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.     

Using molecular dynamics simulations to identify the key factors responsible for chiral recognition by an amino acid-based molecular micelle

Molecular dynamics (MD) simulations were used to investigate the binding of six chiral compounds to the amino acid-based molecular micelle (MM) poly-(sodium undecyl-(L)-leucine-leucine) or poly(SULL). The MM investigated is used as a chiral selector in capillary electrophoresis. The project goal was to characterize the chiral recognition mechanism in these separations and to move toward predictive models to identify the best amino acid-based MM for a given separation. Poly(SULL) was found to contain six binding sites into which chiral compounds could insert. Four sites had similar sizes, shapes, and electrostatic properties. Enantiomers of alprenolol, propranolol, 1,1′-bi-2-naphthyl-2,2′-diyl hydrogen phosphate, 1,1′-bi-2-naphthol, chlorthalidone, or lorazepam were separately docked into each binding pocket and MD simulations with the resulting intermolecular complexes were performed. Solvent-accessible surface area calculations showed the compounds preferentially associated with binding sites where they penetrated into the MM core and shielded their non-polar atoms from solvent. Furthermore, with five of the six compounds the enantiomer with the most favorable free energy of MM association also experienced the most favorable intermolecular hydrogen bonding interactions with the MM. This result suggests that stereoselective intermolecular hydrogen bonds play an important role in chiral discrimination in separations using amino acid-based MMs.GRAPHICAL ABSTRACT     

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.     

Third order harmonics generation in multilayer nanoshells

Third order harmonics generation has been investigated for multilayer nanoshell structure. Numerical calculations show that the nonlinear susceptibility of this structure depends on the parameters such as size and kind of structure, relaxation time and pump photon energy. The intensity and position of third order nonlinear susceptibility peaks depend on shell thicknesses; smaller thicknesses have peak susceptibility at shorter wavelength.     

ZEOLITE-SUPPORTED CHROMIUM(VI) OXIDE: A MILD,EFFICIENT, AND INEXPENSIVE REAGENT FOR OXIDATIVE DEPROTECTION OF TRIMETHYLSILYL ETHERS UNDER MICROWAVE IRRADIATION

Primary and secondary trimethylsilyl ethers are effeciently converted to the corresponding carbonyl compounds using HZSM-5 zeolite-supported CrO ₃ under microwave irradiation in solventless system.     

Functionalization of Multi Carbon Nanotubes with 1,2‐Naphthoquinone‐4‐sulfonic Acid Sodium: A Novel Sulphydryl Compounds Sensor Based on Functionalized Carbon Nanotube Film Using Michael Addition

The functionalized multi‐wall carbon nanotube with 1,2‐naphthoquinone‐4‐sulfonic acid sodium (Nq‐MWNT) was fabricated by a simple and low‐cost method. Techniques of scanning electron microscope (SEM) with energy dispersive X‐ray (EDX) analysis, fourier transform infrared spectroscopy (FT‐IR), ultraviolet visible spectroscopy (UV‐vis) and cyclic voltammetry (CV) were used to characterize the property of the Nq‐MWNT. The results showed that the MWNT with high functionalization of Nq can be obtained using this simple method. The Nq‐MWNT modified carbon paste electrode (Nq‐MWNT/CPE) was fabricated by drop‐casting technique. The resulted modified electrode was tested successfully to detection D‐penicillamine (D‐PA) and captopril (CAP) in an aqueous solution. It is found that D‐PA and CAP participate in Michael addition reaction with Nq on MWNT to form the corresponding thioquinone derivative. The reoxidation of adducts at a potential of less positive than D‐PA and CAP at the surface of the bare CPE leads to an increase in the oxidative current, which is proportional to the concentration of D‐PA and CAP. The catalytic response showed a wide linear range (3‐200 μM and 1‐130 μM for D‐PA and CAP, respectively) as well as its experimental limit of detection can be achieved 0.8 μM, and 0.4 μM for D‐PA and CAP, respectively. The modified electrode for D‐PA and CAP determination is of the property of simple preparation, good stability and high sensitivity. Furthermore, the fabricated electrode was used to determine the content of D‐PA and CAP in the tablet, suggesting the good accuracy of the method.