phrase it is heavily misleading.\nL164: free energy at 500 K is totally irrelevant, water clusters evaporate already around 100-150 K.\nL182: \"predicated\" should be \"predicted\"?\nL183: \"delocalized\" I do not see the delocalization of H bonding here.\n210: \"two water trimer cluster pairs\" I do not see any trimers in isomer 11B.\n\nMy recommendation is to reconsider the manuscript after major revision. Without a convincing line of argument how the detection scheme works, supported by actual mass spectra, it remains open which cluster size - or a mixture of neighboring cluster sizes - is represented by the experimental spectrum.", "reviewer_2": "Wang et al. reported the size-selected IR spectra and ab initio calculations of the neutral (H2O)11 cluster produced in a supersonic jet, and they determined the hydrogen bond structures (three major isomer motifs) of the cold cluster. The conclusion is well supported by the experimental and theoretical evidences. The conclusion seems very reasonable, though minor contributions of other isomers (motifs) cannot be excluded. This study offers the first clear spectroscopic information on the hydrogen bond structures of neutral water clusters larger than n=10.\n\nThis work is an undoubtedly very high-quality study performed with the state-of-the-art experimental and theoretical techniques. However, I also wonder whether the increase of cluster size from n=10 to n=11 is a giant step to understand the size-dependent development of hydrogen bond structures of (H2O)n. The most important finding in the present work is the insertion process of the11th. water to the “5+5” cage of (H2O)10. This is very interesting, but this is essentially the same scenario as that for the “4+4” cage of (H2O)8 to (H2O)9. I think the strong impact of this study is somewhat limited to specialists of this field, and a more specialized high-quality journal, such as J. Phys. Chem. Lett., is suitable for this paper, though I am not against publication of this paper in Nature Communication if other reviewers recommend it.\n\nMinor comments\nIn Table 1, two small peaks in the 2900-3050 cm-1 region are listed. However, a greater number of peaks are seen in this region. Why only these two are listed? Are only these two reproducible?\n\nThe small peak at 2965 cm-1 is attributed to the strong band at 2960 cm-1 of the simulated spectrum of isomer 11A. However, the simulated and observed intensities seem largely mismatched. Line broadening due to the strong hydrogen bond formation can be a reason, but the weak peak seems sharp enough.\n\nThe isomer distribution is calculated in the temperature range of 0-600 K (under the harmonic approximation). However, evaporation of water molecules would occur at ~300 K or lower in small neutral water clusters, and results in the 400 – 600 K are not realistic.", "reviewer_3": "This manuscript reports infrared spectroscopy of isolated undecamer of water cluster (H2O)11. The experimental spectrum is interpreted by a combination of three lowest isomer families that were identified via extensive structural search and optimizations. The work is an extension of a series investigations on smaller water clusters (n = 6-10) using the state-of-the-art gas-phase spectroscopy that combines infrared excitation followed by ultraviolet free electron laser soft-ionization. The technique has been proved by the team in their previous studies of small water clusters, leading credence for the current (H2O)11 spectrum recorded in the O-H stretching region. Theoretical simulations of the lowest lying isomers and a combination of three of them nicely reproduce major observed peaks, thus enabling the authors to draw concrete conclusions for the observed structures of (H2O)11. The analyses on the transitions among three isomers and how (H2O)11 evolves from the previously identified (H2O)10 are illuminating. Overall this work represents another outstanding effort by the team to probe water clusters structures and binding motifs.\n\nI have one general comment. In the first paragraph, the authors summary the importance of water cluster studies and the relevance of such studies to bulk properties of water. Indeed several recent studies on hydrated clusters illustrated this point. Cluster studies can provide multifaced values to help understanding the bulk properties, e.g., the water coordination structure around hydroxide in the cluster and aqueous solutions is similar (Science Advances 9 (12), eadf4309); kosmotropic and chaotropic anions change local water structures distinctively different, amplifying the ion specific effect at the cluster scale (JPC B 120 , 1518-1525; JCP 138, 031101 (2013). Elaborating a little more along this line may enhance the paper to appeal to broader readers of this journal.\n\nIn the 3rd paragraph, the authors mentioned that the (H2O)11 cluster has been probed previously by attaching it to phenol and 'fused-cube' structures were assigned. I am wondering if the authors can comment back on this point at the end of the manuscript to discuss the effect of 'phenol' molecule on influence of the water network.\n\nFig 3 indicates a ~ 5.5 kcal/mol barrier (TS2) while the number mentioned in the text is 3.22 kcal/mol (11B --> 11A). Is it a typo?"}, "author_response": "Responses to the Reviewers’ Comments\nWe are grateful to the critical comments and constructive suggestions provided by the reviewers,\nwhich significantly help to improve the quality of the manuscript. Our manuscript has been revised\naccordingly. The following lists our responses to the comments from the reviewers.\nAs the reply to the comments of Reviewer #1:\nComments:\nThe manuscript by Wang et al. reports an IR spectrum of (H O) clusters, measured by a\n2 11\ncombination of IRMPD and VUV photoionization. Quantum chemical calculations indicate that\nthree of the calculated structures can explain most of the features in the spectrum. The three\nstructures are basically isoenergetic, with energy differences well below 1 kcal/mol. Many more\nstructures are close in energy, see Fig. S1, and almost equally populated. The authors single out the\nthree low-lying isomers in Fig. 2, but it would be relevant to know if any, and if yes, which isomers\nshown in Fig. S1 would not be compatible with the experimental spectrum.