The ground state energy of a Bose gas with Coulomb interaction

LetH _N be the 2N particle Hamiltonian $$\begin{array}{*{20}c} {H_N = \sum\limits_{i = 1}^{2N} {( - \Delta _\iota ) + \sum\limits_{i< j = 1}^N {\left| {x_i - x_j } \right|^{ - 1} + } \sum\limits_{i< j = 1}^N {\left| {x_{i + N} - x_{j + N} } \right|^{ - 1} } } } \\ { - \sum\limits_{i,j< j = 1}^N {\left| {x_i - x_{j + N} } \right|^{ - 1} ,} } \\ \end{array} $$ whereΔ _i is the Laplacian in the variablex _i ∈?³, 1≦i≦2N. The operatorH _N is assumed to act on wave functionsΨ(x ₁, ...,x _N ;x _N+1, ...,x _2N ) which are symmetric in the variables (x ₁, ...,x _N ) and (x _N+1, ...,x _2N ). SupposeΨ is supported in a setΛ ^2N , whereΛ is a cube in ?³. It is shown that if a normalized wave functionΨ can be written as a product of two wave functions $$\psi (x_1 ,...,x_N ;x_{N + 1} ,...,x_{2N} ) = \psi _1 (x_2 ,...,x_N )\psi _2 (x_{N + 1} ,...,x_{2N} ),$$ and the density of particles inΛ is constant, then 〈Ψ|H _N |Ψ〉≧?CN ^7/5 for some universal constantC.     

Synthesis of the methanesulfonates of α-(4-chlorophenyl)-α-[1-(2-chlorophenyl)emenyl]-1H-1,2,4-triazole-1-ethanol and α-[1-(2-chlorophenyl)ethenyl]-α-(2,4-difluorophenyl)-1H-1,2,4-triazole-1-ethanol,alpha styryl carbinol antifungal agents

The methanesulfonates of (α-(4-chlorophenyl)-α-[1-(2-chlorophenyl)ethenyl]-1H-1,2,4-triazole-1-ethanol and α-[1-(2-chlorophenyl)ethenyl]-α-(2,4-difluorophenyl)-1H-1,2,4-triazole-1-ethanol ( 1a, b ) are orally effective α-styryl carbinol derivatives developed for the treatment and prevention of systemic fungal infections. Practical new processes amenable for the large-scale production of these compounds are described. Of note is the selection of dichlorostyrene as a convenient precursor of the styryl portion, modification of a sensitive Grignard addition into a realistic preparative reaction and the use of 1,2,4-triazole simultaneously as a base transfer agent and nucleophile.     

Second-order Green's function calculations of the ionization potential of a (H2)7 chain embedded in a homogeneous electric field

Summary The vertical ionization potential and the related pole strength of a model alternant chain of 14 hydrogen atoms subject to a homogeneous electric field, parallel to the chain and of increasing intensity are calculated, in the framework of a 6–31G** basis set, at the second-order level of the many-body Green's function theory. Trends observed with orbital relaxation, pair removal and pair relaxation effects are interpreted in terms of deformations of the electron density.     

Efficient unimolecular deprotonation of aniline radical cations

[reaction: see text] Deprotonation of the radical cations of aromatic amines, such as anilines, generally occurs much more slowly than other fragmentation reactions. Here we report a stereoelectronic effect involving twisting of the anilino group out of the plane of the benzene ring that results in a significantly increased rate of reactivity toward deprotonation. Quantitative studies of the rate constants for deprotonation as a function of aniline radical cation pKa (Br?nsted plots) demonstrate that the effect is not simply due to a change in the reaction thermodynamics. By combining this stereoelectronic effect with covalent attachment of carboxylate as a base, aniline radical cations that undergo unimolecular deprotonation with rate constants as high as 10(8) s(-1), even in unfavorable protic media, are described.     

Dinitrogen reduction by TmII,DyII, and NdII with simple amide and aryloxide ligands

Dinitrogen can be reduced to the planar M2(mu-eta2:eta2-N2) structure without employing cyclopentadienyl or complicated polydentate ligands using the recently discovered divalent oxidation states of Tm(II), Dy(II), and Nd(II). Complexes of these ions with common monodentate amide and aryloxide ligands can effect N2 reduction. THF solutions of LnI2 (Ln = Tm, Dy) in the presence of 2 equiv of NaN(SiMe3)2 reduce dinitrogen to form {[(Me3Si)2N]2(THF)Ln}2(mu-eta2:eta2-N2) complexes that have planar Ln2N2 units and 1.264(7) and 1.305(6) A NN bonds consistent with (N2)2- moieties. With the stronger reductant Nd(II), aryloxides are sufficient ancillary ligands: the NdI2/2KOC6H3tBu2-2,6 (KOAr) system forms [(ArO)2(THF)2Nd]2(mu-eta2:eta2-N2), which has a 1.242(7) A NN bond.     

A study of method robustness for arsenic speciation in drinking water samples by anion exchange HPLC-ICP-MS

Regulating arsenic species in drinking waters is a reasonable objective, since the various species have different toxicological impacts. However, developing robust and sensitive speciation methods is mandatory prior to any such regulations. Numerous arsenic speciation publications exist, but the question of robustness or ruggedness for a regulatory method has not been fully explored. The present work illustrates the use of anion exchange chromatography coupled to ICP-MS with a commercially available "speciation kit" option. The mobile phase containing 2 mM NaH(2)PO(4) and 0.2 mM EDTA at pH 6 allowed adequate separation of four As species (As(III), As(V), MMAA, DMAA) in less than 10 min. The analytical performance characteristics studied, including method detection limits (lower than 100 ng L(-1) for all the species evaluated), proved the suitability of the method to fulfill the current regulation. Other parameters evaluated such as laboratory fortified blanks, spiked recoveries, and reproducibility over a certain period of time produced adequate results. The samples analyzed were taken from water utilities in different areas of the United States and were provided by the U.S. EPA. The data suggests the speciation setup performs to U.S. EPA specifications but sample treatment and chemistry are also important factors for achieving good recoveries for samples spiked with As(III) as arsenite and As(V) as arsenate.     

Synthesis of fluorinated 1,8-naphthyridinone derivatives

Processes for the synthesis of fluorinated 1,8-naphthyridinone derivatives including 6,7-difluoro-1,8-naphthyridin-2-one are described.     

Optical electron transfer processes. The dependence of intervalence line shape and transition energy on chromophore concentration

Optical electron transfer in the mixed-valence cation of biferrocenylacetylene (BF⁺) has been examined in CD₂Cl₂ solvent. The intervalence absorption line shape is relatively narrow at both low and high chromophore concentrations, but broader at intermediate concentrations. The transition energy for metal-to-metal charge transfer increases from ≈4440 cm⁻¹ at infinite dilution to 5995 cm⁻¹ for 3.8 mM BF⁺. Related effects exist due to added electrolyte. Neither the electrolyte nor chromophore concentration effects are expected from a simple reading of electron transfer theories. Nevertheless, both phenomena can be understood and within the context of theory upon careful consideration of the effects of ion-pairing (and tripling) equilibria upon electron-transfer energetics.     

cis-Enhanced cyclopropanation catalysts: reaction chemistry of three isomers of Rh2[N(C6H5)COCH3]4

The catalytic activities of three structural isomers of Rh₂[N(C₆H₅)COCH₃]₄ in cyclopropanation reactions were surveyed. These studies showed cis cyclopropanation selectivity with bulky alkenes for 2,2-cis- and 2,2-trans-Rh₂[N(C₆H₅)COCH₃]₄.