Berhane Temelso

Structures of Cage, Prism, and Book Isomers of Water Hexamer from Broadband Rotational Spectroscopy

Cage, Book, and Prism The array of hydrogen bonds governing the extended structure of liquid water is so intricate that chemists have often sought to understand it by studying simpler clusters. Even so, it has been challenging to get a handle on the preferred arrangement adopted by just six water molecules. Interdependent theoretical and spectroscopic studies have narrowed down the lowest-energy hexamer structures to three isomers—respectively designated the cage, the book, and the prism—but their relative energies remain uncertain. Now, Pérez et al. (p. 897; see the Perspective by Saykally and Wales) have observed all three isomers in a single experiment, using Fourier transform microwave spectroscopy, and were able to establish definitively their energy ordering. Observing three distinct water clusters in the same experiment resolves long-standing questions about their relative stabilities. Theory predicts the water hexamer to be the smallest water cluster with a three-dimensional hydrogen-bonding network as its minimum energy structure. There are several possible low-energy isomers, and calculations with different methods and basis sets assign them different relative stabilities. Previous experimental work has provided evidence for the cage, book, and cyclic isomers, but no experiment has identified multiple coexisting structures. Here, we report that broadband rotational spectroscopy in a pulsed supersonic expansion unambiguously identifies all three isomers; we determined their oxygen framework structures by means of oxygen-18–substituted water (H218O). Relative isomer populations at different expansion conditions establish that the cage isomer is the minimum energy structure. Rotational spectra consistent with predicted heptamer and nonamer structures have also been identified.

Benchmark Structures and Binding Energies of Small Water Clusters with Anharmonicity Corrections

For (H(2)O)(n) where n = 1-10, we used a scheme combining molecular dynamics sampling with high level ab initio calculations to locate the global and many low lying local minima for each cluster. For each isomer, we extrapolated the RI-MP2 energies to their complete basis set limit, included a CCSD(T) correction using a smaller basis set and added finite temperature corrections within the rigid-rotor-harmonic-oscillator (RRHO) model using scaled and unscaled harmonic vibrational frequencies. The vibrational scaling factors were determined specifically for water clusters by comparing harmonic frequencies with VPT2 fundamental frequencies. We find the CCSD(T) correction to the RI-MP2 binding energy to be small (<1%) but still important in determining accurate conformational energies. Anharmonic corrections are found to be non-negligble; they do not alter the energetic ordering of isomers, but they do lower the free energies of formation of the water clusters by as much as 4 kcal/mol at 298.15 K.

Accurate Predictions of Water Cluster Formation, (H2O)n=2-10

An efficient mixed molecular dynamics/quantum mechanics model has been applied to the water cluster system. The use of the MP2 method and correlation consistent basis sets, with appropriate correction for BSSE, allows for the accurate calculation of electronic and free energies for the formation of clusters of 2-10 water molecules. This approach reveals new low energy conformers for (H(2)O)(n=7,9,10). The water heptamer conformers comprise five different structural motifs ranging from a three-dimensional prism to a quasi-planar book structure. A prism-like structure is favored energetically at low temperatures, but a chair-like structure is the global Gibbs free energy minimum past 200 K. The water nonamers exhibit less complexity with all the low energy structures shaped like a prism. The decamer has 30 conformers that are within 2 kcal/mol of the Gibbs free energy minimum structure at 298 K. These structures are categorized into four conformer classes, and a pentagonal prism is the most stable structure from 0 to 320 K. Results can be used as benchmark values for empirical water models and density functionals, and the method can be applied to larger water clusters.

Concerted hydrogen-bond breaking by quantum tunneling in the water hexamer prism

Gear-like rotation by a wobbly water duo The molecules in liquid water move about constantly, but on average they cling to each other through hydrogen bonds, like dancers who keep switching partners. Richardson et al. uncovered a fresh twist in this molecular dance (see the Perspective by Clary). Studying clusters of six molecules each—essentially the smallest three-dimensional water droplets—they observed coupled motion of two different molecules in the cluster. The process breaks two different hydrogen bonds concurrently in a pattern akin to rotating gears. Science, this issue p. 1310; see also p. 1267 Rotational spectroscopy and accompanying theory uncover gearlike joint motion of a pair of water molecules in a cluster. [Also see Perspective by Clary] The nature of the intermolecular forces between water molecules is the same in small hydrogen-bonded clusters as in the bulk. The rotational spectra of the clusters therefore give insight into the intermolecular forces present in liquid water and ice. The water hexamer is the smallest water cluster to support low-energy structures with branched three-dimensional hydrogen-bond networks, rather than cyclic two-dimensional topologies. Here we report measurements of splitting patterns in rotational transitions of the water hexamer prism, and we used quantum simulations to show that they result from geared and antigeared rotations of a pair of water molecules. Unlike previously reported tunneling motions in water clusters, the geared motion involves the concerted breaking of two hydrogen bonds. Similar types of motion may be feasible in interfacial and confined water.