\nAuthor reply: Thanks for the comments. Since unambiguous identification of all the isomers of the\n515A, 43′4A, and 55′1A families is cumbrous, it appears to be more rational to analyze the trend of\nstructural motifs for (H O) . In the revised version of the manuscript, the structures of the three\n2 11\nlowest-energy isomers of each family are representatively shown in Supplementary Fig. 4 and the\ncorresponding calculated IR spectra are compared with the experimental spectrum in Supplementary\nFig. 5, respectively. The 515A, 43′4A, and 55′1A isomer families are found to be the major\ncontributors to the experimental spectrum, whereas the three lowest-energy isomers of the 44′3′A\nfamily are the trivial contributors to the experimental spectrum. These discussions have been added\ninto the revised manuscript (page 7, first and second paragraph).\nThe authors seem to imply, at least as far as I understand, that they photoionize (H O) cluster and\n2 11\nobserve (H O) + in their TOF mass spectrum. This does not make sense to me. It is well established\n2 11\nthat these clusters rearrange to (H O+)(OH)(H O) after photoionization. The hydration energy of\n3 2 9\nH O+ is then released in the cluster, which is very high, and will lead to immediate loss of water\n3\nmolecules. I have thus severe doubts that the IR spectrum of neutral (H O) can be inferred from\n2 11\nthe ion intensity of (H O) , or rather (H O+)(OH)(H O) . The intensity of this peak will rather\n2 11 3 2 9\n1\nreflect the ion spectroscopy of a larger cluster. The authors have to discuss this issue and clearly\njustify how they can be sure that the measured ion intensity is representative of the abundance of\nthe neutral cluster, without loss of water molecules. In this respect, I expect to see a few mass spectra\nobtained with IR laser on/off and different wavelengths. In addition, some information on the\nperformance parameters of the TOF (resolution, mass accuracy) must be given.\nAuthor reply: Thanks for the comments and the concerns that we share as well. The loss of OH\nfrom the photoionization of water clusters is on the subpicosecond time scale and is much more\nthermodynamically and kinetically favorable than the loss of water molecules (Tachikawa, H., J.\nPhys. Chem. A 2004, 108, 7853; Belau, L.; et al., J. Phys. Chem. A 2007, 111, 10075; Garrett, B. C.,\net al., Chem. Rev. 2005, 105, 355.). Furthermore, a relatively slow loss of H O can be suspended by\n2\nreducing the excess energy from the VUV photoionization via the fine tuning of the wavelength and\npulse energy of VUV-FEL, as demonstrated in our previous studies of water clusters (H O) (n =\n2 n\n2−10) (J. Phys. Chem. Lett., 2020, 11, 851; Proc. Natl. Acad. Sci. U.S.A., 2020, 117, 15423; Nat.\nCommun., 2020, 11, 5449; Cell Rep. Phys. Sci., 2022, 3, 100748; J. Chem. Phys., 2023, 158, 014301;\nJ. Phys. Chem. Lett., 2024, 15, 3055.). Therefore, the depletion efficiency of mass spectral intensity\nof (H O) + reflects the IR spectrum of neutral (H O) , rather than the spectrum of a larger cluster.\n2 n 2 n\nMass spectra obtained with IR laser ON/OFF modes are shown in Fig. R1. The mass resolution\nfor (H O) + is 1178. It can be seen from Fig. R1 that the intensity of the (H O) + peak remarkably\n2 11 2 11\ndepletes with IR laser ON (e.g., at 3557 cm-1), whereas that of the H+(H O) peak does not\n2 11\nsignificantly change. This result indicates that IR spectrum of neutral (H O) is indeed free from\n2 11\nspectral contamination of larger water clusters. Such discussions have been added into the\nmanuscript (page 4, third and fourth paragraph; Supplementary Fig. 2).\nFig. R1. Mass spectra of (H O) + obtained with IR laser on/off modes.\n2 11\nclusters (H O) (n = 2−11) and the corresponding experimental IR spectra are shown in Figs. R2\n2 n\nand R3, respectively. Various experimental conditions (i.e., the wavelength and pulse energy of\nVUV-FEL, concentration of water mixture, stagnation pressure, etc.) were optimized to maximize\nthe signal of a size-specific water cluster of interest with no interference from larger clusters. As\nshown in Fig. R3, the IR spectra of each individual cluster (H O) (n = 2−11) are all different from\n2 n\neach other, indicating that these IR spectra are free from spectral contamination of larger water\nclusters. Such discussions have been added into the revised manuscript (page 4, fourth paragraph;\nSupplementary Figs. 1 and 3).\nFig. R2. Mass spectra obtained with different VUV Fig. R3. Experimental IR spectra of neutral (H O) (n =\n2 n\nwavelengths and beam conditions. 2−11) clusters.\nL24: I do not understand what the authors mean with “hydrogen-bonding motions” and “unusual\nproperties” of water.\nAuthor reply: Thanks for the comment. We are sorry that we did not make it clear. “hydrogen-\nbonding motions” has been changed to “hydrogen-bonding interactions” and “unusual properties”\nhas been changed to “the properties”, respectively (page 2, first paragraph).\nL28/29: I would not call an UV chromophore “confinement”. For a host matrix, this is appropriate,\nbut not for a chromophore or a messenger tag.\nAuthor reply: Thanks for the comment. “confinement” has been changed to “interference”\nthroughout the manuscript.\nL35: “5+1+5 assembling of two water pentamer cluster pairs with one connecting water molecule.”\nThis sounds like to separate rings, connected by one H O molecule. In reality, it is two stacked rings,\n2\nheavily hydrogen bonded with each other, and an additional H O on the side. This must become\n2\nclear from the wording in the abstract, in a less ambiguous way.