Chiral Lithiated Phosphoric Triamides: Structure,Reactivity, and Salt Effects

The theoretical structure of a cyclic phosphoric triamide 3 and of its monolithiated isomers 4 – 6 was calculated by ab initio methods (Fig. 1, Tables 1 and 2). The global minimum in 4 consists of a five-membered Li−C−N−P−O chelate. The intermediates 5 and 6 are, relative to 4 , energetically unfavorable by 15 and 18 kcal mol⁻¹, respectively, due to distortion in order to accommodate the N-complexation of the Li⁺ ions. NMR Investigations (¹H, ¹³C, ³¹P, and ⁷Li) of the lithiated bicyclic phosphoric triamide 1 were performed (Tables 3 – 5). The lithium aminomethanide 2 is characterized by a sp³-hybridized anion supporting Li−C contacts. The anions exist in a monomer-dimer equilibrium in solution (Scheme 2). Trapping reactions of rac- 2 with carbonyl compounds generated the corresponding amino-alcohol derivatives with high diastereoselectivities (Scheme 3, Table 6). A rational for the stereochemical outcome is given (Fig. 4). In the presence of LiBr, a P−N bond cleavage occurred on reaction of rac- 2 with aldehydes, which allowed the synthesis of (1-hydroxylalkyl)phosphonic diamides (Scheme 5, Table 7).     

Syntheses and Crystal Structures of 4,5-Dihydro-2-(2′-hydroxyphenyl)oxazole-Containing Metal Complexes

The synthesis of the complexes 3 of various metals ligated to chiral 4,5-dihydro-2-(2′-oxidophenyl-?O)oxazoles-?N is described (Scheme). Three of them, i.e. 3a , 3e , and 3f containing Cu^II, Zn^II and Ni^II, respectively, were analyzed by X-ray diffraction studies. A series of Cu^II complexes ( 6a – d ) with differently substituted dihydrooxazoles have been synthesized.     

Variants of Solid-State and Solution Structures of (η3-Allyl)- {2-[2′-(diphenylphosphino)phenyl]-4,5-dihydrooxazole-P,N}palladium(II) hexafluorophosphates and tetraphenylborates

Crystal and solution structures of the enantiomerically pure and the racemic pairs of (η³-allyl) {2-[2′-(diphenylphosphino)phenyl]-4,5-dihydro-4-phenyloxazole}palladium(II) hexafluorophosphates ( 1 , and rac- 1 , resp.) and tetraphenylborates ( 2 , and rac- 2 , resp.) as well as (η³-allyl){2-[2′-(diphenylphosphino)phenyl]-4,5-dihydro-4-isopropyloxazole}palladium(II) tetraphenylborate ( 3 ) were characterized by X-ray crystallography and ¹H-NMR spectroscopy. In the solid state, rac- 1 and rac- 2 proved to be disordered with both diastereoisomeric complexes in the crystal. The complexes 2 and 3 exist only in the ‘exo’ form. The X-ray structures show that the [Pd^II(η³-allyl)] moiety may adopt different configurations between a nearly symmetrical three-electron Pd^II(π³-allyl) system and an asymmetrical allyl group with a η¹- and a η²-bonding to the metal center. The [Pd^II(η³-allyl)] system of rac- 1 and of ‘endo’ rac- 2 is closer to the former, and that of 2 , ‘exo’-rac- 2 , and 3 closer to the later geometry. The ¹H-NMR spectra of the hexafluorophosphates 1 and rac- 1 show two sets of signals of the allylic protons in an ‘exo’/‘endo’ ratio of 2:3. The tetraphenylborates 2, rac- 2 , and 3 give only one set of broad signals of the allylic protons.     

KAM theory in configuration space

A new approach to the Kolmogorov-Arnold-Moser theory concerning the existence of invariant tori having prescribed frequencies is presented. It is based on the Lagrangian formalism in configuration space instead of the Hamiltonian formalism in phase space used in earlier approaches. In particular, the construction of the invariant tori avoids the composition of infinitely many coordinate transformations. The regularity results obtained are applied to invariant curves of monotone twist maps. The Lagrangian approach has been prompted by a recent study of minimal foliations for variational problems on a torus by J. Moser. This research has been supported by the Nuffields Foundation under grant SCI/180/173/G and by the Stiftung Volkswagenwerk.     

An inverse function theorem in Fréchet-Spaces

A technical inverse function theorem of Nash-Moser type is proved for maps between Fréchet spaces allowing smoothing operators. A counterexample shows that the growth requirements on the rightinverse of the linearized map needed are minimal.     

Periodic solutions of asymptotically linear Hamiltonian systems

We prove existence and multiplicity results for periodic solutions of time dependent and time independent Hamiltonian equations, which are assumed to be asymptotically linear. The periodic solutions are found as critical points of a variational problem in a real Hilbert space. By means of a saddle point reduction this problem is reduced to the problem of finding critical points of a function defined on a finite dimensional subspace. The critical points are then found using generalized Morse theory and minimax arguments.     

