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.

Experimentation with different thermodynamic cycles used for pKa calculations on carboxylic acids using Complete Basis Set and Gaussian-n Models combined with CPCM Continuum Solvation Methods

Complete basis set and Gaussian-n methods were combined with Barone and Cossi's implementation of the polarizable conductor model (CPCM) continuum solvation methods to calculate pKa values for six carboxylic acids. Four different thermodynamic cycles were considered in this work. An experimental value of −264.61 kcal/mol for the free energy of solvation of H+, ΔGs(H+), was combined with a value for Ggas(H+) of −6.28 kcal/mol, to calculate pKa values with cycle 1. The complete basis set gas-phase methods used to calculate gas-phase free energies are very accurate, with mean unsigned errors of 0.3 kcal/mol and standard deviations of 0.4 kcal/mol. The CPCM solvation calculations used to calculate condensed-phase free energies are slightly less accurate than the gas-phase models, and the best method has a mean unsigned error and standard deviation of 0.4 and 0.5 kcal/mol, respectively. Thermodynamic cycles that include an explicit water in the cycle are not accurate when the free energy of solvation of a water molecule is used, but appear to become accurate when the experimental free energy of vaporization of water is used. This apparent improvement is an artifact of the standard state used in the calculation. Geometry relaxation in solution does not improve the results when using these later cycles. The use of cycle 1 and the complete basis set models combined with the CPCM solvation methods yielded pKa values accurate to less than half a pKa unit. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001

Accurate pKa Calculations for Carboxylic Acids Using Complete Basis Set and Gaussian-n Models Combined with CPCM Continuum Solvation Methods”

Complete Basis Set and Gaussian-n methods were combined with CPCM continuum solvation methods to calculate pKa values for six carboxylic acids. An experimental value of −264.61 kcal/mol for the free energy of solvation of H+, ΔGs(H+), was combined with a value for Ggas(H+) of −6.28 kcal/mol to calculate pKa values with Cycle 1. The Complete Basis Set gas-phase methods used to calculate gas-phase free energies are very accurate, with mean unsigned errors of 0.3 kcal/mol and standard deviations of 0.4 kcal/mol. The CPCM solvation calculations used to calculate condensed-phase free energies are slightly less accurate than the gas-phase models, and the best method has a mean unsigned error and standard deviation of 0.4 and 0.5 kcal/mol, respectively. The use of Cycle 1 and the Complete Basis Set models combined with the CPCM solvation methods yielded pKa values accurate to less than half a pKa unit.

Accurate relative pKa calculations for carboxylic acids using complete basis set and Gaussian-n models combined with continuum solvation methods

The complete basis set methods CBS-4, CBS-QB3, and CBS-APNO, and the Gaussian methods G2 and G3 were used to calculate the gas phase energy differences between six different carboxylic acids and their respective anions. Two different continuum methods, SM5.42R and CPCM, were used to calculate the free energy differences of solvation for the acids and their anions. Relative pKa values were calculated for each acid using one of the acids as a reference point. The CBS-QB3 and CBS-APNO gas phase calculations, combined with the CPCM/HF/6-31+G(d)//HF/6-31G(d) or CPCM/HF/6-31+G(d)//HF/6-31+G(d) continuum solvation calculations on the lowest energy gas phase conformer, and with the conformationally averaged values, give results accurate to ½ pKa unit. © 2001 American Institute of Physics.

Thermodynamics of the Hydroxyl Radical Addition to Isoprene

Oxidation of isoprene by the hydroxyl radical leads to tropospheric ozone formation. Consequently, a more complete understanding of this reaction could lead to better models of regional air quality, a better understanding of aerosol formation, and a better understanding of reaction kinetics and dynamics. The most common first step in the oxidation of isoprene is the formation of an adduct, with the hydroxyl radical adding to one of four unsaturated carbon atoms in isoprene. In this paper, we discuss how the initial conformations of isoprene, s-trans and s-gauche, influences the pathways to adduct formation. We explore the formation of pre-reactive complexes at low and high temperatures, which are often invoked to explain the negative temperature dependence of this reaction’s kinetics. We show that at higher temperatures the free energy surface indicates that a pre-reactive complex is unlikely, while at low temperatures the complex exists on two reaction pathways. The theoretical results show that at low temperatures all eight pathways possess negative reaction barriers, and reaction energies that range from −36.7 to −23.0 kcal·mol−1. At temperatures in the lower atmosphere, all eight pathways possess positive reaction barriers that range from 3.8 to 6.0 kcal·mol−1 and reaction energies that range from −28.8 to −14.4 kcal·mol−1.