\nAuthor reply: Thanks for the comment. We are sorry that we did not make it clear. “water pentamer\ncluster pairs with one connecting water molecule” has been changed to “stacked 5-membered rings\nwith an additional H O on the side” (page 2, first paragraph).\nAuthor reply: Thanks for the comment. “is one of the most essential sources of life” has been\nremoved from the manuscript (page 3, first paragraph).\nL59: “fine structure” is a technical term from atomic physics, misplaced here.\nAuthor reply: Thanks for the comment. “fine structure” has been changed to “precise structure” in\nthe revised manuscript (page 3, second paragraph).\nL85: “water-argon-helium mixture” why argon? can argon tagging be ruled out?\nhelp to generate larger neutral water clusters. The argon tagging can be ruled out by its absence in\nthe mass spectra.\nLine 154 and following: barriers heights must be referenced to the starting point, not to a\nneighboring local minimum. The way the authors phrase it is heavily misleading.\nAuthor reply: Thanks for the comment. We are sorry that the original expression is misleading. In\nthis work, the barrier denotes the barrier height of elementary process (e.g., the barrier of the IM1\n→ IM2 isomerization is 3.22 kcal/mol (TS2)). Accordingly, “barrier” has been changed to “barrier\nof elementary process” in the revised manuscript (page 8, second paragraph).\nL164: free energy at 500 K is totally irrelevant, water clusters evaporate already around 100-150\nK.\nAuthor reply: Thanks for the comment. You are absolutely right. Together with the comment of\nReviewer #2, the temperature range for Gibbs free energies has been changed to 0-300 K (page 8,\nsecond paragraph).\nL182: “predicated” should be “predicted”?\nAuthor reply: Thanks for the comment. We are sorry for this typo. “predicated” has been changed\nto “predicted” (page 9, second paragraph).\nL183: “delocalized” I do not see the delocalization of H bonding here.\nAuthor reply: Thanks for the comment. As shown in Supplementary Figs. 8-10, the AdNDP results\nreveal extensive delocalized HB interactions in (H O) , which indicates that O lone pair is partially\n2 11\nshared with the antibonding orbital of O-H bond. Such revision has been made in the manuscript\n(page 9, second paragraph).\nL210: “two water trimer cluster pairs” I do not see any trimers in isomer 11B.\nAuthor reply: Thanks for the comment. “one water tetramer and two water trimer cluster pairs” has\nbeen changed to “two 4-membered rings connected by a water trimer chain” (page 10, first\nparagraph).\nof argument how the detection scheme works, supported by actual mass spectra, it remains open\nwhich cluster size - or a mixture of neighboring cluster sizes - is represented by the experimental\nspectrum.\nAuthor reply: Thank you for the careful thinking and comments. We hope the current revised\nmanuscript has solved the major concerns.\nAs the reply to the comments of Reviewer #2:\nComments:\nWang et al. reported the size-selected IR spectra and ab initio calculations of the neutral (H O)\n2 11\ncluster produced in a supersonic jet, and they determined the hydrogen bond structures (three major\nisomer motifs) of the cold cluster. The conclusion is well supported by the experimental and\ntheoretical evidences. The conclusion seems very reasonable, though minor contributions of other\nisomers (motifs) cannot be excluded. This study offers the first clear spectroscopic information on\nthe hydrogen bond structures of neutral water clusters larger than n=10.\nAuthor reply: We thank the reviewer for the comments.\nThis work is an undoubtedly very high-quality study performed with the state-of-the-art\nexperimental and theoretical techniques. However, I also wonder whether the increase of cluster\nsize from n=10 to n=11 is a giant step to understand the size-dependent development of hydrogen\nbond structures of (H O) . The most important finding in the present work is the insertion process\n2 n\nof the 11th water to the “5+5” cage of (H O) . This is very interesting, but this is essentially the\n2 10\nsame scenario as that for the “4+4” cage of (H O) to (H O) . I think the strong impact of this study\n2 8 2 9\nis somewhat limited to specialists of this field, and a more specialized high-quality journal, such as\nJ. Phys. Chem. Lett., is suitable for this paper, though I am not against publication of this paper in\nNature Communication if other reviewers recommend it.\nAuthor reply: Thanks for the comment. We hope publication of this work will stimulate more\ninterest in exploring the complicated bonding and properties of water, which are important in\nunderstanding the processes of cloud, aerosol, and ice formation, especially under rapid cooling.\nCommunications journal aims at.\nMinor comments\nIn Table 1, two small peaks in the 2900-3050 cm-1 region are listed. However, a greater number of\npeaks are seen in this region. Why only these two are listed? Are only these two reproducible?\nAuthor reply: Thanks for the comment. We agree with the reviewer that it is inappropriate to list\nonly two peaks (2965 and 3028 cm-1) in the 2900-3050 cm-1 region. The list of 2965 and 3028 cm-1\nhas been removed from Table 1 (page 5).\nThe small peak at 2965 cm-1 is attributed to the strong band at 2960 cm-1 of the simulated spectrum\nof isomer 11A. However, the simulated and observed intensities seem largely mismatched. Line\nbroadening due to the strong hydrogen bond formation can be a reason, but the weak peak seems\nsharp enough.\nAuthor reply: Thanks for the comment. The coupling between hydrogen-bond fluctuation and OH\nstretch broadens the OH stretching band. Furthermore, the fluctuation of single H-donor OH\nstretching mode is larger than that of double H-donor OH stretching mode. This makes it more\ndifficult to directly compare the simulated and experimental intensities of vibrational bands of\nhydrogen-bonded molecular clusters, owing to the challenge of theory (anharmonicity,\nintermolecular zero-point motions, etc.) and the complexity of experiment (IR absorption combined\nwith dissociation, intramolecular vibrational-energy redistribution (IVR), etc.), as reported\npreviously (Buck, U., et al, Phys. Rev. Lett., 1998, 80, 2578; Cole, W. T. S., et al., Science, 2016,\n352, 1194; Jiang, S., et al., J. Phys. Chem. Lett., 2021, 12, 2259). Such comments have been added\ninto the revised manuscript (page 7, second paragraph).