Catalytically active mu-Oxodiiron(IV) oxidants from Iron(III) and dioxygen

The reaction between an Fe(III) complex and O(2) to afford a stable catalytically active diiron(IV)-mu-oxo compound is described. Phosphonium salts of orange five-coordinated Fe(III)-TAML complexes with an axial aqua ligand ([PPh(4)]1-H(2)O, tetraamidato macrocyclic Fe(III) species derived from 3,3,6,6,9,9-hexamethyl-3,4,8,9-tetrahydro-1H-1,4,8,11-benzotetraazacyclotridecine-2,5,7,10(6H,11H)-tetraone) react rapidly with O(2) in CH(2)Cl(2) or other weakly coordinating solvents to produce black mu-oxo-bridged diiron(IV) complexes, 2, in high yields. Complexes 2 have been characterized by X-ray crystallography (2 cases), microanalytical data, mass spectrometry, UV/Vis, Mossbauer, and (1)H NMR spectroscopies. Mossbauer data show that the diamagnetic Fe-O-Fe unit contains antiferromagnetically coupled S = 1 Fe(IV) sites; diamagnetic (1)H NMR spectra are observed. The oxidation of PPh(3) to OPPh(3) by 2 was confirmed by UV/Vis and GC-MS. Labeling experiments with (18)O(2) and H(2)(18)O established that the bridging oxygen atom of 2 derives from O(2). Complexes 2 catalyze the selective oxidation of benzylic alcohols into the corresponding aldehydes and bleach rapidly organic dyes, such as Orange II in MeCN-H(2)O mixtures; reactivity evidence suggests that free radical autoxidation is not involved. This work highlights a promising development for the advancement of green oxidation technology, as O(2) is an abundant, clean, and inexpensive oxidizing agent.     

Algebraic theory of difference equations and Mahler functions

Algebraic independence of certain Mahler functions constructed from Rudin–Schapiro sequences and Baum–Sweet sequences is proved, using difference Riccati equations and the notion of difference field extension of valuation ring type.     

Upper bounds to atomic electron densities in position and momentum spaces

Modified functions r ^–(r) and p ^–(p) of the spherically averaged electron densities (r) in position space and (p) in momentum space are found to be convex (i.e., the second derivatives are nonnegative everywhere) for all the 103 ground-state atoms from hydrogen (atomic number Z=1) to lawrencium (Z=103), if the parameters are chosen to be 0.6 and 1.4. The convex property of r ^–(r) and p ^–(p) is used to derive upper bounds to the density functions (r) and (p) in terms of their radial moments r ^s and p ^s or frequency moments ^t and ^t . In most cases, the present bounds are shown to be more general and more accurate than those reported in the literature.     

Linear integrability of wave functions

Finiteness is usually imposed as a condition for physical admissibility of a wave function. Examination of this condition in both position- and momentum-space shows that finiteness of the wave function at the origin in one space implies “linear” integrability in the reciprocal space, except in some pathological cases. Some implications of this result are discussed.     

Expansion coefficients and moments of electron momentum densities for singly charged ions

Numerical Hartree–Fock calculations of the first three coefficients of the MacLaurin expansion and the leading coefficient of the large-p asymptotic expansion of the electron momentum densities Π(p) are reported for 54 singly charged atomic cations from He⁺ (atomic number Z = 2) to Cs⁺ (Z = 55) and 43 anions from H⁻ (Z = 1) to I⁻ (Z = 53) in their experimental ground states. We also report all the finite moments <p ^k > (−2≤k≤+4) of the momentum densities Π(p) for the above-mentioned 97 ionic species. The results are compared with the previous ones for neutral atoms [Koga and Thakkar (1996) J Phys B 29: 2973], and the dependence of the expansion coefficients and moments on nuclear charge is discussed among isoelectronic species. Received: 20 November 1998 / Accepted: 15 January 1999 / Published online: 7 June 1999     

InGaAs/GaAs photorefractive multiple quantum well device in quantum confined Stark geometry

We have demonstrated photorefractive InGaAs/GaAs multiple-quantum-well devices in the quantum confined Stark geometry. A four-wave-mixing diffraction efficiency up to 0.3% is obtained at a wavelength of 949 nm. Proton implantation strongly reduces the maximum diffraction efficiency although it saturates the diffraction efficiency at smaller grating period comparing to as-grown device. We have also observed higher order diffractions. It is found that the space-charge field changes its pattern temporally from a sinusoidal pattern to a rectangular one with decreasing its modulation depth. Received: 7 December 2000 / Published online: 27 April 2001     

Double- and triple-zeta Slater-type basis sets with common exponents

Double- and triple-zeta basis sets of Slater-type functions (STFs) are developed for the 17 atoms from He to Ar. For computational economy, the exponents of STFs corresponding to the same atomic subshell are restricted to be common. Instead, the principal quantum numbers of the STFs are thoroughly optimized within the framework of integer values to reduce the energy loss due to the common exponent restriction. Received: 10 November 1999 / Accepted: 25 January 2000 / Published online: 19 April 2000     

Fracture of piezoelectric materials: energy density criterion

In this paper, the concept of energy density factor S for piezoelectric materials is presented. In addition to the mechanical energy the electrical energy is included as well. The direction of crack initiation is assumed to occur when S_min reaches a critical value S_cr that can be used as an intrinsic materials parameter and is independent of the crack geometry and loading. The result agrees with empirical evidence qualitatively and explains rationally the effect of applied electric field on fracture strength: positive electric fields decrease the apparent fracture toughness of piezoelectric materials while negative electric fields increase it.