Article Accurate Experimental Values for the Free Energies of Hydration of H+, OH-, and H3O+

Accurate experimental values for the free energies of hydration, or the free energies of solvation, of the H+, OH-, and H3O+ ions are of fundamental importance. By use of the most accurate value for the free energy of solvation of H+, the known value for the free energy of solvation of water, and the known values for the gas phase and aqueous phase deprotonation of water, the corresponding experimental free energy of solvation for OH- is −106.4 ± 0.5 kcal/mol. Similarly, by use of the known values for ΔGf 0 for H3O, H2O+, and OH-, the known values for ΔGs for H+ and OH-, and the known value for the aqueous phase autoionization of water, we obtain an experimental free energy of solvation value for H3O+ of −103.4 ± 0.5 kcal/mol. These values are in excellent agreement with the commonly accepted values and with the value for ΔGs(OH-) obtained from embedding clusters of OH-(H2O)n in a dielectric continuum.

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.

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.

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.

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 (H2SO4)2(H2O)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 HSO4−, the hydronium cation H3O+, 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 (H2SO4)2(H2O)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, (HSO4−)2(H3O+)2(H2O)2, becomes as favorable as the di-ionic cluster H2SO4(HSO4−)(H3O+)(H2O)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.

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.

Hydration of the Sulfuric Acid−Methylamine Complex and Implications for Aerosol Formation

The binary H2SO4−H2O nucleation is one of the most important pathways by which aerosols form in the atmosphere, and the presence of ternary species like amines increases aerosol formation rates. In this study, we focus on the hydration of a ternary system of sulfuric acid (H2SO4), methylamine (NH2CH3), and up to six waters to evaluate its implications for aerosol formation. By combining molecular dynamics (MD) sampling with high-level ab initio calculations, we determine the thermodynamics of forming H2SO4(NH2CH3)(H2O)n, where n = 0−6. Because it is a strong acid−base system, H2SO4−NH2CH3 quickly forms a tightly bound HSO4−−NH3CH3+ complex that condenses water more readily than H2SO4 alone. The electronic binding energy of H2SO4−NH2CH3 is −21.8 kcal mol−1 compared with −16.8 kcal mol−1 for H2SO4−NH3 and −12.8 kcal mol−1 for H2SO4−H2O. Adding one to two water molecules to the H2SO4−NH2CH3 complex is more favorable than adding to H2SO4 alone, yet there is no systematic difference for n ≥ 3. However, the average number of water molecules around H2SO4−NH2CH3 is consistently higher than that of H2SO4, and it is fairly independent of temperature and relative humidity.

Full Cups, Full Coffers: Tax Strategies and Consumer Culture in the Early Modern German Cities

During the sixteenth and seventeenth centuries, the excise taxes (Ungeld) paid by town residents on the consumption of beer, wine, mead and brandy represented the single most important source of civic revenue for many German cities. In a crisis, these taxes could spike to 70-80% of civic income. This paper examines civic budgets and 'behind-the-scenes' deliberations in a sample of towns in southern Germany in order to illuminate how decisions affecting consumer taxes were made. Even during the sobriety movements of the Reformation and post-Reformation period, tax income from drinkers remained attractive to city leaders because the bulk of the excise tax burden could easily be shifted away from privileged members of society and placed on the population at large. At the same time, governments had to maintain a careful balance between what they needed in order to govern and what the consumer market could bear, for high taxes on drinks were also targeted in many popular revolts. This led to nimble politicking by those responsible for tax decisions. Drink taxes were introduced, raised, lowered and otherwise manipulated based not only on shifting fashions and tastes but also on the degree of economic stress faced by the community. Where civic rulers were successful in striking the right balance, the rewards were considerable. The income from drink sales was a major factor in how the cities of the Empire survived the wars and other crises of the early modern period without going into so much debt that they lost their independence.

Hydration of the Sulfuric Acid-Methylamine Complex and Implications for Aerosol Formation

The binary H2SO4-H2O nucleation is one of the most important pathways by which aerosols form in the atmosphere, and the presence of ternary species like amines increases aerosol formation rates. In this study, we focus on the hydration of a ternary system of sulfuric acid (H2SO4), methylamine (NH2CH3), and up to six waters to evaluate its implications for aerosol formation. By combining molecular dynamics (MD) sampling with high-level ab initio calculations, we determine the thermodynamics of forming H2SO4(NH2CH3)(H2O)n, where n = 0-6. Because it is a strong acid-base system, H2SO4-NH2CH3 quickly forms a tightly bound HSO4(-)-NH3CH3(+) complex that condenses water more readily than H2SO4 alone. The electronic binding energy of H2SO4-NH2CH3 is -21.8 kcal mol(-1) compared with -16.8 kcal mol(-1) for H2SO4-NH3 and -12.8 kcal mol(-1) for H2SO4-H2O. Adding one to two water molecules to the H2SO4-NH2CH3 complex is more favorable than adding to H2SO4 alone, yet there is no systematic difference for n ≥ 3. However, the average number of water molecules around H2SO4-NH2CH3 is consistently higher than that of H2SO4, and it is fairly independent of temperature and relative humidity.

Full Cups, Full Coffers: Tax Strategies and Consumer Culture in the Early Modern German Cities

During the sixteenth and seventeenth centuries, the excise taxes (Ungeld) paid by town residents on the consumption of beer, wine, mead and brandy represented the single most important source of civic revenue for many German cities. In a crisis, these taxes could spike to 70–80% of civic income. This paper examines civic budgets and ‘behind-the-scenes’ deliberations in a sample of towns in southern Germany in order to illuminate how decisions affecting consumer taxes were made. Even during the sobriety movements of the Reformation and post-Reformation period, tax income from drinkers remained attractive to city leaders because the bulk of the excise tax burden could easily be shifted away from privileged members of society and placed on the population at large. At the same time, governments had to maintain a careful balance between what they needed in order to govern and what the consumer market could bear, for high taxes on drinks were also targeted in many popular revolts. This led to nimble politicking by those responsible for tax decisions. Drink taxes were introduced, raised, lowered and otherwise manipulated based not only on shifting fashions and tastes but also on the degree of economic stress faced by the community. Where civic rulers were successful in striking the right balance, the rewards were considerable. The income from drink sales was a major factor in how the cities of the Empire survived the wars and other crises of the early modern period without going into so much debt that they lost their independence.