Infrared spectroscopic study of hydrogen bonding topologies in the water octamer: The smallest ice cube

The water octamer, with its cubic structure consisting of six four-membered rings, presents an excellent system in which to unravel the cooperative interactions driven by subtle changes in the hydrogen-bonding topology. Although many distinct structures are calculated to exist, it has not been possible to extract the structural information encoded in their vibrational spectra because this requires size-selectivity of the neutral clusters with sufficient resolution to identify the contributions of the different isomeric forms. Here we report the size-specific infrared spectra of the isolated cold, neutral water octamer using a scheme based on threshold photoionization using a tunable vacuum ultraviolet free electron laser. A plethora of sharp vibrational bands features are observed for the first time. Theoretical analysis of these patterns reveals the coexistence of five cubic isomers, including two with chirality. The relative energies of these structures are found to reflect topology-dependent, delocalized multi-center hydrogen-bonding interactions. These results demonstrate that even with a common structural motif, the degree of cooperativity among the hydrogen-bonding network creates a hierarchy of distinct species. The implications of these results on possible metastable forms of ice are considered.

As the most vital matter on the earth, water and its interactions with other substances are essential in the life of our planet. Understanding the structure of bulk water and its hydrogenbonding networks, however, remains a grand challenge 1,2 . Spectroscopic investigation of water clusters provides a quantitative description of hydrogen-bond motions that occur in ice and liquid water 3,4 . Currently, cationic or anionic forms of water clusters have been extensively investigated because of relative ease in size-selection and detection [5][6][7][8][9] . These studies have provided essential knowledge on the structure and dynamics of the ionic water clusters.
Inasmuch as hydrogen-bonding networks in neutral water clusters are substantially different from those in ionic ones, to investigate neutral water clusters is a prerequisite to gain fundamental insights into the structures and properties of ice and liquid water. Previous experimental and theoretical studies demonstrated that the water trimer, tetramer, and pentamer all have cyclic minimum-energy structures with all oxygen atoms in a two-dimensional plane, while the hexamer and heptamer have rather complex three-dimensional noncyclic structures [10][11][12][13][14][15][16][17][18] . Of particular interest is the water octamer, which was proposed to represent the transition to cubic structures dominated in larger systems and display behavior characteristic of a solid  liquid phase transition [19][20][21][22] . Experiments strongly suggest the presence of ice nanocrystals [23][24][25][26] .
The hydrogen bonds within the mostly crystalline subsurface layer are found to be stretched by the interaction with the diverse component 25 . The water octamer has thus become a superb benchmark for accurate quantification of the hydrogen-bonding interactions that govern the surface and bulk properties of ice.
Experimental characterization of the water octamer has been awkward due to the difficulty in size-selection and detection of neutral water clusters in general. Only a few gasphase studies have been achieved [27][28][29][30] , and two nearly isoenergetic structures with D2d and S4 symmetry are found. Here we report the well-resolved infrared (IR) spectra of confinementfree, neutral water octamer based on threshold photoionization using a tunable vacuum ultraviolet free electron laser (VUV-FEL). Distinct new features observed in the spectra identify additional cubic isomers with C2 and Ci symmetry, which coexist with the globalminimum D2d and S4 isomers at finite temperature of the experiment. Analysis of the electronic structure reveals a remarkable stability of these cubic water octamers arising from extensively delocalized multi-center hydrogen-bonding interaction. Multiple coexisting cubic octamers provide a coherent picture of structural diversity of bulk water and a cluster-scale precursor to the phase transition between solid and liquid water.
The vibrational spectra were obtained using a VUV-FEL-based IR spectroscopy apparatus described in detail in the supplementary information (SI) 31 . In the experiment, neutral water clusters were generated by supersonic expansions of water vapor seeded in helium using a high-pressure pulsed valve (Even-Lavie valve, EL-7-2011-HT-HRR) that is capable of producing very cold molecular beam conditions 32 . For the IR excitation of neutral water clusters, we used a tunable IR optical parametric oscillator/optical parametric amplifier system  Table S1. The comparison of present and previously measured spectra is given in Fig. S1. From Fig. S1, the present spectrum displays three distinct new absorptions at 2980, 3002, and 3378 cm −1 ; the 3460 cm −1 band is now observed with high intensity, which was not observed in the helium-scattering IR spectrum 27 and only appeared with low intensity in the IR-UV spectra of benzene-tagged (H2O)8 28 .
