Model Reduction Methods for Solving Symmetric Rational Eigenvalue Problems

We consider large and sparse rational eigenproblems where the rational term is of low rank compared to the dimension of the problem. Exploiting model‐order reduction techniques the dimension can be reduced considerably, and problems of this type can be solved very efficiently. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

From heterobimetallic transition metal complexes to linear coordination polymers based on cis‐ and trans‐L2Pt(CCPh)2

The reaction of cis‐(2,2′‐bipyridine) Pt(CCPh)₂ cis‐(4,4′‐dimethyl‐2,2′‐bipyridine) Pt‐(CCPh)₂ and trans‐(Ph₃P)₂Pt(CCPh)₂ towards different group 11 transition‐metal salts [M′X] (M′ = Cu, Ag; X = inorganic ligand) to give heterobimetallic or linear oligomeric and polymeric transition metal complexes is described. Different coordination modes for M′, PhCC, PPh₃, and X were found in these species. The structural aspects as well as the preference for one coordination mode over another is discussed. © 2002 Wiley Periodicals, Inc. Heteroatom Chem 13:521–533, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/hc.10097     

Synthesis and Structures of Amino(triphenylgermyl) Boranes and Trihydro(triphenylgermyl) Borates

The B‐(triphenylgermyl)borazines 4 a and 4 b , the 1,2‐bis(dimethylamino)‐1,2‐bis(triphenylgermyl)‐diborane(4), 5 , and the (2,2,6,6‐tetramethylpiperidino)(triphenylgermyl)‐boranes 6 and 7 were prepared by allowing LiGePh₃ to react with the corresponding B‐bromoborazines and aminochloroboranes, respectively. BH₃ dissolved in thf readily adds to LiGePh₃ generating Li(H₃BGePh₃), 8 a , in thf solution. Addition of N‐bases to the solution of 8 a produced (tmen · thf)Li(H₃BGePh₃), 8 b , and dimeric (py)₂Li(H₃BGePh₃), 8 c . The borazine ring in 4 b is distorted into a boat shape. In 5 the NBGe planes are twisted against each other by 85°. Comparison with analogous (triphenylstannyl)boranes points to a more pronounced steric effect of the Ph₃Ge group over the Ph₃Sn group due to the shorter B–Ge bond. A fairly short B–Ge bond is found for the (triphenylgermyl)trihydroborates. The molecular structure of (Et₂O)₃LiGePh₃ shows compressed C–Ge–C bond angles. Its molecular parameters fit well into the series L_nLiEPh₃ (E = Si, Sn, Pb).     

Ammonia and Chlorine Additions to a Tetrasilabuta‐1,3‐diene: Conglomerate versus Racemate Crystallization [1]

Treatment of hexakis(2,4,6‐triisopropylphenyl)tetrasilabuta‐1,3‐diene ( 1 ), R₂Si=SiR–SiR=SiR₂, with ammonia and chlorine furnishes the correspondingly substituted 1,4‐diaminotetrasilane ( 3 ) and 1,2,3,4‐tetrachlorotetrasilane ( 6 ). While product 6 crystallizes as a racemate, 3 forms a conglomerate of enantiomerically pure crystals. The change of colors during the formation of 6 indicates a stepwise reaction sequence.     

Synthesis and Structures of some Trisorganylstannyl Boranes and Triorganylstannyl Borates [1]

New stannylboranes were prepared from tetramethylpiperidino dichloroborane or B‐bromo‐pentamethylborazine with lithium triorganylstannides LiSnR₃. Only double stannylation was possible with tmpBCl₂ and LiSnMe₃, while tmpBCl(SnPh₃) was obtained by employing LiSnPh₃. This chloride reacted with LiGePh₃ to the stannyl germyl borane tmpB(GePh₃)(SnPh₃). On the other hand, PhMeNBCl₂ and an excess of LiSnMe₃ gave the borate Li[B(NMePh)(SnMe₃)₃], which was isolated as a solvate with 4 molecules of THF. The compound is present in the solid state as a solvent separated ion pair. The borate Li(H₃BSnMe₃) · 2 THF is dimeric in the solid state. Dimerization occurs via two single Li–H–B bridges and a Li–H(B)–Li bridge. The B–Sn bonds in the borates are practically of the same lengths as those in the boranes. In solution all BH bonds of this trihydridoborate are equivalent.     

Unsystematische Zinkchemie: zufällige Bildung und Struktur von Zn6(SC6F5)10(BPPAE)2

Non‐systematic Zinc Chemistry: Accidental Formation and Structure of Zn₆(SC₆F₅)₁₀(BPPAE)₂ The reaction between pyridine‐2‐carbaldehyde and ammonia‐contaminated zinc‐bis(pentafluorothiophenolate) yielded, beside the expected 1 : 1 adduct, small amounts of the hexanuclear cluster Zn₆(SC₆F₅)₁₀(BPPAE)₂. Its ligand BPPAE (1,2‐bis‐pyridine‐2‐yl‐2[(pyridine‐2‐ylmethylene)‐amino]‐ethenolate) results from condensation of three molecules of pyridine‐2‐carbaldehyde with one molecule of ammonia. The Zn₆ cluster consists of two centrosymmetrically arranged Zn₃ units which contain three differently coordinated zinc ions in ZnS₄, ZnS₂ON and ZnSON₃ environments.     

