Adducts of organogallium chlorides with hydrazines and the formation of dimeric dialkylgallium hydrazides possessing different ring sizes

The dialkylgallium chlorides R₂GaCl (R = Me, Et, CMe₃) reacted with hydrazines H₂N-N(H)R′ (R′ = CMe₃, C₆H₅) to form the adducts R₂ClGa ← NH₂-N(H)R′ (1-4), in which the gallium atoms are coordinated by the NH₂ nitrogen atoms of the hydrazine ligands. Treatment of these adducts with tert-butyllithium as a base afforded dialkylgallium hydrazides (R₂Ga-N₂H₂R′)₂ [5 (R = R′ = CMe₃) and 6 (R = CMe₃, R′ = C₆H₅)] by deprotonation of the hydrazine ligands and precipitation of LiCl in two cases only. The remaining adducts gave a substitution reaction at gallium or an unclear reaction course. The hydrazides 5 and 6 adopt different structures in the solid state. The tri(tert-butyl) compound 5 possesses a four-membered Ga₂N₂ heterocycle in its molecular core with two exocyclic N-N bonds, which represents the structural motif usually observed for dialkylgallium hydrazides. 6 has a five-membered Ga₂N₃ heterocycle with one endocyclic and one exocyclic N-N bond. That structure is preserved in solution as clearly shown by NMR spectroscopy. The behaviour of 5 in solution is more complicated, which may be caused by cis/trans isomerization.     

Minimization of empirical energy functions in proteins including hydrophobic surface area effects

We present analytical expressions to calculate the gradient of the water-accessible surface area of proteins with respect to Cartesian coordinates and dihedral angles. A detailed mathematical analysis leads to corrected equations for the gradient calculation used previously in the ANAREA program. To study the hydrophobic effect of solvent-protein interactions, our expressions have been implemented to further improve the program package FANTOM. We used this version of FANTOM to minimize the ECEPP/2 and the hydrophobic energy of tendamistat. © 1993 John Wiley & Sons, Inc.     

‘Lone pair’ Electronic Structure,Conformation and Oxidation Behaviour of Diaziridines

Photoelectron spectroscopic investigations indicate that (i) monocyclic diaziridines prefer a trans-conformation of the nitrogen-lone pairs, and (ii) the interaction between these is comparable to that exhibited by open-chain analogues, i.e. alkyl-substituted hydrazines. The chemical experience concerning the particular case of ? NH? NH? →? N?N? oxidation of diaziridines can therefore not be accounted for by a prevailing unfavorable ‘lone pair’ interaction. Thermochemical as well as entropy arguments may serve as an explanation. A rather unsatisfactory agreement between predictions from various theoretical procedures and experimental results for the ionization potentials of ‘lone pair’ MO electrons is noted.     

An analogue to a conjecture of S. Chowla and H. Walum

It is proved that (for every ε > 0)

$\text{∑}\text{n?T}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}\text{∑n<}\text{T}\text{n}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{n}{}^{\mathrm{a}}\text{m}{}^{\mathrm{b}}\text{B}{}_{\mathrm{k}}\text{({}\text{T}\text{nm}\text{}) = O(T}{}^{\mathrm{<mtext>(a+b+1)</mtext><mtext>3?</mtext>}}\text{)}$

(where {·} denotes the fractional part and B_k the Bernoulli polynomial of order k) under the suppositions that k ≥ 2 and 2a ? 1 ≥ b ≥ 1. If (1) were true for k = 1, a = b = 0, then Piltz' divisor problem (for n = 3) would be readily solved. This is an analog to a conjecture formulated by S. Chowla and H. Walum in 1963 and settled in the affirmative (under suitable suppositions) quite recently by S. Kanemitsu and R. Sita Rama Chandra Rao.     

Configurationally and conformationally homogeneous cyclicN-aryl sulfimides. II.13C-and1H NMR spectra

The configuration and (in case of mobile ring systems) the preferred conformation in a series of thiane- and ofcis-andtrans-1-thiadecalin-1-N-4-chlorophenyl imides were assigned by means of¹³C- and¹H nmr spectroscopy.¹H nmr criteria known to be valid for determination of the stereochemistry of cyclic sulfoxides may be applied (with limitations) to cyclicN-aryl sulfimides, if both isomers (S–N bond equatorial and axial, respectively) are known. The assignments are easier, and unambiguous for single isomers, by comparison of¹³C nmr chemical shifts of ring carbon atoms of sulfimides and sulfides. The influence of equatorially and axially oriented sulfimide groups on the chemical shifts of neighbouring protons, and on the carbon atoms of the heterocyclic rings are discussed in detail.