Quantum Mechanical Study of Sulfuric Acid Hydration: Atmospheric Implications

The role of the binary nucleation of sulfuric acid in aerosol formation and its implications for global warming is one of the fundamental unsettled questions in atmospheric chemistry. We have investigated the thermodynamics of sulfuric acid hydration using ab initio quantum mechanical methods. For H(2)SO(4)(H(2)O)(n) where n = 1-6, we used a scheme combining molecular dynamics configurational sampling with high-level ab initio calculations to locate the global and many low lying local minima for each cluster size. For each isomer, we extrapolated the Møller-Plesset perturbation theory (MP2) energies to their complete basis set (CBS) limit and added finite temperature corrections within the rigid-rotor-harmonic-oscillator (RRHO) model using scaled harmonic vibrational frequencies. We found that ionic pair (HSO(4)(-)·H(3)O(+))(H(2)O)(n-1) clusters are competitive with the neutral (H(2)SO(4))(H(2)O)(n) clusters for n ≥ 3 and are more stable than neutral clusters for n ≥ 4 depending on the temperature. The Boltzmann averaged Gibbs free energies for the formation of H(2)SO(4)(H(2)O)(n) clusters are favorable in colder regions of the troposphere (T = 216.65-273.15 K) for n = 1-6, but the formation of clusters with n ≥ 5 is not favorable at higher (T > 273.15 K) temperatures. Our results suggest the critical cluster of a binary H(2)SO(4)-H(2)O system must contain more than one H(2)SO(4) and are in concert with recent findings (1) that the role of binary nucleation is small at ambient conditions, but significant at colder regions of the troposphere. Overall, the results support the idea that binary nucleation of sulfuric acid and water cannot account for nucleation of sulfuric acid in the lower troposphere.

The Role of Anharmonicity in Hydrogen-Bonded Systems: The Case of Water Clusters.

The nature of vibrational anharmonicity has been examined for the case of small water clusters using second-order vibrational perturbation theory (VPT2) applied on second-order Møller-Plesset perturbation theory (MP2) potential energy surfaces. Using a training set of 16 water clusters (H2O)n=2-6,8,9 with a total of 723 vibrational modes, we determined scaling factors that map the harmonic frequencies onto anharmonic ones. The intermolecular modes were found to be substantially more anharmonic than intramolecular bending and stretching modes. Due to the varying levels of anharmonicity of the intermolecular and intramolecular modes, different frequency scaling factors for each region were necessary to achieve the highest accuracy. Furthermore, new scaling factors for zero-point vibrational energies (ZPVE) and vibrational corrections to the enthalpy (ΔHvib) and the entropy (Svib) have been determined. All the scaling factors reported in this study are different from previous works in that they are intended for hydrogen-bonded systems, while others were built using experimental frequencies of covalently bonded systems. An application of our scaling factors to the vibrational frequencies of water dimer and thermodynamic functions of 11 larger water clusters highlights the importance of anharmonic effects in hydrogen-bonded systems.

Computational Study of the Hydration of Sulfuric Acid Dimers: Implications for Acid Dissociation and Aerosol Formation

We have investigated the thermodynamics of sulfuric acid dimer hydration using ab initio quantum mechanical methods. For (H(2)SO(4))(2)(H(2)O)(n) where n = 0-6, we employed high-level ab initio calculations to locate the most stable minima for each cluster size. The results presented herein yield a detailed understanding of the first deprotonation of sulfuric acid as a function of temperature for a system consisting of two sulfuric acid molecules and up to six waters. At 0 K, a cluster of two sulfuric acid molecules and one water remains undissociated. Addition of a second water begins the deprotonation of the first sulfuric acid leading to the di-ionic species (the bisulfate anion HSO(4)(-), the hydronium cation H(3)O(+), an undissociated sulfuric acid molecule, and a water). Upon the addition of a third water molecule, the second sulfuric acid molecule begins to dissociate. For the (H(2)SO(4))(2)(H(2)O)(3) cluster, the di-ionic cluster is a few kcal mol(-1) more stable than the neutral cluster, which is just slightly more stable than the tetra-ionic cluster (two bisulfate anions, two hydronium cations, and one water). With four water molecules, the tetra-ionic cluster, (HSO(4)(-))(2)(H(3)O(+))(2)(H(2)O)(2), becomes as favorable as the di-ionic cluster H(2)SO(4)(HSO(4)(-))(H(3)O(+))(H(2)O)(3) at 0 K. Increasing the temperature favors the undissociated clusters, and at room temperature we predict that the di-ionic species is slightly more favorable than the neutral cluster once three waters have been added to the cluster. The tetra-ionic species competes with the di-ionic species once five waters have been added to the cluster. The thermodynamics of stepwise hydration of sulfuric acid dimer is similar to that of the monomer; it is favorable up to n = 4-5 at 298 K. A much more thermodynamically favorable pathway forming sulfuric acid dimer hydrates is through the combination of sulfuric acid monomer hydrates, but the low concentration of sulfuric acid relative to water vapor at ambient conditions limits that process.

