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 Delta H degrees and Delta G degrees values for neutral clusters of water, (H(2)O)(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 x 10(14) molecules/cm(3), water trimer concentrations of 2.6 x 10(12) molecules/cm(3), tetramer concentrations of approximately 5.8 x 10(11) molecules/cm(3), and pentamer concentrations of approximately 3.5 x 10(10) molecules/cm(3) in saturated air at 298 K. These results have important implications for understanding the gas-phase chemistry of the lower troposphere.     

Bellman Systems with Mean Field Dependent Dynamics

The authors deal with nonlinear elliptic and parabolic systems that are the Bellman like systems associated to stochastic differential games with mean field dependent dynamics. The key novelty of the paper is that they allow heavily mean field dependent dynamics. This in particular leads to a system of PDE’s with critical growth, for which it is rare to have an existence and/or regularity result. In the paper, they introduce a structural assumptions that cover many cases in stochastic differential games with mean field dependent dynamics for which they are able to establish the existence of a weak solution. In addition, the authors present here a completely new method for obtaining the maximum/minimum principles for systems with critical growths, which is a starting point for further existence and also qualitative analysis.     

Critical properties of non-spherical molecule fluids from the virial expansion

Critical constants of pure fluids (as important reference data in constructing vapour-liquid phase diagrams and basic input of various estimation methods) were determined for systems of non-spherical Kihara molecules; values of the critical temperature, density, compression factor and pressure of fluids composed of prolate and oblate molecules were evaluated from the fourth-order virial expansion. The second and third virial coefficients of the Kihara molecules were determined by applying the recently proposed method in which the effect of molecular core geometry and functional dependence of a pair interaction on the surface-surface distance are factorized and the former contribution determined from a formula for the corresponding hard convex body virial coefficient. The virial expansion for non-spherical Kihara molecules is applied to determine the critical constants of n-alkanes (methane to octane) and cyclic hydrocarbons (cyclopentane, cyclohexane, benzene and naphthalene); a fair agreement with experimental data was found.     

Critical properties of non-spherical molecule fluids from virial expansion

For systems of Kihara molecules with circular cores, the values of the reduced critical constants were determined from the fourth-order virial expansion as functions of the core diameter/thickness ratio. From expressions for the reduced functions both for the oblate and prolate shapes, the values of critical constants of four cyclic hydrocarbons and four branched alkanes were evaluated and compared with the experimental data and values obtained from the perturbation theory.