\nThe isomer distribution is calculated in the temperature range of 0-600 K (under the harmonic\napproximation). However, evaporation of water molecules would occur at ~300 K or lower in small\nneutral water clusters, and results in the 400-600 K are not realistic.\nAuthor reply: Thanks for the comment. The temperature range for Gibbs free energies has been\nchanged to 0-300 K (page 8, second paragraph).\nComments:\nThis manuscript reports infrared spectroscopy of isolated undecamer of water cluster (H O) .\nThe\n2 11\nexperimental spectrum is interpreted by a combination of three lowest isomer families that were\nidentified via extensive structural search and optimizations. The work is an extension of a series\ninvestigations on smaller water clusters (n = 6-10) using the state-of-the-art gas-phase spectroscopy\nthat combines infrared excitation followed by ultraviolet free electron laser soft-ionization. The\ntechnique has been proved by the team in their previous studies of small water clusters, leading\ncredence for the current (H O) spectrum recorded in the O-H stretching region. Theoretical\n2 11\nsimulations of the lowest lying isomers and a combination of three of them nicely reproduce major\nobserved peaks, thus enabling the authors to draw concrete conclusions for the observed structures\nof (H O) . The analyses on the transitions among three isomers and how (H O) evolves from the\n2 11 2 11\npreviously identified (H O) are illuminating. Overall this work represents another outstanding\n2 10\neffort by the team to probe water clusters structures and binding motifs.\nAuthor reply: We thank the reviewer for the comments.\nI have one general comment. In the first paragraph, the authors summary the importance of water\ncluster studies and the relevance of such studies to bulk properties of water. Indeed several recent\nstudies on hydrated clusters illustrated this point. Cluster studies can provide multifaced values to\nhelp understanding the bulk properties, e.g., the water coordination structure around hydroxide in\nthe cluster and aqueous solutions is similar (Science Advances 9(12), eadf4309); kosmotropic and\nchaotropic anions change local water structures distinctively different, amplifying the ion specific\neffect at the cluster scale (JPC B 120 , 1518-1525; JCP 138, 031101 (2013). Elaborating a little\nmore along this line may enhance the paper to appeal to broader readers of this journal.\nAuthor reply: Thanks for the comment. Such elaborations and citations have been added into the\nrevised manuscript (page 3, first paragraph).\nIn the 3rd paragraph, the authors mentioned that the (H O) cluster has been probed previously by\n2 11\nattaching it to phenol and 'fused-cube' structures were assigned. I am wondering if the authors can\ncomment back on this point at the end of the manuscript to discuss the effect of 'phenol' molecule on\ninfluence of the water network.\nmanuscript (page 10, first paragraph).\nFig. 3 indicates a ~5.5 kcal/mol barrier (TS2) while the number mentioned in the text is 3.22\nkcal/mol (11B → 11A). Is it a typo?\nAuthor reply: Thanks for the comment. We are sorry that we did not make it clear. In this work,\nthe barrier denotes the barrier height of elementary process (e.g., the barrier of the IM1 → IM2\nisomerization is 3.22 kcal/mol (TS2)). Accordingly, “barrier” has been changed to “barrier of\nelementary process” in the revised manuscript (page 8, second paragraph).\n9"}, {"round": 2, "reviewer_comments": {"reviewer_1": "I appreciate very much the additional effort which the authors put into their manuscript and the supporting information. Many issues have been resolved, but the main problem persists: Photoionization of (H2O)11 leads to an ultrafast rearrangement of (H2O)11(+) into (H3O)(OH)(H2O)9(+). This takes on the order of 100 fs, and substantial energy is released in the cluster. I do not understand how a water cluster of this size, with excess energy of probably several eV, should possibly survive the > 1us flight time until it reaches the channel plates of the TOF. The authors need to estimate the relaxation energy of the (H2O)11(+) cluster following ionization. This can be done by calculating the SCF energy of (H2O)11(+) at the geometry of the neutral cluster, followed by geometry optimization of the charged cluster. The relaxation energy is the difference between the SCF energy before and after geometry optimization. This value can be used to calculate the lifetime against dissociation with RRKM theory. I expect that this will show that the (H2O)11(+) cluster cannot reach the TOF detector on the experimental time scale without fragmenting.\n\nThe mass spectrum in Supplementary Figure 2 shows a peak at m/z 197. Has this peak been asssigned? The mass spectrum in Supplementary Figure 2 as well as Suppl. Figure 1 are qualitatively consistent with a contaminant, 1 amu below H2O, e.g. NH3. The peak at m/z 197 would thus be (NH3)(NH4)(H2O)9(+), and m/z 198 would be (NH4)(H2O)10(+). Such a contaminant must be ruled out, and this requires assigning the peak at m/z 197.", "reviewer_2": "In the revised manuscript, the authors have addressed all the issues I concerned in the first review. I agree to publication of the present manuscript in Nat. Comm. without further revision."}, "author_response": "Responses to the Reviewers’ Comments\nWe are grateful for the critical comments and constructive suggestions provided by the reviewers,\nwhich are very helpful to improve the quality of the manuscript. Our manuscript has been revised\naccordingly. The following lists our responses to the comments from the reviewers.