Congruences for generalized Frobenius partitions with 4 colors

We present some congruences involving the functions c?₄(n) and which denote, respectively, the number of generalized Frobenius partitions of n with 4 colors and 4-order generalized Frobenius partitions of n with 4 colors.     

New binuclear Mn(II) and Fe(II) complexes supported by 1,4,8-triazacycloundecane

Two new binuclear metal complexes supported by 1,4,8-triazacycloundecane (tacud) are reported. [Fe(2)(tacud)(2)(μ-Cl)(2)Cl(2)] (1) and [Mn(2)(tacud)(2)(μ-Cl)(2)Cl(2)] (2) are isomorphs consisting of bis(μ-chloro) bridged metal centers along with terminal chloro groups and tacud ligands. Both compounds 1 and 2 crystallize in the P1 space group. For 1, a = 7.7321(12) ?, b = 7.8896(12) ?, c = 11.4945(17) ?, α = 107.832(2)°, β = 107.827(2)°, γ = 92.642(2)°, V = 627.85(17) ?(3) and Z = 1. For 2, a = 7.7607(12) ?, b = 7.9068(12) ?, c = 11.6111(18) ?, α = 108.201(2)°, β = 108.041(2)°, γ = 92.118(3)°, V = 636.47(17) ?(3) and Z = 1. Variable-temperature and variable-field magnetic susceptibility studies on 1 indicate the presence of weak ferromagnetic interactions between the high-spin iron(ii) centers in the dimer (J = + 1.6 cm(-1)) and the crystalline field anisotropy of the ferrous ion (D = - 2.8, E = - 0.1 cm(-1)). Variable temperature magnetic susceptometry studies on 2 indicate that weak antiferromagnetic coupling exists between the manganese(ii) centers (J = - 1.8 cm(-1)). Compounds 1 and 2 retain their dinuclearity in weakly coordinating or low polarity solvents, while both become mononuclear in solvents such as methanol.     

Synthesis,Structure, and Characterization of [FeIIILCl3] (L = 1, 4, 8‐Triazacycloundecane, 1, 4, 7‐Triazacyclononane)

The structures of [Fe^III(tacud)Cl₃] ( 1 ) and [Fe^III(tacn)Cl₃] ( 2 ) (tacud = 1, 4, 8‐triazacycloundecane, tacn = 1, 4, 7‐triazacyclononane) are reported. Both compounds crystallize in the orthorhombic space group Pnma with a = 12.5570(9), b = 12.0028(9), c = 8.2577(6) Å, V = 1244.59(16) ų, and Z = 4 for 1 and a = 12.095(4), b = 11.125(4), c = 7.963(3) Å, V = 1071.5(6) ų, and Z = 4 for 2 . The structures of 1 and 2 feature iron(III) in distorted octahedral arrangement with three facially coordinated nitrogen ligands and three chlorides. Bidirectional intermolecular hydrogen bonding between N–H groups and coordinated chlorides is seen for 1 and 2 . Compound 1 is the first example of iron(III) bonded to tacud and compound 2 is only the second structure reported of a 1:1 complex between iron and tacn. The Fe^3+/2+ redox couple for 1 is observed at E_1/2 = 0.25 V (ΔE_p = 99 mV), and for 2 at E_1/2 = 0.09 V (ΔE_p = 108 mV) versus NHE in DMF at 298 K. Comparison of structural, magnetic, and electrochemical properties for 1 and 2 reveal subtle differences consistent with the stronger coordinating properties of tacn relative to tacud.     

Chemical routes to GeS2 and GeSe2 nanowires

Nanowires of GeS(2) and GeSe(2) have been obtained by novel chemical routes involving the decomposition of organo-ammonium precursors containing super-tetrahedral Ge(4)S(10) and the dimeric Ge(2)Se(6) units.     

Isolation and characterization of iridium(III) and iridium(V) complexes of 2-(arylazo)pyridine and studies of amine fusion reactions at the coordinated diazo-ligand

The reaction of IrCl3.3H2O with 2-(arylazo)pyridine (HL1) in boiling methanol has afforded [Ir(III)Cl2(L1)(HL1)](1) and [Ir(V)Cl4(HL1)]Cl (2). In complex , one of the two ligands [L1]- is orthometallated via coordination of an ortho-carbon of the aryl ring of [L1]- and one of the two azo nitrogens to form a five-membered chelate. X-Ray crystal structures of the two representative complexes, viz. 1a and 2a, have been solved. Notably, the Ir-N length (2.140(3) A)trans to the Ir-C bond in 1a is appreciably longer than the other three Ir-N lengths present in the same molecule. The N-N lengths in these two compounds lie close to that observed in the uncoordinated ligand. Thorough NMR studies were made to authenticate the carbon-bonded structure of compound 1a. In its 13C NMR spectrum, the resonance near delta 148 is assigned to the carbon bonded to the iridium metal center. UV-visible spectra along with the redox properties of these complexes are reported. The iridium(V) complex, 2 showed a reversible response near 1.40 V, presumably due to the iridium(V)-iridium(VI) couple. Several reductive responses at cathodic potentials, due to ligand reductions, were also observed. Metal promoted aromatic ring amination reactions at the coordinated HL1 ligand in complexes 1 and 2 were investigated. The products were characterized using X-ray diffraction.     