Observations of the low Earth orbit radiation environment from Mir

Recent measurements of the high-energy charged particle environment with the Radiation Environment Monitor (REM) aboard the Russian Mir space station are presented. Ionizing dose rates in a silicon detector have been measured with two shieldings. The dose is mainly accumulated in two distinct areas, the South Atlantic Anomaly (SAA) and the region of closest approach to the magnetic poles. Whereas the radiation in the South Atlantic Anomaly varied little during 1995, large changes of the daily absorbed doses in the polar regions are observed. A comparison of REM doses with the NASA AP-8 and AE-8 radiation models revealed major differences. AP-8 tends to underestimate the average REM doses, whereas AE-8 overestimates REM doses, and rather describes the worst case.     

Electronic energy transfer and collection in luminescent molecular rods containing ruthenium(II) and osmium(II) 2,2':6',2"-terpyridine complexes linked by thiophene-2,5-diyl spacers

The electronic absorption spectra, luminescence spectra and lifetimes (in MeCN at room temperature and in frozen n-C3H7CN at 77 K), and electrochemical potentials (in MeCN) of the novel dinuclear [(tpy)Ru(3)Os(tpy)]4+ and trinuclear [(tpy)Ru(3)Os(3)Ru(tpy)]6- complexes (3 = 2,5-bis(2,2':6',2'-terpyridin-4-yl)thiophene) have been obtained and are compared with those of model mononuclear complexes and homometallic [(tpy)Ru(3)Ru(tpy)]4+, [(tpy)Os(3)Os(tpy)]4+ and [(tpy)Ru(3)Ru(3)Ru(tpy)]6+ Complexes. The bridging ligand 3 is nearly planar in the complexes, as seen from a preliminary X-ray determination of [(tpy)Ru(3)Ru(tpy)][PF6]4, and confers a high degree of rigidity upon the polynuclear species. The trinuclear species are rod-shaped with a distance of about 3 nm between the terminal metal centres. For the polynuclear complexes, the spectroscopic and electrochemical data are in accord with a significant intermetal interaction. All of the complexes are luminescent (phi in the range 10(-4)-10(-2) and tau in the range 6-340 ns, at room temperature), and ruthenium- or osmium-based luminescence properties can be identified. Due to the excited state properties of the various components and to the geometric and electronic properties of the bridge, Ru --> Os directional transfer of excitation energy takes place in the complexes [(tpy)Ru(3)Os(tpy)]4+ (end-to-end) and [(tpy)Ru(3)Os(3)Ru(tpy)]6+ (periphery-to-centre). With respect to the homometallic case, for [(tpy)Ru(3)Os(3)Ru(tpy)]6+ excitation trapping at the central position is accompanied by a fivefold enhancement of luminescence intensity.     

Network dimensionality and ligand flexibility in lanthanide terephthalate hydrates

Various lanthanide open framework materials incorporating the terephthalate (TP) entity were prepared using hydrothermal synthesis methods at a moderate temperature of 170 °C. The compounds Nd₂(TP)₃(H₂O)₄(1), Er₂(TP)₃(H₂O)₄(2), Yb₂(TP)₃(H₂O)₂(3), Yb₂(TP)₃(H₂O)₆(4), and Yb₂(TP)₃(H₂O)₈·2H₂O (5), were characterized by single crystal structural analysis and FT-IR spectroscopy. While compounds 1 and 2 have been reported before on the basis of powder X-ray diffraction, the structural characterization of any ytterbium terephthalate species is unprecedented. Compounds 1-5 crystallize in triclinic settings with space group P-1. The compounds are compared with their previously reported Er and Tb-counterparts and the reduction of the dimensionality of the resulting networks from 3D over 2D to 1D with increasing level of hydration is discussed. Compounds 1, 2, and 3 with the lowest water content assemble in three-dimensional network lattices. Compounds 4 and 5, however, form 2D layered systems and 1D rod like chains, respectively, which are held together by hydrogen bonds originating from coordinating H₂O. The crystal lattices of the 3D networks experience higher levels of tension as can be seen by increasing out-of-plane torsion with regard to the terephthalate carboxylate groups. Moreover, there seems to be a correlation between the level of strain on the aromatic ligands and the reduction of the number of carboxylate oxygen atoms that are part of the coordination polyhedra.     

On the numerical treatment of a small divisor problem

Summary Quasiperiodic solutions of perturbed integrable Hamiltonian equations such as weakly coupled harmonic oscillators can be found by constructing an appropriate coordinate transformation which leads to a small divisor problem. However the numerical difficulties are not merely caused by the small divisors but rather by the appearence of ghost solutions, which appear in any reasonable discretization of the problem. Our numerical treatment, based on a Newton-type iteration, guarantees an approximation of the relevant solution of the nonlinear problem. Numerical solutions are found up to a critical value of the coupling constant, which is much larger than the coupling constants allowed by the existence theory available so far.