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At least 37 records · Page 2

Photodissociation of CH2. I - Potential energy surfaces of the dissociation into CH and H

The possible photodissociation pathways of the CH2 radical are studied using ab initio multireference configuration-interaction methods, and accurate photodissociation cross sections and branching ratios for the production of CH + H and C + H2 are obtained. Potential energy surfaces were calculated using the Wuppertal-Bonn self-consistent field plus a multireference single and double-excitation configuration interaction package of programs. Two-dimensional potential energy surfaces of the ten lowest triplet states correlating with the seven lowest states of CH were calculated as functions of bond angle and one C-H bond distance, keeping the other C-H bond distance fixed at the equilibrium CH2 value.

Bearda, Robert A.↗

Structure and mechanical properties of grain boundaries in molybdenum disulfide (MoS 2 )

Molybdenum disulfide (MoS 2 ) is a two-dimensional material widely used as a lubricant in many applications involving mechanical loading under a wide range of operating temperatures. Since many synthesis and processing techniques yield MoS 2 in its polycrystalline form, establishing grain boundary (GB) structure–property relations is key to designing MoS 2 microstructures with tailored properties. Here, we employ classical, reactive atomistic simulations to investigate the structure and mechanical behavior of a wide range of GBs in MoS 2 as a function of temperature. Using a bicrystal MoS 2 geometry, we characterize the atomic structure and calculate the energy of several low-angle GBs. Then, we simulate the tensile deformation behavior of MoS 2 bicrystals at several temperatures. Our results reveal that at temperatures above 100 K, the deformation of MoS 2 bicrystals is characterized by the nucleation of shear bands from GBs that grow, with subsequent loading, into the MoS 2 crystals. At low temperatures, the tensile deformation is characterized by the nucleation and propagation of deformation fronts, resulting in altered bond angles and bond lengths. Quantitative analysis reveals a decrease in the ultimate tensile stress and ultimate failure strain of MoS 2 bicrystals with the increase in temperature. Furthermore, our simulations of the mechanical behavior of metastable GBs reveal that the strength and ductility decrease with the increase in energy of these boundary structures. In broad terms, our work provides future avenues to employ GB engineering as a strategy to tailor the properties of MoS 2 microstructures.

Moore, Robert D. [Lehigh Univ., Bethlehem, PA (Uni↗

Efficient and interpretable graph network representation for angle-dependent properties applied to optical spectroscopy

Abstract Graph neural networks are attractive for learning properties of atomic structures thanks to their intuitive graph encoding of atoms and bonds. However, conventional encoding does not include angular information, which is critical for describing atomic arrangements in disordered systems. In this work, we extend the recently proposed ALIGNN (Atomistic Line Graph Neural Network) encoding, which incorporates bond angles, to also include dihedral angles (ALIGNN-d). This simple extension leads to a memory-efficient graph representation that captures the complete geometry of atomic structures. ALIGNN-d is applied to predict the infrared optical response of dynamically disordered Cu(II) aqua complexes, leveraging the intrinsic interpretability to elucidate the relative contributions of individual structural components. Bond and dihedral angles are found to be critical contributors to the fine structure of the absorption response, with distortions that represent transitions between more common geometries exhibiting the strongest absorption intensity. Future directions for further development of ALIGNN-d are discussed.

36 MATERIALS SCIENCE↗

A Laboratory and Theoretical Study of Silicon Hydroxide SiOH

The rotational spectrum of the triatomic free radical SiOH in its X 2A' ground electronic state has been observed in a supersonic molecular beam by Fourier transform microwave spectroscopy. The fundamental (10,1 yields 00,0) transition has been detected for normal SiOH and for three rare isotopic species: (30)SiOH, Si(18)OH, and SiOD. The same transition has also been observed in two of three excited vibrational states, v2 and v3, for the most abundant species. Precise spectroscopic constants, including those that describe the effective spin doubling and hydrogen hyperfine structure, have been derived for each isotopic species or vibrational state. To complement the laboratory work, theoretical calculations of the structure, dipole moment, and energies of the X 2A' and low-lying 1 2A'' states have also been undertaken at the coupled cluster level of theory. In agreement with theoretical predictions, we conclude from the hyperfine constants that SiOH is a best described as a pi-type radical, with the unpaired electron localized on a p orbital on the silicon atom. Assuming a bond angle of 118.5 deg, the Si-O bond length is 1.647(2) Angstroms and the O-H bond length is 0.969(4) Angstrom.