Isotopic Ratios in Titan's Methane: Measurements and Modeling

The existence of methane in Titan’s atmosphere (∼ 6% level at the surface) presents a unique enigma, as photochemical models predict that the current inventory will be entirely depleted by photochemistry in a timescale of ∼20 Myr. In this paper, we examine the clues available from isotopic ratios ( 12 C/ 13 C and D/H) in Titan’s methane as to the past atmosphere history of this species. We first analyze recent infrared spectra of CH4 collected by the Cassini Composite Infrared Spectrometer, measuring simultaneously for the first time the abundances of all three detected minor isotopologues: 13 CH4, 12 CH3D, and 13 CH3D. From these we compute estimates of 12 C/ 13 C = 86.5 ± 8.2 and D/H = (1.59 ± 0.33) × 10 −4 , in agreement with recent results from the Huygens GCMS and Cassini INMS instruments. We also use the transition state theory to estimate the fractionation that occurs in carbon and hydrogen during a critical reaction that plays a key role in the chemical depletion of Titan’s methane: CH4 +C 2H → CH3 +C 2H2. Using these new measurements and predictions we proceed to model the time evolution of 12 C/ 13 C and D/H in Titan’s methane under several prototypical replenishment scenarios. In our Model 1 (no resupply of CH4), we find that the present-day 12 C/ 13 C implies that the CH4 entered the atmosphere 60–1600 Myr ago if methane is depleted by chemistry and photolysis alone, but much more recently—most likely less than 10 Myr ago—if hydrodynamic escape is also occurring. On the other hand, if methane has been continuously supplied at the replenishment rate then the isotopic ratios provide no constraints, and likewise for the case where atmospheric methane is increasing. We conclude by discussing how these findings may be combined with other evidence to constrain the overall history of the atmospheric methane.

Hydrogen Bond Cooperativity and the Three‐Dimensional Structures of Water Nonamers and Decamers

Broadband rotational spectroscopy of water clusters produced in a pulsed molecular jet expansion has been used to determine the oxygen atom geometry in three isomers of the nonamer and two isomers of the decamer. The isomers for each cluster size have the same nominal geometry but differ in the arrangement of their hydrogen bond networks. The nearest neighbor OO distances show a characteristic pattern for each hydrogen bond network isomer that is caused by three-body effects that produce cooperative hydrogen bonding. The observed structures are the lowest energy cluster geometries identified by quantum chemistry and the experimental and theoretical OO distances are in good agreement. The cooperativity effects revealed by the hydrogen bond OO distance variations are shown to be consistent with a simple model for hydrogen bonding in water that takes into account the cooperative and anticooperative bonding effects of nearby water molecules.

Hydration of the Bisulfate Ion: Atmospheric Implications

Using molecular dynamics configurational sampling combined with ab initio energy calculations, we determined the low energy isomers of the bisulfate hydrates. We calculated the CCSD(T) complete basis set (CBS) binding electronic and Gibbs free energies for 53 low energy isomers of HSO(4)(-)(H(2)O)(n=1-6) and derived the thermodynamics of adding waters sequentially to the bisulfate ion and its hydrates. Comparing the HSO(4)(-)/H(2)O system to the neutral H(2)SO(4)/H(2)O cluster, water binds more strongly to the anion than it does to the neutral molecules. The difference in the binding thermodynamics of HSO(4)(-)/H(2)O and H(2)SO(4)/H(2)O systems decreases with increasing number of waters. The thermodynamics for the formation of HSO(4)(-)(H(2)O)(n=1-5) is favorable at 298.15 K, and that of HSO(4)(-)(H(2)O)(n=1-6) is favorable for T < 273.15 K. The HSO(4)(-) ion is almost always hydrated at temperatures and relative humidity values encountered in the troposphere. Because the bisulfate ion binds more strongly to sulfuric acid than it does to water, it is expected to play a role in ion-induced nucleation by forming a strong complex with sulfuric acid and water, thus facilitating the formation of a critical nucleus.