Strikingly, the OH stretch spectra in the 3516−3628 cm −1 region include many absorptions spanning multiple vibrational bands, which are considerably more complex than the spectra contributed by high-symmetry D2d and S4 cubic octamers 27,28 , suggesting the presence of more low-symmetry minima of the water octamer.  As pointed out previously 27,30 , direct comparison between theory and experiment for the relative intensities of vibrational bands is very difficult, owing to the complexity of experiment (infrared absorption combined with dissociation, saturation effects) as well as the limitation of theoretical calculation (implicit description of intermolecular zero-point motions).
Here, the stick spectra of calculated harmonic vibrational frequencies are utilized to compare with the experimental data. Fig. 1 shows the comparison of experimental spectrum of the water octamer and calculated spectra of isomers I−V. The harmonic OH stretch vibrational frequencies of isomers I−V are listed in Tables S2−S5 and the animation of vibrational modes responsible for the experimental bands is given in the Additional information. and H-donor-free OH groups. As noted previously 11,24,[27][28][29] , the AAD → ADD hydrogen bonds are remarkably shorter than ADD → AAD hydrogen bonds and the corresponding frequency of single H-donor OH stretch is typically lower than that of double H-donor OH stretch (vide infra). Due to the high symmetry of the cubic structures, the normal modes of vibrational stretch of a given type of OH group differ from the other type. As a result, the vibrational frequencies of the single H-donor OH, double H-donor OH, and H-donor-free OH groups are well separated in the OH stretch spectra ( Fig. 1 and Tables S2−S5).
In the calculated spectrum of isomer I (D2d) (Fig. 1, trace I (Table S3), which might be responsible for the broad band observed at 3106 cm −1 . The calculated IR spectra of isomers I and II are much too simple to explain the newly observed absorptions at 2980, 3002, and 3378 cm −1 , but these features match rather well with those of isomers III, IV, and V ( Fig. 1) that are energetically low-lying. Moreover, the III, IV, and V isomers yield various double H-donor OH stretch vibrational fundamentals that cover the spectral range of 3487−3599 cm −1 (Tables S4 and S5), which are consistent with the experimentally congested bands in the 3516−3628 cm −1 region. The agreement of the calculated spectra with experiment is reasonably good to confirm the assignment of the I−V isomers responsible for the experimental spectra.
In addition, the two well-separated free OH bands at 3698 cm −1 (labeled F) and 3726 cm −1 (marked with an asterisk) can be related to two distinct AD and AAD sites, because the H-donor free OH groups of the AAD sites generally appear at ~3700 cm −1 and those of the AD sites at a higher-frequency range 6,9 . The asterisk-labeled band likely originates from a noncubic isomer of water-solvated heptamer (Fig. S3). Under the pulsed supersonic expansion condition in the present work, the presence of all five cubic isomers is quite surprising, indicating that our VUV-FEL spectroscopic technique is apt to explore low-lying neutral isomers unknown before.
The five isomers I−V all have interesting cubic structures. The fact that the five cubic isomers I−V lie within 3 kcal/mol indicates that they can possibly coexist according to Boltzmann distribution. The interconversion barrier among them is larger than 4 kcal/mol at the MP2/AVDZ level (Fig. S4). For instance, the interconversion between the two enantiomeric isomers III and IV need go through four transition states and three intermediates, with the largest barrier of about 5 kcal/mol. Such interconversion barrier might be sufficiently large so that the ultra-high-pressure supersonic expansion cooling is capable of kinetically quenching the nonequilibrium octamer system prior to its rearrangement to the global-minimum energy structure 22 . To evaluate the temperature effect on the distribution of the isomers, Gibbs free energies G of isomers I−V were calculated for the temperature from 0 K to 1000 K (Fig. S5).