\nAs the reply to the comments of Reviewer #1:\nComments:\nI appreciate very much the additional effort which the authors put into their manuscript and the\nsupporting information. Many issues have been resolved, but the main problem persists:\nPhotoionization of (H O) leads to an ultrafast rearrangement of (H O) + into\n2 11 2 11\n(H O)(OH)(H O) +. This takes on the order of 100 fs, and substantial energy is released in the\n3 2 9\ncluster. I do not understand how a water cluster of this size, with excess energy of probably several\neV, should possibly survive the > 1 µs flight time until it reaches the channel plates of the TOF.\nThe authors need to estimate the relaxation energy of the (H O) + cluster following ionization.\n2 11\nThis can be done by calculating the SCF energy of (H O) + at the geometry of the neutral cluster,\n2 11\nfollowed by geometry optimization of the charged cluster. The relaxation energy is the difference\nbetween the SCF energy before and after geometry optimization. This value can be used to\ncalculate the lifetime against dissociation with RRKM theory. I expect that this will show that the\n(H O) + cluster cannot reach the TOF detector on the experimental time scale without\n2 11\nfragmenting.\nAuthor reply: Thanks for the comments. The calculations for the energies of the dissociation of\n(H O) + and rate constant of unimolecular conversion and half-life time of reactant have been\n2 11\nadded in the new revised version and the results are given in Supplementary Figs. 1 and 2 and\nSupplementary Tables 1 and 2, respectively.\nAs shown in Supplementary Fig. 1 and Supplementary Table 1, the rearrangement of\n(H O) + (labeled 11A+) into [(H O)(OH)(H O) ]+ (iso 2) need go through several transition states\n2 11 3 2 9\nand intermediates, with the largest barrier of elementary process of 4.03 kcal/mol at the MP2/aug-\ncc-pVDZ level of theory. The largest barrier of elementary process for the [(H O)(OH)(H O) ]+\n3 2 9\n(iso 2) → [(H O)(H O) (OH)]+ (iso 1) isomerization is calculated to be 7.37 kcal/mol at the same\n3 2 9\ntheoretical level. It can be seen from Supplementary Table 2 that when the temperature is lower\n1\nthan 80 K, there is a pretty large window of temperature for which the half-life time of the (H O) +\n2 11\n(11A+) → [(H O)(OH)(H O) ]+ (iso 2) and [(H O)(OH)(H O) ]+ (iso 2) → [(H O)(H O) (OH)]+ (iso 1)\n3 2 9 3 2 9 3 2 9\n(iso 1) isomerization is longer than the millisecond time scale. The conditions with such\ntemperature are available in the supersonic expansions, because the rotational temperature of\nclusters should be less than 10 K and the vibrational temperature could be higher (i.e., a finite\ntemperature) (Refs. 26 and 48). Accordingly, it is reasonable to conclude that the (H O) + (11A+)\n2 11\ncluster can reach the time-of-flight mass spectrometer (TOF-MS) detector. These results are\nconsistent with previous observation of the (H O) + clusters via the VUV near-threshold\n2 n\nphotoionization (Refs. 49-51).\nSuch discussions have been added into the revised manuscript (page 4, third paragraph).\nThe mass spectrum in Supplementary Figure 2 shows a peak at m/z 197. Has this peak been\nassigned? The mass spectrum in Supplementary Figure 2 as well as Suppl. Figure 1 are\nqualitatively consistent with a contaminant, 1 amu below H O, e.g. NH . The peak at m/z 197\n2 3\nwould thus be (NH )(NH )(H O) +, and m/z 198 would be (NH )(H O) +. Such a contaminant\n3 4 2 9 4 2 10\nmust be ruled out, and this requires assigning the peak at m/z 197.\nAuthor reply: Thanks for the comments. The water-argon-helium mixture in our experiments\nwas prepared by using the ultrapure water with resistivity > 18 megohm-centimeters (MΩ-cm).\nFurthermore, the mass spectral intensities of a series of the m/z=17+18n peaks are very weak,\nsuggesting that the present mass spectra are not contaminated with NH . Previous studies of VUV\n3\nphotoionization of water clusters indicated that the m/z=17+18n peaks could be ascribed to the\nmetastable fragments of [(OH)(H O) ]+ (Belau, L., et al., J. Phys. Chem. A 111, 10075-10083\n2 n\n(2007); Golan, A. & Ahmed, M. J. Phys. Chem. Lett. 3, 458-462 (2012)), which might be formed\nthrough the following pathways:\n(H O) + + hv → (H O+)(OH)(H O) (1)\n2 n+2 3 2 n\n(H O+)(OH)(H O) → H O+ + (OH)(H O) (2)\n3 2 n 3 2 n\n(OH)(H O) + hv → [(OH)(H O) ]+ (3)\n2 n 2 n-1\nAccordingly, the m/z=197 peak is assigned to (OH)(H O) +, which indication has been added\n2 10\ninto Supplementary Fig. 4. The relevant description and discussions have been added to the\nrevised manuscript (page 4, third paragraph) and Supplementary Information.\nComments:\nIn the revised manuscript, the authors have addressed all the issues I concerned in the first review.\nI agree to publication of the present manuscript in Nat. Comm. without further revision.\nAuthor reply: We thank the reviewer for the comments.\n3"}, {"round": 3, "reviewer_comments": {"reviewer_1": "It is well known that NH4+ ions form in the presence of air in ion sources, see e.g. DOIs 10.1063/1.3149784, 10.1016/j.ijms.2019.116254. The mass spectra in Supplementary Figure 3 show traces of air, evidenced by m/z = 28 (N2+) and 32 (O2+). This means, the formation of NH4+ in the authors' experiment would be consistent with examples in the literature, and is not ruled out by the authors' argument that they used ultra high purity water.\n\nReaction (2) on page 7 of the Supplementary Information is in my opinion completely unrealistic, although it has been mentioned in the literature. The loss of an H3O+ ion from a water cluster is energetically highly unfavorable. I do not see any mechanism that would favor such an uphill process over the loss of neutral water molecules.\n\nObviously, there is no way to settle this question by further discussion. It all comes down to the absolute mass measurement in the experiment. In this respect, it is certainly not helpful that the resolution of the mass spectrum is only 1178, according to Supplementary Figure 4. It is highly recommended that the authors upgrade their instrument to at least 10,000 resolution for future work. Such instruments are available commercially from various vendors for integration into a home-built experimental setup.