Fractional occupation numbers and spin density functional calculations of degenerate systems

We implemented ab initio self‐consistent field (SCF) fractional occupation numbers (FON) calculation with Dunlap's interpolation scheme for the twisted ethylene, which is a prototype molecule of a σ–π biradical system. The calculational results are compared with those of complete‐active‐space (CAS) SCF and spin‐unrestricted Kohn–Sham (UKS) calculations on potential surfaces, occupation numbers of natural orbitals, and correlation entropies. It was found that the UKS methods gave similar results to CASSCF, while the FON solutions appeared in only the nearly complete degenerate region. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 93: 317–323, 2003     

Infinitesimal obstructions to weakly mixing

Let ^t be the flow (parametrized with respect to arc length) of a smooth unit vector field v on a closed Riemannian manifold M ⁿ , whose orbits are geodesics. Then the (n-1)-plane field normal to v, v, is invariant under d ^t and, for each x M, we define a smooth real function _x (t) : (1 + _i (t)), where the _i(t) are the eigenvalues of AA ^T, A being the matrix (with respect to orthonormal bases) of the non-singular linear map d^2t , restricted to v at the point _x ^-t M ⁿ.Among other things, we prove the Theorem (Theorem II, below). Assume v is also volume preserving and that _x ^' (t) 0 for all x M and real t; then, if _x ^t : M M is weakly missng for some t, it is necessary that vx 0 at all x M.     

From Weakly Coordinating to Non‐Coordinating Anions? A Simple Preparation of the Silver Salt of the Least Coordinating Anion and Its Application To Determine the Ground State Structure of the Ag(η2‐P4)2+ Cation

The unexpected but facile preparation of the silver salt of the least coordinating [(RO)₃Al‐F‐Al(OR)₃]^? anion (R=C(CF₃)₃) by reaction of Ag[Al(OR)₄] with one equivalent of PCl₃ is described. The mechanism of the formation of Ag[(RO)₃Al‐F‐Al(OR)₃] is explained based on the available experimental data as well as on quantum chemical calculations with the inclusion of entropy and COSMO solvation enthalpies. The crystal structures of (RO)₃Al←OC₄H₈, Cs⁺[(RO)₂(Me)Al‐F‐Al(Me)(OR)₂]^?, Ag(CH₂Cl₂)₃⁺[(RO)₃Al‐F‐Al(OR)₃]^? and Ag(η²‐P₄)₂⁺[(RO)₃Al‐F‐Al(OR)₃]^? are described. From the collected data it will be shown that the [(RO)₃Al‐F‐Al(OR)₃]^? anion is the least coordinating anion currently known. With respect to the fluoride ion affinity of two parent Lewis acids Al(OR)₃ of 685 kJ mol^?1, the ligand affinity (441 kJ mol^?1), the proton and copper decomposition reactions (?983 and ?297 kJ mol^?1) as well as HOMO level and HOMO–LUMO gap and in comparison with [Sb₄F₂₁]^?, [Sb(OTeF₅)₆]^?, [Al(OR)₄]^? as well as [B(R^F)₄]^? (R^F=CF₃ or C₆F₅) the [(RO)₃Al‐F‐Al(OR)₃]^? anion is among the best weakly coordinating anions (WCAs) according to each value. In contrast to most of the other cited anions, the [(RO)₃Al‐F‐Al(OR)₃] anion is available by a simple preparation in conventional inorganic laboratories. The least coordinating character of this anion was employed to clarify the question of the ground state geometry of the Ag(η²‐P₄)₂⁺ cation (D_2h, D₂ or D_2d?). In agreement with computational data and NMR spectra it could be shown that the rotation along the Ag‐(P‐P‐centroid) vector has no barrier and that the structure adopted in the solid state depends on packing effects which lead to an almost D_2h symmetric Ag(η²‐P₄)₂⁺ cation (0 to 10.6° torsion) for the more symmetrical [Al(OR)₄]^? anion, but to a D₂ symmetric Ag(η²‐P₄)₂⁺ cation with a 44° twist angle of the two AgP₂ planes for the less symmetrical [(RO)₃Al‐F‐Al(OR)₃]^? anion. This implies that silver back bonding, suggested by quantum chemical population analyses to be of importance, is only weak.     

