Diagrammatic structure of the general coupled cluster equations

The general formula for the number of diagrammatic terms occurring in the T_n equation within a particular coupled cluster model is derived. Both the antisymmetrized and Goldstone diagrams are considered. In addition to the full coupled cluster equation approximate approaches are discussed, and for each the general formula for the number of terms is given. Analogous expressions are presented for the number of diagrammatic terms contributing to the elements of the transformed Hamiltonian [Hbar] = e^?T He^T .     

Plane Sources of Waves in the Presence of Magnetic Field

In this paper the generation of harmonic waves in an elastic magneticmaterial, which is a perfect conductor of electricity, isconsidered. It has been assumed that an infinite body is subjected tothe action of an initially constant magnetic fieldH = (H,0,0) and in the plane ax+by=0 acts a source ofdistortion. It has been shown that this source may produce bothtransverse and longitudinal waves and each of them consists of two parts,which propagate with different speeds. The amplitudes and speeds in dependence on theangle between the direction of wave propagation and the magnetic fieldintensity H have been discussed.     

Coordination complexes of molybdenum with 3,6-di-tert-butylcatechol. Addition products of DMSO, pyridine N-oxide, and triphenylarsine oxide to the putative [MoVIO(3,6-DBCat)2] monomer and self-assembly of the chiral [(MoVIO(3,6-DBCat)2)4] square

Molybdenum complexes of 3,6-di-tert-butylcatechol have been prepared from the reaction between [Mo(CO)(6)] and 3,6-di-tert-butyl-1,2-benzoquinone. A putative "[MoO(3,6-DBCat)(2)]" monomer is assumed to form initially by reaction with trace quantities of oxygen. Condensation of the reaction mixture leads to the formation of oligomeric products, including the [(MoO(3,6-DBCat)(2))(4)] chiral square isolated by chromatographic separation. Molybdenum centers at the corner of the square are bridged by oxo ligands centered along edges. Four-fold and inversion crystallographic symmetry gives tetramers as either LambdaLambdaLambdaLambda or DeltaDeltaDeltaDelta isomers, and the crystal structure consists of parallel columns of squares with the same chirality. Addition of O-Subst (O-Subst = dmso, pyridine N-oxide, triphenylarsine oxide) ligands to [MoO(3,6-DBCat)(2)] occurs selectively to give cis-[MoO(O-Subst)(3,6-DBCat)(2)] products. All three addition complexes are fluxional in solution. The temperature-dependent stereodymanic behavior of [MoO(dmso)(3,6-DBCat)(2)] has been shown to occur via a trigonal prismatic intermediate (Bailar twist) that conserves the cis disposition of oxo and dmso ligands. Electrochemical and chemical reduction reactions have been investigated for [MoO(dmso)(3,6-DBCat)(2)] with interest in displacement of SMe(2) with formation of cis-[MoO(2)(3,6-DBCat)(2)](2-). Cyclic voltammetry shows an irreversible two-electron reduction for the complex at -0.852 V (vs Fc/Fc(+)). Chemical reduction using CoCp(2) was observed to give a product with an electronic spectrum that is generally associated with cis-[MoO(2)(Cat)(2)](2-) complexes. Structural characterization revealed that the product was [CoCp(2)][MoO(3,6-DBCat)(2)], possibly formed as the product of dmso displacement upon one-electron reduction of [MoO(dmso)(3,6-DBCat)(2)].     

Synthetic Approaches to (smif)(2)Ti (smif = 1,3-di-(2-pyridyl)-2-azaallyl) Reveal Redox Non-Innocence and C-C Bond-Formation