\n\nGiven the quite substantial mass difference of 0.024 amu between NH4+ and H2O+, I still see a chance to settle this dispute on the basis of the experimental data. I therefore ask the authors to provide the complete mass spectra of Supplementary Figure 3 as text files. If at all possible, I would appreciate also to have acces to the raw data, i.e. time of flight channel vs. intensity data, for these mass spectra."}, "author_response": "Responses to the Reviewers’ Comments\nWe are very grateful to the critical comments and constructive suggestions provided by the reviewers,\nwhich significantly help to improve the quality of the manuscript. Our manuscript has been revised\naccordingly. The following lists our responses to the comments from the reviewers.\nAs the reply to the comments of Reviewer #1:\nComments:\nIt is well known that NH + ions form in the presence of air in ion sources, see e.g. DOIs\n4\n10.1063/1.3149784, 10.1016/j.ijms.2019.116254. The mass spectra in Supplementary Figure 3 show\ntraces of air, evidenced by m/z = 28 (N +) and 32 (O +). This means, the formation of NH + in the\n2 2 4\nauthors' experiment would be consistent with examples in the literature, and is not ruled out by the\nauthors' argument that they used ultra high purity water.\nAuthor reply: Thanks for the comments. This is an important point indeed. In our experimental\nsetting, the ultimate pressure of our source chamber and time-of-flight mass spectrometer (TOF-MS)\nchamber is 210−6 Pa and 510−6 Pa, respectively. Before the preparation of the water-argon-helium\nmixture, the pressures of gas cylinder and the entire gas inlet were vacuumed to ~10−3 Pa. Then, the\nwater vapor was produced by heating the stainless container of ultra high purity water to 353 K and\nwas mixed with 99.9999% argon and 99.9999% helium. The resulting mixture was of high purity and\nwas kept in the gas cylinder. The water-argon-helium mixture was supersonically expanded into the\nsource chamber, where the pressure was kept at ~10−4 Pa. The molecular beam passed through a 4\nmm diameter skimmer (Beam Dynamics, Model 50.8) and entered the TOF-MS chamber, where the\npressure was kept at ~10−5 Pa.\nIn the mass spectra (Supplementary Fig. 3), the m/z = 28 and 32 peaks were observed at the\nexperimental conditions for (H O) and (H O) , but not for other water clusters. As shown in\n2 2 2 3\nSupplementary Fig. 3a and 3b, the intensity of the m/z = 28 peak was much smaller than that of the\nm/z = 32 peak, indicating the ratio of the m/z = 28 and 32 peak intensities is quite different from the\nrelative abundances of N and O in the air (approximately 4:1).\n2 2\nConsidering that the IR spectra of (H O) and (H O) were measured at the early stage of the use\n2 2 2 3\nof our new instrument in 2017, the m/z = 28 and 32 peaks could most likely come from the fragment\npeaks of oil impurities in the chamber, for which the m/z = 28 and 32 peaks may be assigned to CO+\nand CH OH+, respectively. With the continuous purification of the chamber, the impurity peaks were\n3\nremarkably reduced in the subsequent experiments of (H O) (n  4) (Supplementary Fig. 3c-3j). To\n2 n\n1\nconfirm this point, we recently have remeasured the mass spectrum of (H O) (added as\n2 2\nSupplementary Fig. 4 in the revised manuscript), in which the impurity peaks (i.e., the m/z = 28 and\n32 peaks) disappeared. These results confirm that there were no apparent traces of air in our\nexperiments.\nSupplementary Fig. 4 Mass spectrum of (H O) measured in December 25, 2022.\n2 2\nIn the literature mentioned by the reviewer (DOIs 10.1063/1.3149784,\n10.1016/j.ijms.2019.116254), NH + ion was produced in the ion sources of proton transfer mass\n4\nspectrometer, where high voltage discharge generated a high concentration of H O plasma region and\n2\ninduces subsequent reactions to generate NH +. Such reactions were unlikely to occur during the VUV\n4\nsoft photoionization in our experimental conditions. It has been proved that the reaction to produce\nammonia was a free radical reaction and occurred on the metal surface (E. Carrasco, et al., Phys. Chem.\nChem. Phys., 2011, 13, 19561; J. Shah, et al., Catalysts, 2018, 8, 437). In our instrument, the VUV\nphotoionization was in the center of extraction plates of TOF-MS, which were powered by a high-\nvoltage direct current (DC) of 2950 V. The ionic species were immediately deflected out by the DC\nelectric field of the extraction plates. After the VUV photoionization, there was no ion-molecule\nreaction in the high vacuum chamber (~10−5 Pa). Therefore, even if NH was produced, it would be\n3\nextremely difficult to react with H O+ to generate NH +.\n3 4\nIn addition to the mass spectroscopic evidence, we can also exclude the possibility of\nNH +(H O) from the IR spectral data of water clusters. For example, in the infrared spectrum of\n4 2 m\n2\nwater dimer, we observed the OH stretching vibrational peaks (B. Zhang, et al., J. Phys. Chem. Lett.,\n2020, 11, 851), but did not observe the NH stretching vibrational peak ( ) of NH + (3343 cm-1:M. W.\n3 4\nCrofton and T. Oka, J. Chem. Phys., 1983, 79, 3157; J. Chem. Phys., 1987, 86, 5983; E. Schafer, et\nal., J. Chem. Phys., 1983, 79, 3159; J. Chem. Phys., 1984, 80, 3969). In addition, no NH stretching\nvibrational peaks of NH + were observed in the IR spectra of (H O) (n = 3-10) (B. Zhang, et al.,\n4 2 n\nProc. Natl. Acad. Sci., 2020, 117, 15423; G. Li, et al., Nat. Commun., 2020, 11, 5449; Y.-Y. Zhang,\net al., Cell Rep. Phys. Sci., 2022, 3, 100748); H. Zheng, et al., J. Chem. Phys., 2023, 158, 014301; Y.