Konfigurations- und konformationsisomere paratrope,rotationsdynamische Tetraepoxy[32]annulene(6.2.6.2) und diatrope Tetraoxa[30]porphyrin(6.2.6.2)-Dikationen : Nachweis eines Tetraepoxy[31]annulen(6.2.6.2)-Radikalkations

Configurational and Conformational Isomeric Paratopic, Rotational Dynamics Tetraepoxy[30]annulenes(6.2.6.2) and Diatropic Tetraoxa[30]porphyrin(6.2.6.2) Dications: Detection of a Tetraepoxy[31]annulene(6.2.6.2)Radical Cation The synthesis of tetraepoxy[32]annulenes(6.2.6.2) ( 4 ) by a cyclizing twofold Wittig reaction of (E,E,E)-5,5′-(hexa-1,3,5-triene-1,6-diyl)bis[furan-2-carbaldehyde] ( 6 ) and the corresponding bis-phosphonium salt 7 is described (Scheme 1). Contrary to the configuration of the educts, the obtained annulenes 4a and 4b are (Z,E,E,E,Z,E,E,E)- and (E,Z,E,E,E,Z,E,E)-configurated, respectively. The ¹H-NMR spectra establish the paratropic, antiaromatic character of 4 . The annulenes 4 are highly dynamic systems, the (E)-ethenediyl bridges rotate around the adjacent σ-bonds, these rotations are frozen at −80°. The McMurry condensation of dialdehyde 6 yields the (E,E,Z,E,E,E,Z)-4,5-dihydrotetraepoxy[32]annulene(6.2.6.2) ( 13a ), where the configuration of the dialdehyde 6 – beside the hydrogenated double bond – is retained. As result of an intramolecular McMurry reaction of 6 , (Z,E,Z,Z)-dioxa[16]annulene(6.2) 14 is formed. By oxidation of the [32]annulenes(6.2.6.2) 4a and 4b , a mixture of the four stereoisomeric tetraoxa[30]porphyrin(6.2.6.2) dications 5a / 5a ′/ 5b / 5c is obtained; the configuration of the isomers is determined by COSY, NOESY, and NOE experiments. The Δδ values (26.81, 25.83, and 21.11 ppm) underline the diatropic, aromatic character of the dications 5 , the Soret bands are shifted bathochromically to 550 nm, and the Q-bands are in the NIR region (896 – 1039 nm). The dihydroannulene 13a is dehydrogenated by p-chloroanil (tetrachloro-1,4-benzoquinone) to give the annulenes 4a and 4b , its oxidation with DDQ (=4,5-dichloro-3,6-dioxocyclohexa-1,4-diene-1,2-dicarbonitrile) results in the same mixture of dications 5 . Entirely different results are obtained by reaction of the dihydroannulene 13a with DDQ. Here, the (E,E,E,Z,E,E,E,Z) tetraoxa[30]porphyrin(6.2.6.2) dication 5c – formed only in traces from 4a / 4b – is the main product. Beside 5c , a by-product (3%) can be isolated, which turns out (ESR, conductivity) to be the (E,E,E,Z,E,E,E,Z)-tetraoxa[31]porphyrin(6.2.6.2) radical cation 16 , obviously the intermediate in the oxidation sequence of the annulene to the dication. This result leads to the conclusion that the reaction of the dihydro compound 13a with p-chloroanil and DDQ follows different reaction mechanisms. For all isolated stereoisomeric tetraepoxy annulenes and tetraoxaporphyrin dications, the ΔH_f values are calculated by the semiempiric AM1 method. The results are in agreement with the experimental observations. All data confirm the antiaromaticity of the tetraepoxy[32]annulenes(6.2.6.2) 4 and the aromaticity of the tetraoxa[30]porphyrin(6.2.6.2) dications.     

Phenylselenolato Complexes of Cyclopentadienylrhodium: Structural Variety in the Solid State and in Solution

Diphenyl diselenide reacts with [CpRh(CO)₂] ( 1 ) to give the dimer [CpRh(SePh)(μ-SePh)]₂ ( 2 ), the solid state structure of which has been determined by X-ray analysis; the dimeric structure is retained in solution. In contrast, [Cp*Rh(CO)₂] ( 4 ) gives the ionic product [Cp*Rh(μ-SePh)₃RhCp*][Cp*Rh(SePh)₃] ( 5 ), which dissolves as such in THF but as a monomeric 16-electron complex [Cp*Rh(SePh)₂] ( 6 ) in CDCl₃ or CD₂Cl₂. Upon UV irradiation in CDCl₃, ( 2 ) is converted into the ionic species [CpRh(μ-SePh)₃RhCp]Cl ( 3 ). The monomer ( 6 ) slowly decomposes in CH₂Cl₂, and single crystals of [Cp*Rh(μ-SePh)₃RhCp*][PhSeCl₂] ( 5 a ) have been obtained. The crystal structure of 5 a has been determined by X-ray diffraction methods. The structures in solution were proposed in particular on the basis of ⁷⁷Se NMR spectroscopy where the splitting due to ¹⁰³Rh–⁷⁷Se coupling makes it possible to distinguish between bridging and terminal PhSe groups.