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.

The ability of the Gaussian-2, Gaussian-3, Complete Basis Set–QB3, and Complete Basis Set–APNO model chemistries to model the geometries of small water clusters

The Gaussian-2, Gaussian-3, Complete Basis Set-QB3, and Complete Basis Set-APNO methods have been used to calculate geometries of neutral clusters of water, (H2O)n, where n = 2–6. The structures are in excellent agreement with those determined from experiment and those predicted from previous high-level calculations. These methods also provide excellent thermochemical predictions for water clusters, and thus can be used with confidence in evaluating the structures and thermochemistry of water clusters.

Generation and characterization of ionic and neutral dihydroxy boron B(OH)(2)(+/0) in the gas phase

The dicoordinated borinium ion, dihydroxyborinium, B(OH)(2)(+) is generated from methyl boronic acid CH3B(OH)(2) by dissociative electron ionization and its connectivity confirmed by collisional activation. Neutralization-reionization (NR) experiments on this ion indicate that the neutral B(OH)(2) radical is a viable species in the gas phase. Both vertical neutralization of B(OH)(2)(+) and reionization of B(OH)(2) in the NR experiment are, however, associated with particularly unfavorable Franck-Condon factors. The differences in adiabatic and vertical electron transfer behavior can be traced back to a particular pi stabilization of the cationic species compared to the sp(2)-type neutral radical. Thermochemical data on several neutral and cationic boron compounds are presented based on calculations performed at the G2 level of theory.

Gaussian anamorphosis in the analysis step of the EnKF: a joint state-variable/observation approach

The analysis step of the (ensemble) Kalman filter is optimal when (1) the distribution of the background is Gaussian, (2) state variables and observations are related via a linear operator, and (3) the observational error is of additive nature and has Gaussian distribution. When these conditions are largely violated, a pre-processing step known as Gaussian anamorphosis (GA) can be applied. The objective of this procedure is to obtain state variables and observations that better fulfil the Gaussianity conditions in some sense. In this work we analyse GA from a joint perspective, paying attention to the effects of transformations in the joint state variable/observation space. First, we study transformations for state variables and observations that are independent from each other. Then, we introduce a targeted joint transformation with the objective to obtain joint Gaussianity in the transformed space. We focus primarily in the univariate case, and briefly comment on the multivariate one. A key point of this paper is that, when (1)-(3) are violated, using the analysis step of the EnKF will not recover the exact posterior density in spite of any transformations one may perform. These transformations, however, provide approximations of different quality to the Bayesian solution of the problem. Using an example in which the Bayesian posterior can be analytically computed, we assess the quality of the analysis distributions generated after applying the EnKF analysis step in conjunction with different GA options. The value of the targeted joint transformation is particularly clear for the case when the prior is Gaussian, the marginal density for the observations is close to Gaussian, and the likelihood is a Gaussian mixture.

Gas-phase reactivity of protonated 2-oxazoline derivatives: mass spectrometry and computational studies

RATIONALE: Oxazolines have attracted the attention of researchers worldwide due to their versatility as carboxylic acid protecting groups, chiral auxiliaries, and ligands for asymmetric catalysis. Electrospray ionization tandem mass spectrometric (ESI-MS/MS) analysis of five 2-oxazoline derivatives has been conducted, in order to understand the influence of the side chain on the gas-phase dissociation of these protonated compounds under collision-induced dissociation (CID) conditions. METHODS: Mass spectrometric analyses were conducted in a quadrupole time-of-flight (Q-TOF) spectrometer fitted with electrospray ionization source. Protonation sites have been proposed on the basis of the gas-phase basicity, proton affinity, atomic charges, and a molecular electrostatic potential map obtained on the basis of the quantum chemistry calculations at the B3LYP/6-31 + G(d, p) and G2(MP2) levels. RESULTS: Analysis of the atomic charges, gas-phase basicity and proton affinities values indicates that the nitrogen atom is a possible proton acceptor site. On the basis of these results, two main fragmentation processes have been suggested: one taking place via neutral elimination of the oxazoline moiety (99 u) and another occurring by sequential elimination of neutral fragments with 72 u and 27 u. These processes should lead to formation of R+. CONCLUSIONS: The ESI-MS/MS experiments have shown that the side chain could affect the dissociation mechanism of protonated 2-oxazoline derivatives. For the compound that exhibits a hydroxyl at the lateral chain, water loss has been suggested to happen through an E2-type elimination, in an exothermic step. Copyright (C) 2012 John Wiley & Sons, Ltd.

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.

Symmetrical 2-D Hermite-Gaussian square launch for high bit rate transmission in multimode fiber links

A 2-D Hermite-Gaussian square launch is demonstrated to show improved systems capacity over multimode fiber links. It shows a bandwidth improvement over both center and offset launches and exhibits ±5 μm misalignment tolerance. © 2011 Optical Society of America.

Far-field intensity distribution and M-2 factor of hollow Gaussian beams

The far-field intensity distribution of hollow Gaussian beams was investigated based on scalar diffraction theory. An analytical expression of the M-2 factor of the beams was derived on the basis of the second-order moments. Moreover, numerical examples to illustrate our analytical results are given. (c) 2005 Optical Society of America.

Far-field intensity distribution, M-2 factor of beams generated by Gaussian mirror resonator

We investigated M-2 factor and far-field distribution of beams generated by Gaussian mirror resonator. And we found usable analytical expressions of the M2 factor and the far-field distribution intensity with respect to variation of diffraction parameters. Particular attention was paid to the parameters such as mirror spot size and reflectance of the Gaussian mirror. (c) 2006 Elsevier GrnbH. All rights reserved.

Symmetrical 2-D hermite-gaussian square launch for high bit rate transmission in multimode fiber links

A 2-D Hermite-Gaussian square launch is demonstrated to show improved systems capacity over multimode fiber links. It shows a bandwidth improvement over both center and offset launches and exhibits ±5 ìm misalignment tolerance. © OSA/OFC/NFOEC 2011.

Analysis of randomly time varying systems by gaussian closure technique

The Gaussian probability closure technique is applied to study the random response of multidegree of freedom stochastically time varying systems under non-Gaussian excitations. Under the assumption that the response, the coefficient and the excitation processes are jointly Gaussian, deterministic equations are derived for the first two response moments. It is further shown that this technique leads to the best Gaussian estimate in a minimum mean square error sense. An example problem is solved which demonstrates the capability of this technique for handling non-linearity, stochastic system parameters and amplitude limited responses in a unified manner. Numerical results obtained through the Gaussian closure technique compare well with the exact solutions.

Anisotropic Gaussian Schell-model beams: Passage through optical systems and associated invariants

Anisotropic Gaussian Schell-model (AGSM) fields and their transformation by first-order optical systems (FOS’s) forming Sp(4,R) are studied using the generalized pencils of rays. The fact that Sp(4,R), rather than the larger group SL(4,R), is the relevant group is emphasized. A convenient geometrical picture wherein AGSM fields and FOS’s are represented, respectively, by antisymmetric second-rank tensors and de Sitter transformations in a (3+2)-dimensional space is developed. These fields are shown to separate into two qualitatively different families of orbits and the invariants over each orbit, two in number, are worked out. We also develop another geometrical picture in a (2+1)-dimensional Minkowski space suitable for the description of the action of axially symmetric FOS’s on AGSM fields, and the invariants, now seven in number, are derived. Interesting limiting cases forming coherent and quasihomogeneous fields are analyzed.