A Lieb-Thirring Bound for a Magnetic Pauli Hamiltonian

A Lieb-Thirring-Sobolev type inequality for Pauli Hamiltonians with magnetic fields is derived. The bound is in terms of an effective field, whose energy is comparable to that of the magnetic field itself. An application to the stability of matter in magnetic fields is given. Received: 19 September 1996 / Accepted: 3 January 1997     

Fiber Optical Bragg Grating Refractometer

We have demonstrated an evanescent field refractive indexfiber sensor comprising a 42-mm Bragg grating in an etched fiber together with a tunable Distributed Bragg Reflector (DBR) laser. Characterization of different aqueous sucrose solutions resulted in a resolution of roughly 10 mM sucrose. The sensor in the presented form has a theoretical sensitivity of higher than 10 5 refractive index unit (riu) in a refractive index region close to the cladding index of the fiber. However, the technique allows for an even higher sensitivity than 10 6 riu with a proper signal processing scheme.     

Preservation of logarithmic concavity by the Mellin transform and applications to the Schrödinger equation for certain classes of potentials

We prove that the Mellin transform of a function log-concave (convex) is, after division by (+1), where is the argument of the transform, itself log-concave (convex) in . This theorem is first applied to the moments of the ground state wave function of the Schrödinger equation where the Laplacian of the central potential has a given sign, and generalized to other situations. This is used to derive inequalities linking thel ^th derivative of the ground state wave function at the origin for angular momentuml and the expectation value of the kinetic energy, and applied to quarkonium physics. A generalization to higher radial excitations is shown to be plausible by using the WKB approximation. Finally, new bounds on ground-state energies in power potentials are obtained.     

High-frequency (140-GHz) time domain EPR and ENDOR spectroscopy: the tyrosyl radical-diiron cofactor in ribonucleotide reductase from yeast

High-frequency pulsed EPR and ENDOR have been employed to characterize the tyrosyl radical (Y*)-diiron cofactor in the Y2-containing R2 subunit of ribonucleotide reductase (RNR) from yeast. The present work represents the first use of 140-GHz time domain EPR and ENDOR to examine this system and demonstrates the capabilities of the method to elucidate the electronic structure and the chemical environment of protein radicals. Low-temperature spin-echo-detected EPR spectra of yeast Y* reveal an EPR line shape typical of a tyrosyl radical; however, when compared with the EPR spectra of Y* from E. coli RNR, a substantial upfield shift of the g(1)-value is observed. The origin of the shift in g(1) was investigated by 140-GHz (1)H and (2)H pulsed ENDOR experiments of the Y2-containing subunit in protonated and D(2)O-exchanged buffer. (2)H ENDOR spectra and simulations provide unambiguous evidence for one strongly coupled (2)H arising from a bond between the radical and an exchangeable proton of an adjacent residue or a water molecule. Orientation-selective 140-GHz ENDOR spectra indicate the direction of the hydrogen bond with respect to the molecular symmetry axes and the bond length (1.81 A). Finally, we have performed saturation recovery experiments and observed enhanced spin lattice relaxation rates of the Y* above 10 K. At temperatures higher than 20 K, the relaxation rates are isotropic across the EPR line, a phenomenon that we attribute to isotropic exchange interaction between Y* and the first excited paramagnetic state of the diiron cluster adjacent to it. From the activation energy of the rates, we determine the exchange interaction between the two irons of the cluster, J(exc) = -85 cm(-)(1). The relaxation mechanism and the presence of the hydrogen bond are discussed in terms of the differences in the structure of the Y*-diiron cofactor in yeast Y2 and other class I R2s.     

Dipole transition matrix elements for certain classes of potential models

We prove results about vanishing and nonvanishing of radial dipole matrix elements for certain classes of spherically symmetric potentials. A basic tool is a new sum rule based on Ehrenfest's law and the superposition principle for solutions of the Schrödinger equation.     

Enantioselective organic syntheses using chiral transition metal complexes V. (2S,3S)-Bis(dibenzophospholyl)butane, a rigid (S,S)-CHIRAPHOS analog

The P–Ph cleavage of phenyldibenzophosphole (1) with lithium in THF gives lithium dibenzophospholide (2). Reaction of 2 with ethyleneglycol ditosylate produces the known chelate ligand 1,2-bis(dibenzophospholyl)ethane (3) in good yield. Similarly, 2 and (2R,3R)-butanediol ditosylate give the new chiral chelate ligand (2S,3S)-bis(dibenzophospholyl)butane (4). Ligand exchange of [CpRu(PPh₃)₂Cl] with 3 or 4 yields the halfsandwich complexes [CpRu(C₁₂H₈PC₂H₄PC₁₂H₈)Cl] (5) and [CpRu((S,S)-C₁₂H₈PCHMeCHMePC₁₂H₈)Cl] (6). Complex 6 was characterized crystallographically (monoclinic, space group P2₁ (no. 4), a=820.6(4), b=1501.0(3), c=1172.8(6) pm, β=108.87(2)°, V=1.367(1)×10⁹ pm³, Z=2). The most conspicuous feature of the structure of 6 is the perfect coplanarity of the two dibenzophosphole moieties imposed by their steric interaction with the Cp ligand. Complex 6 and the thiophene complex [CpRu((S,S)-C₁₂H₈PCHMeCHMePC₁₂H₈)(SC₄H₄)]BF₄ (7) derived therefrom are remarkably unreactive with regard to ligand substitutions. A possible explanation is the lack of intramolecular

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–C stabilization en route to the transition state of ligand substitution. The enantiomeric purity of 6 and 7 could nevertheless be demonstrated by conversion to diastereomerically pure [CpRu((S,S)-C₁₂H₈PCHMeCHMePC₁₂H₈)((S)-CNCHMePh)]BF₄ (8).