Clearly, the free energy difference GII-I, GIII-I, GIV-I, and GV-I does not alter significantly below room temperature, indicating that the population of the five isomers changes little at low temperature.
To understand the electronic structure of the water octamer, we have analyzed the hydrogen-bond (HB) network of the cubic isomers using delocalized and localized molecular orbital theory. Theoretical approaches were applied of natural bond orbital (NBO) 34 , adaptive natural density partitioning (AdNDP) 35 , energy decomposition analysis-natural orbitals for chemical valence (EDA-NOCV) 36 , and principal interacting orbital (PIO) analysis 37 . Hydrogen bonding between an O-H antibonding orbital (denoted σ*(O−H)) and an adjacent oxygen lonepair (LP) donor can be viewed as a three-center two-electron (3c-2e) interaction, which features the O lone-pair delocalizing to the H−O antibonding region (Fig. S6) 15,38 . As exemplified by water dimer, the contribution of 3c-2e HB energy to the intrinsic total binding energy (EHB/Etotal) is about 81.4% from EDA-NOCV analysis, whereas the PIO contribution from the interaction between the lone pair and the σ * (O−H) antibond is about 88.7% for each 3c-2e HB (Fig. S6).
As shown by the bond distances (Tables S7−S11), bond orders, and hybrid orbitals (Table S12) For the water octamer, the EHB/Etotal values of isomers I−V are all around 89% (Table   S6), which are considerably larger than that in the water dimer (81%). This enhanced HB interaction can be partially attributed to the extensively delocalized HB network (vide infra).
In isomer I (D2d), the AAD → ADD hydrogen bonds (1.698 Å) are much shorter than ADD → AAD hydrogen bonds (1.904 Å) ( Table S7). The NBO second-order perturbation energy (E2) analysis of the D2d isomer I (Table S7) (Tables S8−S11) and benefit the formation of water cubes as well as the stacking of cubic and hexagonal layers that occur in the condensed phase 23,25 .
Since the 3c-2e interaction dominates in each HB, we have constructed a secular equation using the Hückel molecular orbital theory. It follows that the 3c-2e HBs are not isolated but highly correlated by delocalized interaction, which leads to extra stabilization when comparing with isolated HBs. This is reminiscent of the aromatic electron delocalization between the single-and double bonds in Kekule structures of benzene. The calculated stabilization energy of delocalized HB network for the D2d isomer I is calculated to be more stable by 4.06 kcal/mol as compared to the isolated HB network (Fig. S7), indicating that the HB network forming an unexpected aromatic delocalization plays a non-negligible role in stabilizing water clusters.
The five water octamer isomers adopting pseudo-cubic structure is highly remarkable.
As each O−H· · · O HB is dominated by the 3c-2e interaction from O lone-pair delocalizing onto the H−O antibonding region, the pseudo-cubic structure can be viewed as consisting of one pair of electron between every two apex oxygen atoms. Interestingly, this bonding pattern is akin to that in the famous cubane (Oh-C8H8) 39 , where each C−C bond contains two localized electrons, as shown in Fig. 3. While the cubane structure lies much higher in energy than its ring isomer, the D2d cubic isomer of (H2O)8 lies much lower in energy than the ring isomer, by 11.64 kcal/mol at the ab initio DLPNO-CCSD(T)/AVTZ level. Consistent with the extensively delocalized HB interaction, the cubic isomer of water has remarkable thermodynamic stability.
ter has remarkable thermodynamic stability. It is interesting to note that phase transitions between solid and liquid water have been observed in simulations of water clusters as small as the octamer, which is supported by the calculated free energy as a function of temperature [19][20][21][22] . The present study has identified the unexpected coexistence of five water octamer cubes that are stabilized by extensive delocalized HB interaction. These findings provide crucial information for understanding the processes of cloud, aerosol, and ice formation, especially under rapid cooling [41][42][43] . It is hoped that the present results will both provide a benchmark for accurate description of the water intermolecular potentials to understand the macroscopic properties of water and stimulate further study of intermediate-ice structures formed in the crystallization process of ice.

Data availability
The authors declare that all data supporting the findings of this study are available within the paper and its Supplementary information files.