N identical particles under quantum confinement: a many-body dimensional perturbation theory approach

Systems that involve N identical interacting particles under quantum confinement appear throughout many areas of physics, including chemical, condensed matter, and atomic physics. In this paper, we present the methods of dimensional perturbation theory, a powerful set of tools that uses symmetry to yield simple results for studying such many-body systems. We present a detailed discussion of the dimensional continuation of the N-particle Schrödinger equation, the spatial dimension D→∞ equilibrium (D⁰) structure, and the normal-mode (D⁻¹) structure. We use the FG matrix method to derive general, analytical expressions for the many-body normal-mode vibrational frequencies, and we give specific analytical results for three confined N-body quantum systems: the N-electron atom, N-electron quantum dot, and N-atom inhomogeneous Bose-Einstein condensate with a repulsive hard-core potential.     

Schrödinger Equation Solutions for the Central Field Power Potential Energy I. V(r) = V 0(r/a 0)2ν−2, ν ≥ 1

The solution of a generalized non-relativistic Schrödinger equation with radial potential energy V(r)=V ₀(r/a ₀)^2–2 is presented. After reviewing the general properties of the radial ordinary differential equation, power series solutions are developed. The Green's function is constructed, its trace and the trace of its first iteration are calculated, and the ability of the traces to provide upper and lower bounds for the ground eigenvalue is examined. In addition, WKB-like solutions for the eigenvalues and eigenfunctions are derived. The approximation method yields valid eigenvalues for large quantum numbers (Rydberg states).     

The structural and spectroscopic characterisation of three actinyl complexes with coordinated and uncoordinated perrhenate: [UO2(ReO4)2(TPPO)3], [[(UO2)(TPPO)3]2(mu2-O2)][ReO4]2 and [NpO2(TPPO)4][ReO4

The first structural characterization of an actinide complex with coordinated perrhenate is reported, [UO2(ReO4)2(TPPO)3] (1). In this [UO2]2+ complex two [ReO4]- anions and three TPPO (triphenylphosphine oxide) P=O donor ligands are coordinated in the equatorial plane in a cisoid arrangement. This bonding arrangement, and apparent strain observed in the equatorially bonded ligands, is attributed to the solid state packing in adjacent molecules in which hydrophobic TPPO ligands form an effective "shell" around a hydrophilic core of two UO2(ReO4)2 moieties. Solid state vibrational spectroscopy (infrared and Raman), 31P CP MAS NMR and elemental analysis are also consistent with the formula of 1. Solution state vibrational spectroscopy and 31P NMR measurements in EtOH indicate the lability of the TPPO and [ReO4]- groups. The photolytic generation of peroxide in EtOH solutions of 1 leads to the formation of trace quantities of [[(UO2)(TPPO)3]2(mu2-O2)][ReO4]2, 2, in which the coordinated [ReO4]- groups of 1 have been displaced by bridging O2(2-), derived from atmospheric O2. Finally, attempts to synthesise a [NpO2]+ analogue of have resulted only in the formation of [NpO2(TPPO)4][ReO4], 3, in which [ReO4]- acts solely as a counter anion. From these results it can be concluded that [ReO4]- will bond to [UO2]2+, but will be readily displaced by a more strongly coordinating ligand (e.g. peroxide) and will not coordinate to an actinyl cation with a lower charge, [NpO2]+, under the same reaction conditions.     

Centurion — a revolutionary irradiator

The facility characteristics for irradiation of red meat and poultry differ significantly from those of medical disposables. This paper presents the results of the market requirement definition which resulted in an innovative conceptual design. The process and the “state of the art tools” used to bring this abstract idea into a proof of concept are presented.     

Stereochemistry and mechanism of the Brønsted acid catalyzed intramolecular hydrofunctionalization of an unactivated cyclic alkene

Through employment of deuterium-labeled substrates, the triflic acid catalyzed intramolecular exo addition of the X-H(D) (X=N, O) bond of a sulfonamide, alcohol, or carboxylic acid across the C=C bond of a pendant cyclohexene moiety was found to occur, in each case, with exclusive formation (≥90%) of the anti-addition product without loss or scrambling of deuterium as determined by (1)H and (2)H NMR spectroscopy and mass spectrometry analysis. Kinetic analysis of the triflic-acid-catalyzed intramolecular hydroamination of N-(2-cyclohex-2'-enyl-2,2-diphenylethyl)-p-toluenesulfonamide (1a) established the second-order rate law: rate=k(2)[HOTf][1a] and the activation parameters ΔH(++)=(9.7±0.5) kcal mol(-1) and ΔS(++)=(-35±5) cal K(-1) mol(-1). An inverse α-secondary kinetic isotope effect of k(D)/k(H) =(1.15±0.03) was observed upon deuteration of the C2' position of 1a, consistent with partial C-N bond formation in the highest energy transition state of catalytic hydroamination. The results of these studies were consistent with a mechanism for the intramolecular hydroamination of 1a involving concerted, intermolecular proton transfer from an N-protonated sulfonamide to the alkenyl C3' position of 1a coupled with intramolecular anti addition of the pendant sulfonamide nitrogen atom to the alkenyl C2' position.     

Microwave spectrum of silyl methyl ether

The microwave spectra of silyl methyl ether, SiH₃OCH₃, and its isotopic modifications, SiH₃OCD₃, SiD₃OCH₃, and SiD₃OCD₃, have been observed and assigned. Large splittings arising from the internal rotation of the methyl top and somewhat smaller splittings arising from the internal rotation of the silyl top are observed. The “effective barrier” to internal rotation of the methyl top is approximately 550 cal/mole. The effective barrier to internal rotation of the silyl top is approximately 1100 cal/mole. The internal rotation of the two tops is strongly coupled, but no values for the potential coupling constants have been obtained. The dipole moment has been determined to be 1.15 ± 0.02 D (|μ_a| = 0.647 ± 0.01 and |μ_b| = 0.95 ± 0.02 D) from measurements of the Stark effect.