McCarthy, M. C.↗

Adsorption and activation of CO 2 on Pt/CeOx/TiO 2 (110): Role of the Pt-CeO x interface

The adsorption and dissociation of CO 2 on TiO 2 (110), CeO x /TiO 2 (110) and Pt/CeO x /TiO 2 (110) surfaces has been examined using Ambient Pressure X-ray Photoelectron Spectroscopy (AP-XPS). The substrates under study exhibited different degrees of complexity which were tested for the binding of the adsorbate and the cleavage of C-O bonds. The surfaces were prepared by depositing CeO x (0.1 ML) onto TiO 2 (110) to form a mixed oxide support, onto which Pt nanoparticles (0.2 ML) were deposited. This configuration yields a complex set of interfaces between metal and oxides and we have systematically titrated the active role of each component (Pt 4f, Ce 3d and Ti 2p regions) and the arising surface intermediates (C 1s and O 1s regions). CO 2 barely bonds to stoichiometric TiO 2 (110). It heals oxygen vacancies of this oxide surface (CO 2,gas → CO gas + O a ) and does not form stable carbonates. A stable carbonate was seen upon adsorption of CO 2 on CeO x /TiO 2 (110) and on this type of substrate the adsorbate also removed O vacancies leading to the oxidation of Ti 3+ and Ce 3+ sites. Pt nanoparticles dispersed on CeO x /TiO 2 (110) were highly effective for the binding and dissociation of CO 2 , with the formation of CO 3 , CO, C and CH x species on the Pt/CeO x /TiO 2 (110) system. The results of theoretical calculations based on density-functional theory (DFT) show that Pt/CeOx/TiO2(110) binds CO2 much stronger than surfaces of bulk platinum {(111), (100), (110)} or other late transition metals. On a Pt-CeO x interface, the molecule adsorbs with a bent configuration (~ 130° O-C-O bond angle) and with a substantial elongation (~ 0.1 Å) of the C-O bonds, facilitating its transformation into high value chemicals.

36 MATERIALS SCIENCE↗

Interplay between element-specific distortions and electrocatalytic oxygen evolution for cobalt–iron hydroxides

A microscopic understanding of how Fe-doping of Co(OH) 2 improves electrocatalytic oxygen evolution remains elusive. We study two Co 1–x Fex(OH) 2 series that differ in fabrication protocol and find composition alone poorly correlates to catalyst performance. Structural descriptors extracted using X-ray diffraction, X-ray absorption spectroscopy, and Raman spectroscopy reveal element-specific distortions in Co 1–x Fe x (OH) 2 . These structural descriptors are composition-dependent within individual sample series but inconsistent across fabrication protocols, revealing fabrication-dependence in catalyst microstructure. Correlations between structural parameters from different techniques show that Fe–O resists bond length changes, forcing distortion of Co environments. We find the difference in O–M–O bond angles between Co and Fe sites to correlate with electrocatalytic behavior across both sample series, which we attribute to asymmetric distortion of potential energy surfaces for the Co(III) to Co(IV) oxidation. A Tafel slope consistent with a rate-limiting step without electron transfer emerges as the O–Co–O angle decreases, implying a distortion-induced transition in the rate-limiting step. The fabrication dependence of electronic and bonding structure in the catalysts should be considered in theoretical and high-throughput analyses of electrocatalyst materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Atomistic insight into the ferroelastic post-stishovite transition by high-pressure single-crystal X-ray diffraction