Attempted syntheses of (smif)(2)Ti (smif =1,3-di-(2-pyridyl)-2-azaallyl) based on metatheses of TiCl(n)L(m) (n = 2-4) with M(smif) (M = Li, Na), in the presence of a reducing agent (Na/Hg) when necessary, failed, but several apparent Ti(II) species were identified by X-ray crystallography and multidimensional NMR spectroscopy: (smif){Li(smif-smif)}Ti (1, X-ray), [(smif)Ti](2)(μ-κ(3),κ(3)-N,N(py)(2)-smif,smif) (2), (smif)Ti(κ(3)-N,N(py)(2)-smif,(smif)H) (3), and (smif)Ti(dpma) (4, dpma = di-2-pyridylmethyl-amide). NMR spectroscopy and K-edge XAS showed that each compound possesses ligands that are redox noninnnocent, such that d(1) Ti(III) centers AF-couple to ligand radicals: (smif){Li(smif-smif)(2-)}Ti(III) (1), [(smif(2-))Ti(III)](2)(μ-κ(3),κ(3)-N,N(py)(2)-smif,smif) (2), [(smif(2-))Ti(III)](κ(3)-N,N(py)(2)-smif,(smif)H) (3), and (smif(2-))Ti(III)(dpma) (4). The instability of (smif)(2)Ti relative to its C-C coupled dimer, 2, is rationalized via the complementary nature of the amide and smif radical dianion ligands, which are also common to 3 and 4. Calculations support this contention.     

Pt(II) and Pt(IV) amido, aryloxide, and hydrocarbyl complexes: synthesis, characterization, and reaction with dihydrogen and substrates that possess C-H bonds

The Pt(II) amido and phenoxide complexes ((t)bpy)Pt(Me)(X), ((t)bpy)Pt(X)(2), and [((t)bpy)Pt(X)(py)][BAr'(4)] (X = NHPh, OPh; py = pyridine) have been synthesized and characterized. To test the feasibility of accessing Pt(IV) complexes by oxidizing their Pt(II) precursors, the previously reported ((t)bpy)Pt(R)(2) (R = Me and Ph) systems were oxidized with I(2) to yield ((t)bpy)Pt(R)(2)(I)(2). The analogous reaction with ((t)bpy)Pt(Me)(NHPh) and MeI yields the corresponding ((t)bpy)Pt(Me)(2)(NHPh)(I) complex. Reaction of ((t)bpy)Pt(Me)(NHPh) and phenylacetylene at 80 °C results in the formation of the Pt(II) phenylacetylide complex ((t)bpy)Pt(Me)(C≡CPh). Kinetic studies indicate that the reaction of ((t)bpy)Pt(Me)(NHPh) and phenylacetylene occurs via a pathway that involves [((t)bpy)Pt(Me)(NH(2)Ph)][TFA] as a catalyst. The reaction of H(2) with ((t)bpy)Pt(Me)(NHPh) ultimately produces aniline, methane, (t)bpy, and elemental Pt. For this reaction, mechanistic studies reveal that 1,2-addition of dihydrogen across the Pt-NHPh bond to initially produce ((t)bpy)Pt(Me)(H) and free aniline is catalyzed by elemental Pt. Heating the cationic complexes [((t)bpy)Pt(NHPh)(py)][BAr'(4)] and [((t)bpy)Pt(OPh)(py)][BAr'(4)] in C(6)D(6) does not result in the production of aniline and phenol, respectively. Attempted synthesis of a cationic system analogous to [((t)bpy)Pt(NHPh)(py)][BAr'(4)] with ligands that are more labile than pyridine (e.g., NC(5)F(5)) results in the formation of the dimer [((t)bpy)Pt(μ-NHPh)](2)[BAr'(4)](2). Solid-state X-ray diffraction studies of the complexes ((t)bpy)Pt(Me)(NHPh), [((t)bpy)Pt(NH(2)Ph)(2)][OTf](2), ((t)bpy)Pt(NHPh)(2), ((t)bpy)Pt(OPh)(2), ((t)bpy)Pt(Me)(2)(I)(2), and ((t)bpy)Pt(Ph)(2)(I)(2) are reported.     

Methoxide Coordination at the Pocket of [CuIITpCum,Me] and a Simple Model for the Cu Center of Galactose Oxidase

An unusually negative oxidation potential is found for the tyrosine residue in the center of fungal galactose oxidase. The complex [Cu(Tp^Cum,Me){O(MeS)C₆H₄}] (see picture on the right; Tp^Cum,Me=hydrotris(pyrazolyl)borate) offers insight into the mode of (cysteinyl-tyrosine) coordination to the copper center, and the reason for the low oxidation potential.