Critical review of coupled flux formulations for clay membranes based on nonequilibrium thermodynamics

Extensive research conducted over the past several decades has indicated that semipermeable membrane behavior (i.e., the ability of a porous medium to restrict the passage of solutes) may have a significant influence on solute migration through a wide variety of clay-rich soils, including both natural clay formations (aquitards, aquicludes) and engineered clay barriers (e.g., landfill liners and vertical cutoff walls). Restricted solute migration through clay membranes generally has been described using coupled flux formulations based on nonequilibrium (irreversible) thermodynamics. However, these formulations have differed depending on the assumptions inherent in the theoretical development, resulting in some confusion regarding the applicability of the formulations. Accordingly, a critical review of coupled flux formulations for liquid, current, and solutes through a semipermeable clay membrane under isothermal conditions is undertaken with the goals of explicitly resolving differences among the formulations and illustrating the significance of the differences from theoretical and practical perspectives. Formulations based on single-solute systems (i.e., uncharged solute), single-salt systems, and general systems containing multiple cations or anions are presented. Also, expressions relating the phenomenological coefficients in the coupled flux equations to relevant soil properties (e.g., hydraulic conductivity and effective diffusion coefficient) are summarized for each system. A major difference in the formulations is shown to exist depending on whether counter diffusion or salt diffusion is assumed. This difference between counter and salt diffusion is shown to affect the interpretation of values for the effective diffusion coefficient in a clay membrane based on previously published experimental data. Solute transport theories based on both counter and salt diffusion then are used to re-evaluate previously published column test data for the same clay membrane. The results indicate that, despite the theoretical inconsistency between the counter-diffusion assumption and the salt-diffusion conditions of the experiments, the predictive ability of solute transport theory based on the assumption of counter diffusion is not significantly different from that based on the assumption of salt diffusion, provided that the input parameters used in each theory are derived under the same assumption inherent in the theory. Nonetheless, salt-diffusion theory is fundamentally correct and, therefore, is more appropriate for problems involving salt diffusion in clay membranes. Finally, the fact that solute diffusion cannot occur in an ideal or perfect membrane is not explicitly captured in any of the theoretical expressions for total solute flux in clay membranes, but rather is generally accounted for via inclusion of an effective porosity, n(e), or a restrictive tortuosity factor, tau(r), in the formulation of Fick's first law for diffusion. Both n(e) and tau(r) have been correlated as a linear function of membrane efficiency. This linear correlation is supported theoretically by pore-scale modeling of solid-liquid interactions, but experimental support is limited. Additional data are needed to bolster the validity of the linear correlation for clay membranes. Copyright 2012 Elsevier B.V. All rights reserved.

Critical Review of Coupled Flux Formulations for Clay Membranes Based on Nonequilibrium Thermodynamics