-\nY. Zhang, et al., J. Phys. Chem. Lett., 2024, 15, 3055). Furthermore, we have ever measured the IR\nspectra of (NH ) and (NH ) (B. Zhang, et al., CCS Chem., 2020, 2, 829), which spectral features are\n3 2 3 3\nquite different from those of (H O) and (H O) . Therefore, we can conclude that the (H O) + clusters\n2 2 2 3 2 n\nwere detected in our mass spectra, instead of NH +(H O) .\n4 2 m\nThe relevant discussions have been added into the revised manuscript.\nReaction (2) on page 7 of the Supplementary Information is in my opinion completely unrealistic,\nalthough it has been mentioned in the literature. The loss of an H O+ ion from a water cluster is\n3\nenergetically highly unfavorable. I do not see any mechanism that would favor such an uphill process\nover the loss of neutral water molecules.\nObviously, there is no way to settle this question by further discussion. It all comes down to the\nabsolute mass measurement in the experiment. In this respect, it is certainly not helpful that the\nresolution of the mass spectrum is only 1178, according to Supplementary Figure 4. It is highly\nrecommended that the authors upgrade their instrument to at least 10,000 resolution for future work.\nSuch instruments are available commercially from various vendors for integration into a home-built\nexperimental setup.\nGiven the quite substantial mass difference of 0.024 amu between NH + and H O+, I still see a chance\n4 2\nto settle this dispute on the basis of the experimental data. I therefore ask the authors to provide the\ncomplete mass spectra of Supplementary Figure 3 as text files. If at all possible, I would appreciate\nalso to have access to the raw data, i.e. time of flight channel vs. intensity data, for these mass spectra.\nAuthor reply: Thanks for the comments. We agree with the reviewer that the formation mechanism\nof [(OH)(H O) ]+ is quite complicated and is very difficult to be clearly characterized without further\n2 n\ntechnique. We have already started to construct the ultrafast cluster spectroscopic instrument by using\nthe femtosecond pulse mode of our vacuum ultraviolet free electron laser (VUV-FEL).\n4 2\nwhich is a direction for our future efforts. Although our current mass spectrometer cannot directly\ndistinguish between NH + and H O+, the above-mentioned analyses of mass spectra and IR spectra\n4 2\nsupport the conclusion that the (H O) + clusters were detected in our mass spectra, instead of\n2 n\nNH +(H O) .\n4 2 m\nThe raw data for these mass spectra have been provided for further examination.\n4"}, {"round": 4, "reviewer_comments": {"reviewer_1": "I appreciate very much that the authors provide their original mass spectra. Since the resolution is not good enough to decide on the composition based on the measured mass, I tried to get an idea whether the NH4+(H2O)n-1 or the (H2O)n+ sum formula is a better representation of the m/z 162, 180 and 198 peaks. To this end, I shifted the mass spectrum by the difference of NH4+(H2O)n-1 and H3O+(H2O)n-1 (grey line) and the difference between (H2O)n+ and H3O+(H2O)n-1 (orange line), and scaled the spectrum so that it matched most closely the original H3O+(H2O)n-1 peak (blue line). The idea behind this procedure is that we seem to agree on the assignment of the m/z 163, 181 and 199 peaks as H3O+(H2O)n-1. Obviously, for the m/z 162 and 180 peaks, the match of the grey line is better, i.e. the mass spectrum would indeed suggest that the composition is NH4+(H2O)n-1. For the cluster size investigated here, m/z 198, the orange line fits somewhat better. However, the peak shapes of m/z 198 and 199 are heavily distorted. In summary, the mass spectrum is somewhat more consistent with the NH4+(H2O)n-1 assignment, but it does not rule out (H2O)n+. A moderatly higher resolution and overall better quality of the peak shapes would allow for an unambiguous assignment. I would definitely encourage the authors to equip their powerful setup with a TOF that is state of the art.\n\nIn their rebuttal, the authors provide reasonable arguments with respect to more recent experiments, where air contamination was smaller than in the mass spectra provided before. Their arguments about the absence of ammonium ion peaks in their IR spectra, however, are not valid. If NH4+ is the charge carrier in the ionized clusters, it is most likely formed after IR irradiation, upon photoionization. Likewise, the references to the formation of ammonia in discharges or RF plasmas with Ga or In as catalyst are not relevant in the present context. The mechanism of NH4+ formation in the presence of air and water in ion sources is, as far as I know, not at all understood.\n\nBased on the newly provided clean spectra, I now recommend the manuscript for publication in Nature Communications. Should the authors find out later, with an adequately resolving TOF, that the peaks really contain the ammonium ion, I think they are in the best possible position to explore the elusive mechanism of its formation."}, "author_response": "Responses to the Reviewers’ Comments\nWe are very grateful to the critical comments and constructive suggestions provided by the reviewers,\nwhich significantly help to improve the quality of the manuscript. Our manuscript has been revised\naccordingly. The following lists our responses to the comments from the reviewers.\nAs the reply to the comments of Reviewer #1:\nComments:\nI appreciate very much that the authors provide their original mass spectra. Since the resolution is\nnot good enough to decide on the composition based on the measured mass, I tried to get an idea\nwhether the NH +(H O) or the (H O) + sum formula is a better representation of the m/z 162, 180\n4 2 n-1 2 n\nand 198 peaks. To this end, I shifted the mass spectrum by the difference of NH +(H O) and\n4 2 n-1\nH O+(H O) (grey line) and the difference between (H O) + and H O+(H O) (orange line), and\n3 2 n-1 2 n 3 2 n-1\nscaled the spectrum so that it matched most closely the original H O+(H O) peak (blue line). The\n3 2 n-1\nidea behind this procedure is that we seem to agree on the assignment of the m/z 163, 181 and 199\npeaks as H O+(H O) . Obviously, for the m/z 162 and 180 peaks, the match of the grey line is better,\n3 2 n-1\ni.e. the mass spectrum would indeed suggest that the composition is NH +(H O) . For the cluster\n4 2 n-1\nsize investigated here, m/z 198, the orange line fits somewhat better. However, the peak shapes of m/z\n198 and 199 are heavily distorted. In summary, the mass spectrum is somewhat more consistent with\nthe NH +(H O) assignment, but it does not rule out (H O) +. A moderately higher resolution and\n4 2 n-1 2 n\noverall better quality of the peak shapes would allow for an unambiguous assignment. I would\ndefinitely encourage the authors to equip their powerful setup with a TOF that is state of the art.