Thermodynamics of Forming Water Clusters at Various Temperatures and Pressures by Gaussian-2, Gaussian-3, Complete Basis Set-QB3, and Complete Basis Set-APNO Model Chemistries; Implications for Atmospheric Chemistry

The Gaussian-2, Gaussian-3, complete basis set- (CBS-) QB3, and CBS-APNO methods have been used to calculate ΔH° and ΔG° values for neutral clusters of water, (H2O)n, where n = 2−6. The structures are similar to those determined from experiment and from previous high-level calculations. The thermodynamic calculations by the G2, G3, and CBS-APNO methods compare well against the estimated MP2(CBS) limit. The cyclic pentamer and hexamer structures release the most heat per hydrogen bond formed of any of the clusters. While the cage and prism forms of the hexamer are the lowest energy structures at very low temperatures, as temperature is increased the cyclic structure is favored. The free energies of cluster formation at different temperatures reveal interesting insights, the most striking being that the cyclic trimer, cyclic tetramer, and cyclic pentamer, like the dimer, should be detectable in the lower troposphere. We predict water dimer concentrations of 9 × 1014 molecules/cm3, water trimer concentrations of 2.6 × 1012 molecules/cm3, tetramer concentrations of approximately 5.8 × 1011 molecules/cm3, and pentamer concentrations of approximately 3.5 × 1010 molecules/cm3 in saturated air at 298 K. These results have important implications for understanding the gas-phase chemistry of the lower troposphere.

Exploration of the Potential Energy Surfaces, Prediction of Atmospheric Concentrations, and Prediction of Vibrational Spectra for the HO2···(H2O)n (n = 1−2) Hydrogen Bonded Complexes

The hydroperoxy radical (HO2) plays a critical role in Earth's atmospheric chemistry as a component of many important reactions. The self-reaction of hydroperoxy radicals in the gas phase is strongly affected by the presence of water vapor. In this work, we explore the potential energy surfaces of hydroperoxy radicals hydrogen bonded to one or two water molecules, and predict atmospheric concentrations and vibrational spectra of these complexes. We predict that when the HO2 concentration is on the order of 108molecules·cm-3 at 298 K, that the number of HO2···H2O complexes is on the order of 107molecules·cm-3 and the number of HO2···(H2O)2 complexes is on the order of 106molecules·cm-3. Using the computed abundance of HO2···H2O, we predict that, at 298 K, the bimolecular rate constant for HO2···H2O + HO2 is about 10 times that for HO2 + HO2.

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 H2SO4(H2O)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 (HSO4–·H3O+)(H2O)n−1 clusters are competitive with the neutral (H2SO4)(H2O)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 H2SO4(H2O)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 H2SO4–H2O system must contain more than one H2SO4 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.

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 H2SO4(H2O)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 (HSO4–·H3O+)(H2O)n−1clusters are competitive with the neutral (H2SO4)(H2O)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 H2SO4(H2O)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 H2SO4–H2O system must contain more than one H2SO4 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.

Comparison of CBS-QB3, CBS-APNO, G2, and G3 thermochemical predictions with experiment for formation of ionic clusters of hydronium and hydroxide ions complexed with water

The GAUSSIAN 2, GAUSSIAN 3, complete basis set-QB3, and complete basis set-APNO methods have been used to calculate ΔH∘ and ΔG∘ values for ionic clusters of hydronium and hydroxide ions complexed with water. Results for the clusters H3O+(H2O)n andOH−(H2O)n, where n=1–4 are reported in this paper, and compared against experimental values contained in the National Institutes of Standards and Technology (NIST) database. Agreement with experiment is excellent for the three ab initio methods for formation of these clusters. The high accuracy of these methods makes them reliable for calculating energetics for the formation of ionic clusters containing water. In addition this allows them to serve as a valuable check on the accuracy of experimental data reported in the NIST database, and makes them useful tools for addressing unresolved issues in atmospheric chemistry.

Comparison of Model Chemistry and Density Functional Theory Thermochemical Predictions with Experiment for Formation of Ionic Clusters of the Ammonium Cation Complexed with Water and Ammonia; Atmospheric Implications

The G2, G3, CBS-QB3, and CBS-APNO model chemistry methods and the B3LYP, B3P86, mPW1PW, and PBE1PBE density functional theory (DFT) methods have been used to calculate ΔH° and ΔG° values for ionic clusters of the ammonium ion complexed with water and ammonia. Results for the clusters NH4+(NH3)n and NH4+(H2O)n, where n = 1−4, are reported in this paper and compared against experimental values. Agreement with the experimental values for ΔH° and ΔG° for formation of NH4+(NH3)n clusters is excellent. Comparison between experiment and theory for formation of the NH4+(H2O)n clusters is quite good considering the uncertainty in the experimental values. The four DFT methods yield excellent agreement with experiment and the model chemistry methods when the aug-cc-pVTZ basis set is used for energetic calculations and the 6-31G* basis set is used for geometries and frequencies. On the basis of these results, we predict that all ions in the lower troposphere will be saturated with at least one complete first hydration shell of water molecules.

Hydration of OCS with One to Four Water Molecules in Atmospheric and Laboratory Conditions

Carbonyl sulfide is the most abundant sulfur gas in the atmosphere. We have used MP2 and CCSD(T) theory to study the structures and thermochemistries of carbonyl sulfide interacting with one to four water molecules. We have completed an extensive search for clusters of OCS(H2O)n, where n = 1−4. We located three dimers, two trimers, five tetramers, and four pentamers with the MP2/aug-cc-pVDZ method. In each of the complexes with two or more waters, OCS preferentially interacts with low-energy water clusters. Our results match current theoretical and experimental literature, showing correlation with available geometries and frequencies for the OCS(H2O) species. The CCSD(T)/aug-cc-pVTZ thermochemical values combined with the average amount of OCS and the saturated concentration of H2O in the troposphere, lead to the prediction of 106 OCS(H2O) clusters·cm−3 and 102 OCS(H2O)2 clusters·cm−3 at 298 K. We predict the structures of OCS(H2O)n, n = 1−4 that should predominate in a low-temperature molecular beam and identify specific infrared vibrations that can be used to identify these different clusters.

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 HSO4–(H2O)n=1–6 and derived the thermodynamics of adding waters sequentially to the bisulfate ion and its hydrates. Comparing the HSO4–/H2O system to the neutral H2SO4/H2O cluster, water binds more strongly to the anion than it does to the neutral molecules. The difference in the binding thermodynamics of HSO4–/H2O and H2SO4/H2O systems decreases with increasing number of waters. The thermodynamics for the formation of HSO4–(H2O)n=1–5 is favorable at 298.15 K, and that of HSO4–(H2O)n=1–6 is favorable for T < 273.15 K. The HSO4– 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.

Atmospheric Implications for Formation of Clusters of Ammonium and 1−10 Water Molecules

A mixed molecular dynamics/quantum mechanics model has been applied to the ammonium/water clustering system. The use of the high level MP2 calculation method and correlated basis sets, such as aug-cc-pVDZ and aug-cc-pVTZ, lends confidence in the accuracy of the extrapolated energies. These calculations provide electronic and free energies for the formation of clusters of ammonium and 1−10 water molecules at two different temperatures. Structures and thermodynamic values are in good agreement with previous experimental and theoretical results. The estimated concentration of these clusters in the troposphere was calculated using atmospheric amounts of ammonium and water. Results show the favorability of forming these clusters and implications for ion-induced nucleation in the atmosphere.