Extensive research conducted over the past several decades has indicated that semipermeable membrane behavior (i.e., the ability of a porous medium to restrict the passage of solutes) may have a significant influence on solute migration through a wide variety of clay-rich soils, including both natural clay formations (aquitards, aquicludes) and engineered clay barriers (e.g., landfill liners and vertical cutoff walls). Restricted solute migration through clay membranes generally has been described using coupled flux formulations based on nonequilibrium (irreversible) thermodynamics. However, these formulations have differed depending on the assumptions inherent in the theoretical development, resulting in some confusion regarding the applicability of the formulations. Accordingly, a critical review of coupled flux formulations for liquid, current, and solutes through a semipermeable clay membrane under isothermal conditions is undertaken with the goals of explicitly resolving differences among the formulations and illustrating the significance of the differences from theoretical and practical perspectives. Formulations based on single-solute systems (i.e., uncharged solute), single-salt systems, and general systems containing multiple cations or anions are presented. Also, expressions relating the phenomenological coefficients in the coupled flux equations to relevant soil properties (e.g., hydraulic conductivity and effective diffusion coefficient) are summarized for each system. A major difference in the formulations is shown to exist depending on whether counter diffusion or salt diffusion is assumed. This difference between counter and salt diffusion is shown to affect the interpretation of values for the effective diffusion coefficient in a clay membrane based on previously published experimental data. Solute transport theories based on both counter and salt diffusion then are used to re-evaluate previously published column test data for the same clay membrane. The results indicate that, despite the theoretical inconsistency between the counter-diffusion assumption and the salt-diffusion conditions of the experiments, the predictive ability of solute transport theory based on the assumption of counter diffusion is not significantly different from that based on the assumption of salt diffusion, provided that the input parameters used in each theory are derived under the same assumption inherent in the theory. Nonetheless, salt-diffusion theory is fundamentally correct and, therefore, is more appropriate for problems involving salt diffusion in clay membranes. Finally, the fact that solute diffusion cannot occur in an ideal or perfect membrane is not explicitly captured in any of the theoretical expressions for total solute flux in clay membranes, but rather is generally accounted for via inclusion of an effective porosity, ne, or a restrictive tortuosity factor, tr, in the formulation of Fick's first law for diffusion. Both ne and tr have been correlated as a linear function of membrane efficiency. This linear correlation is supported theoretically by pore-scale modeling of solid-liquid interactions, but experimental support is limited. Additional data are needed to bolster the validity of the linear correlation for clay membranes.

Structure and thermodynamics of H3O+(H2O)8 clusters: A combined molecular dynamics and quantum mechanics approach

We have studied the structure and stability of (H3O+)(H2O)8 clusters using a combination of molecular dynamics sampling and high-level ab initio calculations. 20 distinct oxygen frameworks are found within 2 kcal/mol of the electronic or standard Gibbs free energy minimum. The impact of quantum zero-point vibrational corrections on the relative stability of these isomers is quite significant. The box-like isomers are favored in terms of electronic energy, but with the inclusion of zero-point vibrational corrections and entropic effects tree-like isomers are favored at higher temperatures. Under conditions from 0 to 298.15 K, the global minimum is predicted to be a tree-like structure with one dangling singly coordinated water molecule. Above 298.15 K, higher entropy tree-like isomers with two or more singly coordinated water molecules are favored. These assignments are generally consistent with experimental IR spectra of (H3O+)(H2O)8 obtained at 150 K.

Effect of Participant Gender, Professor Gender, and Activity Interventions on the Understanding of Concepts in Thermodynamics

Misconceptions about heat and temperature have been seen across all educational levels, even in undergraduate engineering courses. One way these misconceptions can be remediated is through instructional methods, such as inquiry-based activities. Performance on assessments in sciences and engineering has been found to vary when gender is taken into consideration. The purpose of the current study was to investigate the effects of participant gender, professor gender, and level of inquiry-based activities on the conceptual understanding of 247 undergraduate engineering students in thermodynamics. A pre-test post-test design was used. Conceptual understanding of thermodynamics was measured by students’ scores on the Concept Inventory for Engineering Thermodynamics (CIET; Vigeant, Prince & Nottis, 2011). Inquiry-based activities were developed by the researchers and given to professors who determined if they would do all, some, or none of them as they taught. Significant differences were found among participants of different gender, different gender of the professor instructing the course, and level of inquiry-based activity. The participants who were exposed to all of the activities provided didsignificantly better on the post-test than those who were only exposed to some or none of the activities. The results from this current study indicated that differences in gender, professorgender, and level of inquiry-based activity has an effect on undergraduate engineering students’ conceptual understanding of thermodynamics. Future research should investigate more factorsthat contribute to lower representation of women in the engineering field.