Abstract The post-stishovite transition is a classic pseudo-proper typed ferroelastic transition with a symmetry-breaking spontaneous strain. This transition has been studied using high-pressure spontaneous strains, optic modes, and elastic moduli (Cij) based on the Landau modeling, but its atomistic information and structural distortion remain poorly understood. Here we have conducted synchrotron single-crystal X-ray diffraction measurements on stishovite crystals up to 75.3 GPa in a diamond-anvil cell. Analysis of the data reveals atomic positions, bond lengths, bond angles, and variations of SiO6 octahedra across the transition at high pressure. Our results show that the O coordinates split at ~51.4 GPa, where the apical and equatorial Si-O bond lengths cross over, the SiO6 octahedral distortion vanishes, and the SiO6 octahedra start to rotate about the c axis. Moreover, distortion mode analysis shows that an in-plane stretching distortion (GM1+ mode) occurs in the stishovite structure at high pressure while a rotational distortion (GM2+ mode) becomes dominant in the post-stishovite structure. These results are used to correlate with elastic moduli and Landau parameters (symmetry-breaking strain e1–e2 and order parameter Q) to provide atomistic insight into the ferroelastic transition. When the bond lengths of two Si-O bonds are equal due to the contribution from the GM1+ stretching mode, C11 converges with C12, and the shear wave VS1[110] polarizing along [110] and propagating along [110] vanishes. Values of e1–e2 and Q are proportional to the SiO6 rotation angle from the occurrence of the GM1+ rotational mode in the post-stishovite structure. Our results on the pseudo-proper type transition are also compared with that for the proper type in albite and improper type in CaSiO3 perovskite. The symmetry-breaking strain, in all these types of transitions, arises as the primary effect from the structural angle (such as SiO6 rotation or lattice constant angle) and its relevant distortion mode in the low-symmetry ferroelastic phase.

Geochemistry & Geophysics↗

Ultrafast Correlation Energy Estimator

A virtually no-cost method is proposed that can compute the correlation energies of general, covalently bonded, organic, and inorganic molecules (including conjugated π-electron systems) with a well-defined dominant Lewis structure at the accuracy of 99.5% of the near-exact values determined by the coupled-cluster singles, doubles, and perturbative triples [CCSD(T)] in the complete-basis-set (CBS) limit. This Correlation Energy Per Bond (CEPB) method assigns a partial correlation energy to each bond type (characterized by the identities of the two atoms forming the bond and its integer bond order) and to a lone pair, regardless of the bond length, bond angle, sp-hybridization, π-electron conjugation, ionicity, noncovalent interactions, etc. At its current stage, the method is mainly suitable for near-equilibrium geometries. The correlation energies per bond are determined by a fit to the CCSD(T)/CBS benchmarks. It can neither improve the equilibrium structures nor discern conformers or positional isomers, yet its accuracy for reaction energies rivals that of the second-order Møller–Plesset perturbation theory, which is far more expensive. Its promising performance underscores the possibility that surprisingly compact, chemically intuitive molecular fragments exist into which correlation energies can be partitioned, leading to various ultrafast correlation-energy estimators tailored to different purposes.

Binding energy↗

Structures of fluoride containing aluminosilicate low activity nuclear waste glasses: A molecular dynamics simulations study

Fluorine and other halides commonly exist in nuclear waste forms, and due to their volatile nature, halide retention poses an issue affecting waste loading during vitrification. The compositional effect on fluorine incorporation in aluminosilicate glasses is investigated through molecular dynamics simulations. Oxygen and fluorine coordination numbers around glass former and modifier cations, bond angle distributions, and medium range structure features such as Q n distributions, ring size distributions and neutron diffraction structure factors were calculated. It was found that fluorine has higher preference to bond to Ca 2+ than to Na + , both in the melt and the glass, and there is no Si-F bond formation in the glass but they do exist in the melt. Consequently, CaO for Na 2 O substitution can be an effective way to help fluorine retention without significantly changing the glass chemistry. Furthermore, these results thus provide insights on fluorine incorporation in the aluminosilicate nuclear waste glasses and the strategy on how to improve fluorine retention both in the glass and the melt.

36 MATERIALS SCIENCE↗

Design, fabrication and test of graphite/polyimide composite joints and attachments for advanced aerospace vehicles

Results of an experimental program to develop several types of graphite/polyimide (GR/PI) bonded and bolted joints for lightly loaded flight components for advanced space transportation systems and high speed aircraft are presented. Tasks accomplished include: a literature survey; design of static discriminator specimens; design allowables testing; fabrication of test panels and specimens; small specimen testing; and standard joint testing. Detail designs of static discriminator specimens for each of the four major attachment types are presented. Test results are given for the following: (1) transverse tension of Celion 3000/PMR-15 laminate; (2) net tension of a laminate for both a loaded and unloaded bolt hole; (3) comparative testing of bonded and co-cured doublers along with pull-off tests of single and double bonded angles; (4) single lap shear tests, transverse tension and coefficient of thermal expansion tests of A7F (LARC-13 amide-imide modified) adhesive; and (5) tension tests of standard single lap, double lap, and symmetric step lap bonded joints. Also, included are results of a finite element analysis of a single lap bonded composite joint.