\nAuthor reply: Thanks for the comments. To further verify the assignment of chemical formula of\nclusters, we have recently performed the additional experiments by adding N into the water-argon-\n2\nhelium mixtures, for which the results are shown in Supplementary Figs. 5-7, respectively. The\naddition of N does not generate extra peaks (Supplementary Fig. 5c-5f). As shown in Supplementary\n2\npeaks do not increase but decrease, indicating that N is not involved in these clusters. Thus, the m/z =\n2\n162, 180, and 198 peaks are not attributed to the NH +(H O) clusters. Note that the evaporation of\n4 2 n-1\nthe surrounding Ar atoms is helpful to take away the excess energy formed in the ionization of water\nclusters and thus is favorable for the formation of unprotonated water clusters (H O) + (Golan, A. &\n2 n\nAhmed, M. Ionization of water clusters mediated by exciton energy transfer from argon clusters. J.\nPhys. Chem. Lett. 3, 458-462 (2012); Kocisek, J., et al. Energy and charge transfer in ionized argon\n1\ncoated water clusters. J. Chem. Phys. 139, 214308 (2013)). The addition of N changes the Ar-water\n2\ncluster ratio and consequently reduces the energy transfer efficiency of the Ar evaporation, which\naccounts for the decrease of mass spectral intensities of the m/z = 162, 180, and 198 peaks with the\nincrease of N concentrations.\npeak at m/z 36 is identified as (H O) + and the formation of NH +(H O) is ruled out (Xing, D., et al.\n2 2 4 2\nChallenges in detecting hydroxyl radicals generated in water droplets with mass spectrometry. Anal.\nChem., 97, 7995 (2025); Song, X., et al. Clarifying the identity of the m/z 36 ion in water microdroplet\nmass spectra. J. Phys. Chem. A., 129, 4529 (2025) ; Zhang, X., et al. Detection and characterization\nof water radical cations by mass spectrometry and electron paramagnetic resonance spectroscopy.\nAnal. Chem., 97, 16004 (2025)). The NH +(H O) ion was detected from droplets produced by\n4 2\nelectrospray in the presence of air and water and was proposed to be originated from the gaseous\nammonia or the ammonia formed from ambient N in high intrinsic electric fields at microdroplet\n2\nsurfaces (Chen, C. J. & Williams, E. R. A source of the mysterious m/z 36 ions identified: Implications\nfor the stability of water and unusual chemistry in microdroplets. ACS Cent. Sci., 11, 622 (2025)).\nHowever, our experimental environment of IR-VUV spectroscopy is high vacuum (~10−4 Pa) and\ndoes not involve the gaseous ammonia and N , which condition is completely different from that the\n2\nexperimental environment of electrospray (the air-interface condition, ~105 Pa). Therefore, we can\nrule out the formation of NH +(H O) in our IR-VUV experiment under high-vacuum condition. These\n4 2\nresults further support the identity of (H O) + rather than NH +(H O) in our high-vacuum\n2 n 4 2 n-1\nexperiment.\nSuch discussions have been added into the revised manuscript (Main text: page 5, second\nparagraph; Supplementary Information: pages 4-5).\n2\nthe m/z = 20-230 region.\nSupplementary Fig. 6 Comparison of mass spectra of water clusters without and with the addition of N ,\nin\n2\nthe m/z = 155-205 region.\n2\nconcentration.\nIn their rebuttal, the authors provide reasonable arguments with respect to more recent experiments,\nwhere air contamination was smaller than in the mass spectra provided before. Their arguments about\nthe absence of ammonium ion peaks in their IR spectra, however, are not valid. If NH + is the charge\n4\ncarrier in the ionized clusters, it is most likely formed after IR irradiation, upon photoionization.\nLikewise, the references to the formation of ammonia in discharges or RF plasmas with Ga or In as\ncatalyst are not relevant in the present context. The mechanism of NH + formation in the presence of\n4\nair and water in ion sources is, as far as I know, not at all understood.\nAuthor reply: Thanks for the comments. We agree with the reviewer that the mechanism of NH +\n4\nformation in the presence of air and water in ion sources is rather complicated and requires further\nevaluation. Such discussion is not related to this work and has been removed from Supplementary\nInformation.\nBased on the newly provided clean spectra, I now recommend the manuscript for publication in\nNature Communications. Should the authors find out later, with an adequately resolving TOF,\nthat\nthe peaks really contain the ammonium ion, I think they are in the best possible position to explore\nthe elusive mechanism of its formation.\nAuthor reply: We thank the reviewer very much for the delightful comments.\n4"}, {"round": 5, "reviewer_comments": {"reviewer_1": "Since I recommended publication already at the previous stage, I have nothing to add."}, "author_response": "Responses to Reviewers’ Comments\nWe are very grateful to the comments provided by the reviewers, which significantly help to improve\nthe quality of the manuscript. Our manuscript has been revised accordingly. The responses and\nrevisions are listed as follows:\nAs the reply to the comments of Reviewer #1:\nComments:\nSince I recommended publication already at the previous stage, I have nothing to add.\nAuthor reply: We thank the reviewer very much for this delightful comment.\n1"}]

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