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Konfigurativ und konformationell einheitliche cyclische N-Aryl-sulfimide. II.¹³C- und¹H-NMR-Spektroskopie

Zusammenfassung Die Konfiguration und (bei beweglichen Ringsystemen) die bevorzugte Konformation einer Reihe von Thian- und voncis- undtrans-1-Thiadekalin-1-N-4-chlorophenylimiden wurde durch¹³C- und¹H-NMR-Spektroskopie bestimmt. Bekannte¹H-NMR-Kriterien zur Festlegung der Stereochemie cyclischer Sulfoxide sind (mit Einschränkungen) auch bei cyclischenN-Arylsulfimiden anwendbar, wenn beide Isomere (S–N-Bindung äquatorial bzw. axial) bekannt sind. Leichter, und auch bei Vorliegen von nur einem Isomeren eindeutig, gelingt die Zuordnung durch Vergleich der¹³C-NMR-Verschiebungen der Ringkohlenstoffatome von Sulfimiden und Sulfiden. Die Einflüsse äquatorial oder axial orientierter Sulfimidgruppen auf die chemischen Verschiebungen benachbarter Wasserstoffe und der Kohlenstoffe des Heterorings werden diskutiert.

     

A convenient synthesis of 4-aminoaryl substituted cyclic imides

An efficient one-step synthesis of 4-nitro-N-aryl substituted glutarimides, succinimides and maleimides in polyphosphoric acid is described together with the subsequent reduction to the corresponding anilines. The scope and limitation of this cyclocondensation are presented.     

Die Ungleichungen von Vietoris

The inequalities $$P_{k,l} = \frac{1}{{B(l + 1,k)}}\int\limits_0^{l/(k + l)} {x^l (1 - x)^{k - 1} dx = I_{l/(k + l)} (l + 1,k)< \frac{1}{2}}$$ and $$\Phi _{k,l,\mu } = \frac{1}{{B(k,k\mu + 1)}}\int\limits_0^1 {x^{k - 1} (1 - x)^{k\mu } I_x (l + 1,l\mu )dx< \frac{1}{2}}$$ are shown to be valid for any positive real numbersk, l, μ.     

Solution manifolds and submanifolds of parametrized equations and their discretization errors

Summary The paper concerns solution manifolds of nonlinear parameterdependent equations (1)F(u, )=y₀ involving a Fredholm operatorF between (infinite-dimensional) Banach spacesX=Z× andY, and a finitedimensional parameter space . Differntial-geometric ideas are used to discuss the connection between augmented equations and certain onedimensional submanifolds produced by numerical path-tracing procedures. Then, for arbitrary (finite) dimension of , estimates of the error between the solution manifold of (1) and its discretizations are developed. These estimates are shown to be applicable to rather general nonlinear boundaryvalue problems for partial differential equations.This work was in part supported by the U.S. Air Force Office of Scientific Research under Grant 80-0176, the National Science Foundation under Grant MCS-78-05299, and the Office of Naval Research under Contract N-00014-80-C-0455     

Übergangsmetallphosphidokomplexe. VIII. Strukturuntersuchungen an Übergangsmetallphosphor-Vier- und Sechsringkomplexen. Die Strukturen von [(CO)4MnPH2]2, [(CO)4MnPH2]3 und [cpNiPH2]3

Transition Metal Phosphido Complexes. VIII. X-Ray Diffraction Studies of Transition Metal Phosphorus Four- and Six-Membered Ring Complexes. Structures of [(CO)₄MnPH₂]₂, [(CO)₄MnPH₂]₃, and [cpNiPH₂]₃ [(CO)₄MnPH₂]₂ 1 crystallizes triclinic in the space group P1 with a = 680.4 pm, b = 706.4 pm, c = 919.1 pm, α 110.5°, β = 91.92°, γ 115.65°, and Z = 1 formula unit. The molecule exhibits a centrosymmetrical structure. The bond angles within the planar four-membered (Mn? P)₂-ring are 76.1° at the Mn atoms and 103.9° at the P atoms, respectively. The average Mn? P bond distance is found to be 235.1 pm. [(CO)₄MnPH₂]₃ 2 crystallizes monoclinic in the space group P2/n with a = 905.2 pm, b = 974.8 pm, c = 1264.2 pm, β = 109.1°, and Z = 2 formula units. The framework of the six-membered (Mn? P)₃-ring can be described as having a twist boat conformation. The average endocyclic bond angles are with 89.1° at the Mn atoms and 130.1° at the P atoms, respectively, largely widened compared to 1 . The average Mn? P bond distance, which is found to be 238.5 pm, is also slightly increased compared to 1 . [cpNiPH₂]₃ 3 crystallizes rhombohedral in the space group R3. The cell constants (hexagonal setting) are a = b = 1686.1 pm, c = 561.1 pm and Z = 3 formula units. The six-membered (Ni? P)₃-ring exhibits a chair conformation. The endocyclic bond angles are with 92.3° at the Ni atoms and 124.3° at the P atoms, respectively, comparable with those of the six-membered ring compound 2 . The Ni? P bond distance is found to be 215.2 pm. The eyclopentadienyl ligands are disordered and have been refined as rigid groups.