Barclay, D. L.↗

New Insights into Structural Evolution of LiNiO 2 Revealed by Operando Neutron Diffraction

LiNiO 2 (LNO) represents the end member in the compositional space of the LiNi 1-x-y Mn x Co y O 2 (as x and y approach zero) cathode system. Despite its high theoretical specific capacity (275 mAh/g), LNO suffers from phase transitions with large volume change and unfavorable reactions upon electrochemical cycling, which restricts its practical use in the application of lithium-ion batteries. While the contributing factor to the structural instability is commonly linked to the undesired volume collapse associated with the H2-H3 phase transition, detailed analysis of structural evolution following the entire route of phase transitions (H1-M-H2-H3) in real time under battery operating conditions remains a challenging task. In this work, we employ operando neutron diffraction to study the structural changes (crystal lattice, Li/Ni–O bond length, O–Ni–O bond angles, and LiO 2 /NiO 2 layer thickness) of LNO cathode in a home-built Li x NiO 2 || graphite full cell during Li + de-/intercalation. In particular, the anomalous increase(decrease) of Ni–O(Li–O) bond length at high SOC (>~85 %) in the H3 phase is discussed in the context of O 2- (2p)→Ni 4+ (3d) negative charge transfer.

25 ENERGY STORAGE↗

S 8 ring content in liquid sulfur determined from x-ray diffraction

The S 8 ring content in liquid sulfur has been determined from the 4.47 Å peak in the x-ray pair distribution function over the temperature range −55 °C –330 °C. This peak represents the characteristic 3rd and 4th nearest atom-atom distances across an S 8 -ring. Three procedures were used to calculate the S 8 -ring fraction; scaling to crystalline β-S, a linear combination fit and a direct integration method. All methods gave similar values, indicating that approximately one third of the S 8 -rings break up upon melting into a distribution of short chains with an average length of 5 ± 2 atoms. Our results contradict established models of low temperature sulfur that indicate below the λ-transition the liquid comprises almost entirely of S8-rings. In addition, we find the S 8 -ring fraction increases to 76 ± 10% at −30 °C in the supercooled liquid, and decreases to 23% ± 3% at 330 °C in the high temperature melt. First principle molecular dynamics calculations confirm the onset of dynamic ring distortion via broad bond angle distributions, associated with the interstitial region between the first and second peaks in the pair distribution function. Our results are consistent with the presence of a propensity of short chains in the low temperature liquid, that are required for the bond switching mechanism responsible for the polymerization process to occur at the λ-transition temperature, T λ .

lambda transition↗

An evaluation for geometries, formation enthalpies, and dissociation energies of diatomic and triatomic (C, H, N, O), NO 3 , and HNO 3 molecules from the PAW DFT method with PBE and optB88-vdW functionals

The structural geometries, formation enthalpies, and dissociation energies of all diatomic and triatomic molecules consisting of the four basic elements C, H, N, and/or O are calculated using the projector augmented wave density functional theory (DFT) method with the Perdew–Burke–Ernzerhof and optB88-vdW exchange-correlation functionals. The calculations are also extended to two larger molecules NO 3 and HNO 3 , which consist of four and five atoms, respectively. In total, 82 molecules or isomers are considered in the calculations. The geometric parameters including 42 bond lengths and 15 bond angles of these molecules calculated using the planewave DFT method are highly satisfactory, relative to the available experimental data. The error analysis is also performed for 49 formation enthalpies and 138 dissociation energies (including 51 atomization energies as well as the corresponding bond dissociation energies). The results are also compared with the previous data from various atomic-orbital-based methods for molecules and from similar or different planewave DFT methods for various solids and other molecules. This provides an informative and instructive evaluation especially for calculating the large-size material systems containing these small molecules as well as for developing the DFT methods further.

