Dirac equation with a Coulomb plus scalar potential in D + 1 dimensions

We generalize the Dirac equation to D + 1‐dimensional spacetime. The exact solutions of the D‐dimensional radial equations with a Coulomb plus scalar potential taking the form 1/r are analytically presented by studying the Tricomi equations. The energies E(n, l, D) are exactly presented. The dependences of the energies E(n, l, D) on the dimension D are analyzed in some detail. The energies E(n, 0, D) first decrease and then increase when increasing dimension D, but the energies E(n, l, D) (l ≠ 0) increase when increasing dimension D. The energies E(n, 0, D) are symmetric with respect to D = 1 for D ∈ (0, 2). It is shown that the energies E(n, l, D) (l ≠ 0) are almost independent of the quantum number l for large D and are completely independent of it if the Coulomb potential is equal to the scalar one. The energies E(n, l, D) almost overlap for large D. The dependences of the energies E(n, l, v) and E(n, l, s) on the vector potential parameter v and scalar potential one s are also studied for D = 3. All are found to decrease when these parameters are increased. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Anagostic Interactions under Pressure: Attractive or Repulsive?

Square‐planar d⁸‐ML₄ complexes might display subtle but noticeable local Lewis acidic sites in axial direction in the valence shell of the metal atom. These sites of local charge depletion provide the electronic prerequisites to establish weakly attractive 3c–2e M⋅⋅⋅H C agostic interactions, in contrast to earlier assumptions. Furthermore, we show that the use of the sign of the ¹H NMR shifts as major criterion to classify M⋅⋅⋅H C interactions as attractive (agostic) or repulsive (anagostic) can be dubious. We therefore suggest a new characterization method to probe the response of these M⋅⋅⋅H C interactions under pressure by combined high pressure IR and diffraction studies.     

Determination of cholesterol in milk fat by gas chromatography with direct injection and sample saponification

Summary A rapid and direct gas chromatographic (GC) method for determining free cholesterol in milk fat using a capillary column and programmed-temperature vaporizerinjector was assayed. It was compared with other procedures involving saponification of fat, solvent extraction of unsaponifiable matter—with and without fractionation by thin-layer chromatography—and transformation of sterols into silyl derivatives prior to GC analysis. This paper proposes an alternative to other published procedures. Repeatability of the method was assessed and the coefficient of variation determined as 2.1%. The alternative saponification method exhibited comparable accuracy (coefficient of variation=1.8%). Recovery ranged from 99.1% to 105.6%.     

Anagostic Interactions under Pressure: Attractive or Repulsive?

Square‐planar d⁸‐ML₄ complexes might display subtle but noticeable local Lewis acidic sites in axial direction in the valence shell of the metal atom. These sites of local charge depletion provide the electronic prerequisites to establish weakly attractive 3c–2e M???H? C agostic interactions, in contrast to earlier assumptions. Furthermore, we show that the use of the sign of the ¹H NMR shifts as major criterion to classify M???H? C interactions as attractive (agostic) or repulsive (anagostic) can be dubious. We therefore suggest a new characterization method to probe the response of these M???H? C interactions under pressure by combined high pressure IR and diffraction studies.     

X-ray Crystal Structure of Grandiflorenic Acid [(−)-kaura-9(11)-16-dien-19-oic Acid] Methyl Ester,a Compound Formerly Considered as an Oily Derivative

Abstract  Grandiflorenic acid [(−)-kaura-9(11)-16-dien-19-oic acid] methyl ester (2), C₂₁H₃₀O₂, was synthesized from grandiflorenic acid, isolated from the plant Montanoa tomentosa. Compound (2) was formerly described as an oily derivative. X-ray diffraction analysis of (2) demonstrated that it consists of four rings, three six-membered rings (I, II and III) and one five-membered ring (IV). I, II and III rings occur in chair, twist, and envelope conformations, respectively. Ring IV occurs in a conformation between envelope and half-chair. The crystal of grandiflorenic acid methyl ester is in monoclinic crystal system with space group P2₁, lattice constants: a = 7.2170(10), b = 11.4170(10), c = 11.2850(10) ?, β = 98.700(10)°, V = 919.1(2) ?³ and Z = 2. Index Abstract  Grandiflorenic acid [(−)-kaura-9(11)-16-dien-19-oic acid] methyl ester (2) was synthesized. This compound was formerly considered as an oily derivative. The crystal structure of (2) was obtained by determination of X-ray diffraction from suitable single crystals.      

J(Si,H) Coupling Constants in Nonclassical Transition‐Metal Silane Complexes

We will outline that the sign and magnitude of J(Si,H) coupling constants provide a highly sensitive tool to measure the extent of Si?H bond activation in nonclassical silane complexes. Up to now, this structure–property relationship was obscured by erroneous J(Si,H) sign determinations in the literature. These new findings also help to identify the salient control parameters of the Si?H bond activation process in nonclassical silane complexes.