Phosphoryl‐Rich Flame‐Retardant Ions (FRIONs): Towards Safer Lithium‐Ion Batteries

The functionalized catecholate, tetraethyl (2,3‐dihydroxy‐1,4‐phenylene)bis(phosphonate) (H₂‐DPC), has been used to prepare a series of lithium salts Li[B(DPC)(oxalato)], Li[B(DPC)₂], Li[B(DPC)F₂], and Li[P(DPC)₃]. The phosphoryl‐rich character of these anions was designed to impart flame‐retardant properties for their use as potential flame‐retardant ions (FRIONs), additives, or replacements for other lithium salts for safer lithium‐ion batteries. The new materials were fully characterized, and the single‐crystal structures of Li[B(DPC)(oxalato)] and Li[P(DPC)₃] have been determined. Thermogravimetric analysis of the four lithium salts show that they are thermally stable up to around 200 °C. Pyrolysis combustion flow calorimetry reveals that these salts produce high char yields upon combustion.     

One-dimensional ventsel-freidlin theory and its analogue for singular perturbations of degenerate diffusions

We make some remarks about deriving the large deviations estimates for the Ventsel-Freidlin perturbed system and adapt these methods to derive similar results for singular perturbations of degenerate one-dimensional diffusions where β and ω are independent Brownian motions. This corresponds to a singular perturbation of the degenerate second-order operator     

From Ion‐Like Ethylzinc Aluminates to [EtZn(arene)2]+[Al(ORF)4]− Salts

Attempts to prepare previously unknown simple and very Lewis acidic [RZn]⁺[Al(OR^F)₄]^? salts from ZnR₂, AlR₃, and HO?R^F delivered the ion‐like RZn(Al(OR^F)₄) (R=Me, Et; R^F=C(CF₃)₃) with a coordinated counterion, but never the ionic compound. Increasing the steric bulk in RZn⁺ to R=CH₂CMe₃, CH₂SiMe₃, or Cp*, thus attempting to induce ionization, failed and led only to reaction mixtures including anion decomposition. However, ionization of the ion‐like EtZn(Al(OR^F)₄) compound with arenes yielded the [EtZn(arene)₂]⁺[Al(OR^F)₄]^? salts with arene=toluene, mesitylene, or o‐difluorobenzene (o‐DFB)/toluene. In contrast to the ion‐like EtZn(η³‐C₆H₆)(CHB₁₁Cl₁₁), which co‐crystallizes with one benzene molecule, the less coordinating nature of the [Al(OR^F)₄]^? anion allowed the ionization and preparation of the purely organometallic [EtZn(arene)₂]⁺ cation. These stable materials have further applications as, for example, initiators of isobutene polymerization. DFT calculations to compare the Lewis acidities of the zinc cations to those of a large number of organometallic cations were performed on the basis of fluoride ion affinity. The complexation energetics of EtZn⁺ with arenes and THF was assessed and related to the experiments.     

Dynamic analysis on generalized linear elastic body subjected to large scale rigid rotations

The dynamic analysis of a generalized linear elastic body undergoing large rigid rotations is investigated. The generalized linear elastic body is described in kine-matics through translational and rot...     

A comparative study of truly incompressible and weakly compressible SPH methods for free surface incompressible flows

In this paper, the performance of the incompressible SPH (ISPH) method and an improved weakly compressible SPH (IWCSPH) method for free surface incompressible flows are compared and analyzed. In both methods, the Navier–Stokes equations are solved, and no artificial viscosity is used. The ISPH algorithm in this paper is based on the classical SPH projection method with common treatments on solid boundaries and free surfaces. The IWCSPH model includes some advanced corrective algorithms in density approximation and solid boundary treatment (SBT). In density approximation, the moving least squares (MLS) approach is applied to re‐initialize density every several steps to obtain smoother and more stable pressure fields. An improved coupled dynamic SBT algorithm is implemented to obtain stable pressure values near solid wall areas and, thus, to minimize possible numerical oscillations brought in by the solid boundaries. Three representative numerical examples, including a benchmark test for hydrostatic pressure, a dam breaking problem and a liquid sloshing problem, are comparatively analyzed with ISPH and IWCSPH. It is demonstrated that the present IWCSPH is more attractive than ISPH in modeling free surface incompressible flows as it is more accurate and more stable with comparable or even less computational efforts. Copyright © 2013 John Wiley & Sons, Ltd.     

Generalized matching theorems for closed coverings of convex sets

In this paper we use fixed point and coincidence theorems due to Park [8] to give matching theorems concerning closed coverings of nonempty convex sets in a real topological vector space. Our new results extend previously given ones due to Ky Fan [2], [3], Shih [10], Shih and Tan [11], and Park [7].