Preparation of cross-linked guar gum nanospheres containing tamoxifen citrate by single step emulsion in situ polymer cross-linking method

In the present work, guar gum nanospheres containing tamoxifen citrate (TC) were prepared and characterized for using it as a carrier for targeted drug delivery. Tamoxifen is a non steroidal drug used in the treatment of breast cancer. The compound administered to patients is the citrate salt of the trans isomer, tamoxifen citrate. Single step emulsion in situ polymer crosslinking technique was employed to prepare polymer coated drug nanoparticles. Model polymer used in this study was guar gum, which is commonly used for colon specific drug delivery in the pharmaceutical industry. During preparation four-different drug loading solvents were tried and dichloromethane provided the best drug loading result. Briefly, 5 mg drug was dissolved in dichloromethane and emulsified with an aqueous solution of guar gum using span 80 as emulsifier. Cross-linking was made by the use of cross linker glutaraldehyde during the process. A core shell type particles were observed. Drug load was confirmed by FT-IR and quantitated by HPLC. Nanoparticles were further characterized for particle size and morphology. Particle size between 200 and 300 nm were obtained. Influence of process variables on the size of nanoparticles were studied. It was observed that the concentration of polymer and stabilizer determined the size of nanoparticles.     

Optical properties of SnO2 nanoparticles

In recent times, considerable research efforts have been focused on the exploration of novel optical properties of nanocrystalline SnO₂ particles such as photoluminescence (PL). In the present work, spherical SnO₂ nanoparticles are synthesized by solid state reaction at different temperatures using tin chloride dihydrate and sodium hydroxide flakes as precursors. Transmission electron micrograph shows uniform and spherical SnO₂ nanoparticles of diameter 30–40 nm. Micro-Raman spectra show an inverse relationship of line-width with SnO₂ particle size. The band gap of SnO₂ is calculated by plotting (αhν)² vs. hν and extrapolating the linear portion of it to α = 0 and found it to be 3.76–4.24 eV. Photoluminescence intensity increases with the increase of solid state reaction temperature up to 873 K. This is attributed to the generation of the oxygen ion vacancies in SnO₂.     

Microwave-promoted catalyst- and solvent-free aza-Diels-Alder reaction of aldimines with 6-[2-(dimethylamino)vinyl]-1,3-dimethyluracil

A microwave-promoted aza-Diels-Alder reaction between 6-[2-(dimethylamino)vinyl]-1,3-dimethyluracil and aldimines has been developed for the construction of dihydropyrido[4,3-d]pyrimidines. Urea is effectively employed as an environmentally benign source of ammonia in the absence of any catalyst or solvent. The key step in the reaction is in situ generation and trapping of the reactive aldimine formed from urea and aldehyde by the diene system of the uracil. The reaction is clean, and excellent yields are obtained in a matter of a few minutes.     

Rhodium(I) carbonyl complexes of chalcogen functionalized tripodal phosphines, [CH3C(CH2P(X)Ph2)3] {X = O, S, Se} and their reactivity

The reaction of dimeric rhodium precursor [Rh(CO)₂Cl]₂ with two molar equivalent of 1,1,1-tris(diphenylphosphinomethyl)ethane trichalcogenide ligands, [CH₃C(CH₂P(X)Ph₂)₃](L), where X = O(a), S(b) and Se(c) affords the complexes of the type [Rh(CO)₂Cl(L)] (1a–1c). The complexes 1a–1c have been characterized by elemental analyses, mass spectrometry, IR and NMR (¹H, ³¹P and ¹³C) spectroscopy and the ligands a–c are structurally determined by single crystal X-ray diffraction. 1a–1c undergo oxidative addition (OA) reactions with different electrophiles such as CH₃I, C₂H₅I and C₆H₅CH₂Cl to give Rh(III) complexes of the types [Rh(CO)(COR)ClXL] {R = –CH₃ (2a–2c), –C₂H₅ (3a–3c); X = I and R = –CH₂C₆H₅ (4a–4c); X = Cl}. Kinetic data for the reaction of a–c with CH₃I indicate a first-order reaction. The catalytic activity of 1a–1c for the carbonylation of methanol to acetic acid and its ester is evaluated and a higher turn over number (TON = 1564–1723) is obtained compared to that of the well-known commercial species [Rh(CO)₂I₂]⁻ (TON = 1000) under the reaction conditions: temperature 130 ± 2 °C, pressure 30 ± 2 bar and time 1 h.