Calculation of current densities using gauge-including atomic orbitals

A method for calculating the various components of the magnetically induced current-density tensor using gauge-including atomic orbitals is described. The method is formulated in the framework of analytical derivative theory, thus enabling implementation at the Hartree-Fock self-consistent-field (HF-SCF) as well as at electron-correlated levels. First-order induced current densities have been computed up to the coupled-cluster singles and doubles level (CCSD) augmented by a perturbative treatment of triple excitations [CCSD(T)] for carbon dioxide and benzene and up to the full coupled-cluster singles, doubles, and triples (CCSDT) level in the case of ozone. The applicability of the gauge including magnetically induced current method to larger molecules is demonstrated by computing first-order current densities for porphin and hexabenzocoronene at the HF-SCF and density-functional theory level. Furthermore, a scheme for obtaining quantitative values for the induced currents in a molecule via numerical integration over the current flow is presented. For benzene, a perpendicular magnetic field induces a (field dependent) ring current of 12.8 nA T(-1) at the HF-SCF level using a triple-zeta basis set augmented with polarization functions (TZP). At the CCSD(T)/TZP level the induced current was found to be 11.4 nA T(-1). Gauge invariance and its relation to charge-current conservation is discussed.     

On a problem of Erdős and Lovász: Random lines in a projective plane

Letn(k) be the least size of an intersecting family ofk-sets with cover numberk, and let _k denote any projective plane of orderk–1.Theorem There is a constant A such that ifH is a random set ofm Aklogk lines from _k then P_r(H<)0(k).Corollary If there exists a _k thenn(k)=O(klogk). These statements were conjectured by P. Erds and L. Lovász in 1973.Supported in part by NSF-DMS87-83558 and AFOSR grants 89-0066, 89-0512 and 90-0008     

(2S,5S)-2,5-dibenzyl-1,4-dimethylpiperazine, a novel alkaloid from zanthoxylum arborescens

The isolation and structure determination of (2S,5S)-2,5-dibenzyl-1,4-dimethylpiperazine ($\text{1}$), a new alkaloid biogenetically related to L-phenylalanine diketopiperazine, is described.     

New Metal Oxamates as Precursors of Low-Dimensional Heterobimetallics

The goal of this work was to synthesize new molecular bricks which could be used as precursors of heterobimetallic low-dimensional compounds. Along this line, four compounds have been synthesized and structurally characterized, namely (NBu(4))(2)[Ni(Cl(2)opba)] (1), (NBu(4))(2)[Cu(Cl(2)opba)] (2), (NBu(4))(5)[Mn(Cl(2)opba)(DMSO)(2)](4) (3), and Cu(en)(2)[Mn(Cl(2)opba)(H(2)O)(2)](2).2DMSO (4), with Cl(2)opba = (4,5-dichloro-o-phenylene)bis(oxamato), NBu(4) = tetra-n-butylammonium, en = ethylenediamine, and DMSO = dimethyl sulfoxide. Compounds 1 and 2 are isostructural; they crystallize in the monoclinic system, space group C2/c, Z = 4, with a = 18.708(2) ?, b = 17.525(2) ?, c = 14.763(9) ?, and beta = 92.03(4) degrees for 1 and a = 18.928(2) ?, b = 17.634(2) ?, c = 14.704(9) ?, and beta = 92.38(3) degrees for 2. 3 crystallizes in the tetragonal system, space group P&fourmacr;2(1)c, Z = 2, with a = 26.295(10) ? and c = 12.342(7) ?. The structure shows a random occupation of the metal site by Mn(III) and Mn(II) ions in 3/4 and 1/4 ratios, respectively. 4 crystallizes in the triclinic system, space group P&onemacr;, Z = 1, with a = 7.066(7) ?, b = 11.844(1) ?, c = 14.292(5) ?, alpha = 105.64(2) degrees, beta = 97.67(5) degrees, and gamma = 102.13(3) degrees. The structure consists of Mn(III)Cu(II)Mn(III) trinuclear species, with Cu-O-Mn bridges involving oxygen atoms of the oxamato groups already linked to the metal atom. The magnetic properties of compounds 1-4 have been investigated and quantitatively interpreted. For 3, this magnetic investigation has been performed on a single crystal, which allows us to determine unambiguously the sign of the axial zero-field splitting parameter for the Mn(III) ion. The potentialities of these new molecular bricks have been discussed.     

Synthesis and characterization of dinuclear ruthenium complexes covalently linked to Ru(II) tris-bipyridine: an approach to mimics of the donor side of photosystem II

To mimic the electron-donor side of photosystem II (PSII), three trinuclear ruthenium complexes (2, 2a, 2b) were synthesized. In these complexes, a mixed-valent dinuclear Ru2(II,III) moiety with one phenoxy and two acetato bridges is covalently linked to a Ru(II) tris-bipyridine photosensitizer. The properties and photoinduced electron/energy transfer of these complexes were studied. The results show that the Ru2(II,III) moieties in the complexes readily undergo reversible one-electron reduction and one-electron oxidation to give the Ru2(II,III) and Ru2(III,III) states, respectively. This could allow for photooxidation of the sensitizer part with an external acceptor and subsequent electron transfer from the dinuclear ruthenium moiety to regenerate the sensitizer. However, all trinuclear ruthenium complexes have a very short excited-state lifetime, in the range of a few nanoseconds to less than 100 ps. Studies by femtosecond time-resolved techniques suggest that a mixture of intramolecular energy and electron transfer between the dinuclear ruthenium moiety and the excited [Ru(bpy)3]2+ photosensitizer is responsible for the short lifetimes. This problem is overcome by anchoring the complexes with ester- or carboxyl-substituted bipyridine ligands (2a, 2b) to nanocrystalline TiO2, and the desired electron transfer from the excited state of the [Ru(bpy)3]2+ moiety to the conduction band of TiO2 followed by intramolecular electron transfer from the dinuclear Ru2(II,III) moiety to photogenerated Ru(III) was observed. The resulting long-lived Ru2(III,III) state decays on the millisecond timescale.     

A one-pot synthesis of functionalized 2,2-disubstituted 2H-1-benzopyrans

The synthesis of functionalized 2,2-disubstituted 2H-1-benzopyrans was achieved by condensing 2,3,5-trimethylhydroquinone (TMHQ) with ,β-unsaturated aldehydes or ,β-unsaturated acetals under acidic conditions.     

Preparation and characterization of fibres from a thermotropic liquid crystal polyester with non-coplanar biphenylene units

Abstract

Fibres were prepared from the nematic melt of poly(2,2′-dimethyl-4,4′-biphenylene phenylterephthalate). The phenyl substitution in the terephthalic acid moiety in combination with the non-coplanar biphenyl moiety prevent crystallization of this thermotropic polyester. Oriented fibres were prepared by two different methods. Similarly to other thermotropic liquid crystal polymer fibres, chain orientation can be achieved by an elongational flow in a down draw process. This polyester also allows tensile deformation of the spun fibres around the glass transition temperature. In both routes similar degrees of orientation and mechanical properties were obtained. Tensile moduli in the order of 40–45 GPa and tensile strengths up to 550–650 MPa were obtained. The orientation function values were determined to be in the order of 0·8–0·9. A comparison with other unsubstituted thermotropic liquid crystal polyesters at the same level of orientation revealed that the moduli are the same, although the substituents increase the chain diameter. This result may be attributed to an increase of the apparent shear modulus due to an interlocking mechanism of the rigid lateral substituents.