74 ATOMIC AND MOLECULAR PHYSICS↗

Polyhedral Distortions and Unusual Magnetic Order in Spinel FeMn 2 O 4

Spinel compounds AB 2 X 4 consist of both tetrahedral (AX 4 ) and octahedral (BX 6) environments with the former forming a diamond lattice and the latter a geometrically frustrated pyrochlore lattice. Exploring the fascinating physical properties and their correlations with structural features is critical in understanding these materials. FeMn 2 O 4 has been reported to exhibit one structural transition and two successive magnetic transitions. In this work, we report the polyhedral distortions and their correlations to the structural and two magnetic transitions in FeMn 2 O 4 by employing the high-resolution neutron powder diffraction. The cation distribution is found to be ($Mn_{0.9}^{2+}Fe_{0.1}^{3+}$)$_{A}$($Mn^{3+}Fe_{0.9}^{3+}Mn_{0.1}^{2+}$)$_{B}$O 4 . While large trigonal distortion is found even in the high-temperature cubic phase, the first-order cubic-tetragonal structural transition associated with the elongation of both tetrahedra and octahedra with shared oxygen atoms along the c axis occurs at T S ≈ 750 K, driven by the Jahn–Teller effect of the orbital active B-site Mn 3+ cation. Strong magnetoelastic coupling is unveiled at T N1 ≈ 400 K as manifested by the appearance of Néel-type collinear ferrimagnetic order, an anomaly in both tetrahedral and octahedral distortions, as well as an anomalous decrease of the lattice constants c and a weak anomaly of a. Upon cooling to T N2 ≈ 65 K, it evolves to a noncollinear ferrimagnetic order accompanied by the different moments at the split magnetic sites B1 and B2. Only one-half of the B-site Mn 3+ /Fe 3+ spins, i.e., the B2-site spins in the pyrochlore lattice, are canted, which is a unique magnetic order among spinels. The canting angle between A-site and B2-site moments is ~25°, but the B1-site moment stays antiparallel to the A-site moment even at 10 K. This noncollinear order is accompanied by a modification of the O–B–O bond angles in the octahedra without significant change in lattice constants or tetrahedral/octahedral distortion parameters, indicating a distinct magnetoelastic coupling. We demonstrate distinct roles of the A-site and B-site magnetic cations in the structural and magnetic properties of FeMn 2 O 4 . Our study indicates that FeMn 2 O 4 is a wonderful platform to unveil interesting magnetic order and to investigate their correlations with polyhedral distortions and lattice.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Hydrogen Bonding Analysis of Structural Transition-Induced Symmetry Breaking and Spin Splitting in a Hybrid Perovskite Employing a Synergistic Diffraction-DFT Approach

Two-dimensional (2D) hybrid organic–inorganic perovskites (HOIPs) offer an outstanding opportunity for spin-related technologies owing in part to their tunable structural symmetry breaking and distortions driven by organic–inorganic hydrogen (H) bonds. However, understanding how H-bonds tailor inorganic symmetry and distortions and therefore enhance spin splitting for more effective spin manipulation remains imprecise due to challenges in measuring H atom positions using X-ray diffraction. Here, we report a thermally induced structural transition (at ~209 K) for a 2D HOIP, (2-BrPEA) 2 PbI 4 [2-BrPEA = 2-(2-bromophenyl)ethylammonium], which induces inversion asymmetry and a strong spin splitting (ΔE > 30 meV). While X-ray diffraction generally establishes heavy atom coordinates, we utilize neutron diffraction for accurate H atom position determination, demonstrating that the structural transition-induced rearrangement of H-bonds with distinct bond strengths asymmetrically shifts associated iodine atom positions. Further, consequences of this shift include an increased structural asymmetry, an enhanced difference between adjacent interoctahedra distortions (i.e., Pb–I–Pb bond angles), and therefore significant spin splitting. We further show that H-only density-functional theory (DFT) relaxation of the X-ray structure shifts H atoms to positions that are consistent with the neutron experimental data, validating a convenient pathway to more generally improve upon HOIP H-bonding analyses derived from quicker/less-expensive X-ray data.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Temperature-Dependent Properties of Molten Li 2 BeF 4 Salt Using Ab Initio Molecular Dynamics

