Exact Analytical Solution of the Schrödinger Equation for an N-Identical Body-Force System

A mathematical method is presented for solving the Schr?dinger equation for a system of identical body forces. The N-body forces are more easily introduced and treated within the hyperspherical harmonics. The problem of the N-body potential has been used at the level of both classical and quantum mechanics. The hypercentral interacting potential is assumed to depend on the hyperradius x = (ξ₁² + ξ₂² + ⋯ + ξ_N−1²)^1/2 only, where ξ₁,ξ₂,…,ξ_N−1 are Jacobi relative coordinates which are functions of N-particle relative positions r₁₂,r₂₃,…,r_N1. The problem of the harmonic oscillator and the Coulomb-type potential has been widely studied in different contexts. Using the N-body potential V(x) = ax² + bx − (c/x) as an example, and assuming an ansatz for the eigenfunction, an exact analytical solution of the Schr?dinger equation for an N-body system in three dimensions is obtained. This method is also applicable to some other types of potentials for N-identical interacting particles.     

Microwave Assisted Deprotection of N,N-Dimethylhydrazones in Water Using Palladium Chloride–Tin Chloride as Catalyst

Summary.  N,N-Dimethylhydrazones of ketones and aldehydes undergo facile cleavage to the corresponding carbonyl compounds upon exposure to microwaves in water containing a catalytic amount of PdCl₂–SnCl₂ in high yields. Corresponding authors. E-mail: rahman@umz.ac.ir Received December 27, 2001. Accepted (revised) February 6, 2002     

Enantioselective conjugate addition to α,β-unsaturated esters and amides mediated by lithium perchlorate

An efficient method for the enantioselective 1,4-conjugate addition of amines to α,β-unsaturated esters containing an inexpensive chiral auxiliary, such as (S)-2-methyl-1-butanol and fenchyl alcohol, in solvent-free conditions mediated by solid lithium perchlorate is reported. Over 12 examples of the products are generated in excellent yields, accompanied by moderate enantioselectivity. The concentrated solution of LiClO₄ in a diethyl ether system works well for the enantioselective 1,4-addition of organolithium compounds to α,β-unsaturated amides without any side reactions.     

Use of the differential pulse cathodic adsorptive stripping voltammetric method for the simultaneous determination of trace amounts of cadmium and zinc

A selective and sensitive method for the determination of cadmium and zinc is presented. The method is based on the adsorptive accumulation of the complexes of Cd(II) and Zn(II) ions with 4-amiono-5-methyl-2.4-dihydro-3H-1,2,4-triazol-3-tion (MMTT) onto hanging mercury drop electrode (HMDE), followed by the reduction of the adsorbed species using a voltammetric scan using differential pulse modulation. The ligand concentration, pH, potential and time of accumulation, scan rate, and pulse height were optimized. Under the optimized conditions, a linear calibration curve was obtained for the concentration of Cd(II) and Zn(II) in the range of 5–450 and 5–850 ng/mL, respectively, with a detection limit of 1.7 ng/mL Cd(II) and 1.3 ng/mL Zn(II). The ability of the method was evaluated by analysis of cadmium and zinc in water and alloy samples The text was submitted by the authors in English.     

Microwave-Assisted Aminomethylation of Electron-Rich Compounds Under Solvent-Free Condition

Electron-rich aromatic compounds react with formaldehyde and a secondary amine under solvent-free condition, in the presence of acidic alumina in a commercial microwave oven or at room temperature to produce aminomethylated products in good to excellent yields.     

Kinetic Study of Radical Polymerization v. Determination of Reactivity Ratio in Copolymerization of Acrylonitrile and Itaconic Acid by 1H‐NMR

Many reports exist in the literature about the application of ¹H and ¹³C‐NMR techniques to analyze the copolymer structure and composition and also determination of reactivity ratios. In this work, on‐line ¹H‐NMR spectroscopy has been applied to identify reactivity ratios of itaconic acid and acrylonitrile in the solution phase (DMSO as the solvent) and in the presence of AIBN as the radical initiator. All the peaks corresponding to the existing protons were assigned quietly. Therefore, the kinetics of the copolymerization reaction was investigated by studying the variation of integral of two characteristic peaks regarding each monomer. The obtained data were used to find the reactivity ratios of acrylonitrile and itaconic acid by linear least‐squares methods such as Finemann‐Ross, inverted Finemann‐Ross, Mayo‐Lewis, Kelen‐Tudos, extended Kelen‐Tudos and Mao‐Huglin. In addition, a non‐linear least‐square method (Tidwell‐ Mortimer) was used at low conversions. Extended Kelen‐ Tudos and Mao‐Huglin were applied to determine reactivity ratio values at high conversions as well.     

Bulk polymer nanoparticles containing a tetrakis(3-hydroxyphenyl)porphyrin for fast and highly selective separation of mercury ions

We report on the synthesis of polymeric nanoparticles (PNPs) containing a tetrakis(3-hydroxyphenyl)porphyrin, and their use for the separation of mercury(II) ion. The PNPs were prepared by bulk polymerization from methacrylic acid (the monomer), ethyleneglycol dimethacrylate (the cross-linker), 2,2′-azobisisobutyronitrile (the radical initiator) and the mercury(II) complex of 5,10,15,20-tetrakis(3-hydroxyphenyl)-porphyrin. The Hg(II) ion was then removed by treatment with dilute hydrochloric acid. The PNPs were characterized by colorimetry, FT-IR spectroscopy, and scanning electron microscopy. The material is capable of binding Hg(II) from analyte samples. Bound Hg(II) ions can be eluted with dilute nitric acid and then quantified by cold vapor AAS. The extraction efficiency, the effects of pH, preconcentration and leaching times, sample volume, and of the nature, concentration and volume of eluent were investigated. The maximum adsorption capacity of the PNPs is 249 mg g^?1, the relative standard deviation of the AAS assay is 2.2 %, and the limit of detection (3σ) is 8 ng.L^?1. The nanoparticles exhibit excellent selectivity for Hg(II) ion over other metal ions and were successfully applied to the selective extraction and determination of Hg(II) ion in spiked water samples.