Molten lithium tetrafluoroberyllate (Li 2 BeF 4 ) salt, also known as FLiBe, with a 2:1 mixture of LiF and BeF 2 is being proposed as a coolant and solvent in advanced nuclear reactor designs, such as the molten salt reactor or the fluoride salt cooled high-temperature reactor. We present the results on the structure and properties of FLiBe over a wide range of temperatures, 0–2000 K, from high-throughput ab initio molecular dynamics simulation using a supercell model of 504 atoms. The variations in the local structures of solid and liquid FLiBe with temperature are discussed in terms of a pair distribution function, coordination number, and bond angle distribution. The temperature-dependent electronic structure and optical and mechanical properties of FLiBe are calculated. The optical and mechanical property results are reported for the first time. The results above and below the melting temperature (~732 K) are compared with the experimental data and with data for crystalline FLiBe. The electronic structure and interatomic bonding results are discussed in correlation with the mechanical strength. A novel concept of total bond order density (TBOD), an important quantum mechanical parameter, is used to characterize the internal cohesion and strength in the simulated models. The results show a variation in the rate of change in properties in solid and liquid phases with anomalous behavior across the melting region. The observed trend is the decrease in mechanical strength, band gap, and TBOD in a nonlinear fashion as a function of temperature. The refractive index shows a surprising minimum at 850 K, among the tested temperatures, which lies above the melting point. These findings provide a new platform to understand the interplay between the temperature-dependent structures and properties of FLiBe salt.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Temperature-induced gradual polymorphic structural crossover in liquid indium, tin, and antimony

Temperature-induced polymorphic structural crossover in metallic liquid indium (In), tin (Sn), and antimony (Sb) is investigated by in situ high-energy x-ray diffraction and ab initio molecular dynamics simulations. The results demonstrate the existence of a temperature-induced reversible and gradual structural crossover in these three liquids, reflecting from both “static” structures, e.g., peak positions of the structure factor and pair distribution function, bond angle distribution, number of tetrahedra, cluster connection, free volume, and dynamical behaviors, including the relaxation time, diffusion coefficient, and non-Gaussian parameter. Further, the main difference from liquid In, Sn, to Sb is that not only the large-sized free volume but also the anharmonicity and the dynamical heterogeneity increase significantly with the appearance of strong covalent bonds. These findings will deepen the understanding of liquid structure and the liquid-liquid transition in metallic liquids.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Descriptors of water aggregation

For this work, we rely on a total of 23 (cluster size, 8 structural, and 14 connectivity) descriptors to investigate structural patterns and connectivity motifs associated with water cluster aggregation. In addition to the cluster size n (number of molecules), the 8 structural descriptors can be further categorized into (i) one-body (intramolecular): covalent OH bond length (r OH ) and HOH bond angle (θ HOH ), (ii) two-body: OO distance (r OO ), OHO angle (θ OHO ), and HOOX dihedral angle ($\phi$ HOOX ), where X lies on the bisector of the HOH angle, (iii) three-body: OOO angle (θ OOO ), and (iv) many-body: modified tetrahedral order parameter (q) to account for two-, three-, four-, five-coordinated molecules (q m , m = 2, 3, 4, 5) and radius of gyration (R g ). The 14 connectivity descriptors are all many-body in nature and consist of the AD, AAD, ADD, AADD, AAAD, AAADD adjacencies [number of hydrogen bonds accepted (A) and donated (D) by each water molecule], Wiener index, Average Shortest Path Length, hydrogen bond saturation (% HB), and number of non-short-circuited three-membered cycles, four-membered cycles, five-membered cycles, six-membered cycles, and seven-membered cycles. We mined a previously reported database of 4 948 959 water cluster minima for (H 2 O) n , n = 3–25 to analyze the evolution and correlation of these descriptors for the clusters within 5 kcal/mol of the putative minima. It was found that r OH and % HB correlated strongly with cluster size n, which was identified as the strongest predictor of energetic stability. Marked changes in the adjacencies and cycle count were observed, lending insight into changes in the hydrogen bond network upon aggregation. A Principal Component Analysis (PCA) was employed to identify descriptor dependencies and group clusters into specific structural patterns across different cluster sizes. The results of this study inform our understanding of how water clusters evolve in size and what appropriate descriptors of their structural and connectivity patterns are with respect to system size, stability, and similarity. The approach described in this study is general and can be easily extended to other hydrogen-bonded systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