Experimental and theoretical investigations of lithium and magnesium derivatives of bis(tert-butylamido)cyclodiphosph(III/V)- and (V/V)azane mono- and ditellurides

Deprotonation of bis(tert-butylamido)cyclophosph(III/III)azane with organolithium or organomagnesium reagents followed by oxidation with elemental tellurium is a viable approach to the preparation of metal cyclodiphosphazane mono- and ditellurides. The reaction of the cyclodiphosph(III)azane [tBu(H)NP(mu-NtBu)2PN(H)tBu] (1) with elemental tellurium in boiling toluene affords the monotelluride [tBu(H)N(Te)P(mu-NtBu)2PN(H)tBu] (9). A similar reaction involving the magnesium salt Mg[tBuNP(mu-NtBu)2PNtBu](THF)2 (2) also yields a monotelluride Mg[tBuN(Te)P(mu-NtBu)2PNtBu]-(THF)2 (10). By contrast, reaction of the lithium salt Li2[tBuNP(mu-NtBu)2PNtBu](THF)2 (3) with tellurium results in double oxidation and the formation of the ditellurides Li2[tBuN(Te)P(mu-NtBu)2P(Te)NtBu](THF)4 (11) and Li2-[tBuN(Te)P(mu-NtBu)2P(Te)NtBu](tmeda)2 (12). Compounds 9-12 have been characterized by multinuclear (1H, 7Li, 13C, 31P, and 125Te) NMR, while 9, 10, and 12 have also been characterized by X-ray crystallography. The structure of 9 reveals a typical cis/endo, exo arrangement, with no intermolecular contacts to tellurium. The seco-heterocubic structure, observed in 2, is retained in 10, with the ligand chelating magnesium in an N,N',N"-manner. Unique coordination behavior is exhibited by the ditelluride 12, in which the dianionic ligand is attached to the two lithium centers in both Te,Te' and Te,N bonding modes. Multinuclear NMR data are consistent with retention of the solid-state structures of 9-12 in solution at low temperatures. The reactivity of cyclodiphosph(III/III)azanes toward chalcogens is rationalized by using theoretical calculations (semiempirical PM3 level of theory), which show an inverse correlation between the charge at the phosphorus center and the ease of oxidation.     

Syntheses and X-ray structures of monocyclic,bicyclic, and spirocyclic gallium and indium boraamidinates

The reactions of [Li(2)[PhB(N(t)Bu)(2)]](2) with GaCl(3) in various stoichiometries yield [Li(thf)(4)][PhB(mu-N(t)Bu)(2)GaCl(2) x GaCl(3)] (1), [PhB(mu-N(t)Bu)(2)GaCl](2) (2), and [mu-Li(OEt(2))[PhB(N(t)Bu)(2)]Ga] (3a), a series of complexes in which the three chloride ligands are successively replaced by the dianion [PhB(N(t)Bu)(2)](2-). The X-ray structures of 1, 2, and 3a show that the boraamidinate ligand adopts an N,N'-chelating mode. In the ion-separated complex 1, one of the nitrogen atoms is coordinated to a GaCl(3) molecule. The related indium complexes [mu-LiCl(thf)(2)][PhB(mu-N(t)Bu)(2)InCl](2) (4) and [mu-Li(OEt(2))[PhB(mu-N(t)Bu)(2)]In] (3b) were obtained in a similar manner. Complex 4 is the indium analogue of 2 with the incorporation of a bissolvated LiCl molecule. In 3a and 3b the spirocyclic [[PhB(mu-N(t)Bu)(2)](2)M](-) (M = Ga, In) anions are N,N'-chelated to the [Li(OEt(2))](+) counterion. Prolonged reactions result in the formation of [PhB(mu-N(t)Bu)(2)GaCl][(t)BuN(H)GaCl(2)] (5) and [[PhB(mu-N(t)Bu)(2)InCl][(t)BuN(H)InCl(2)][mu-LiCl(OEt(2))(2)]] (6), respectively. The X-ray structures of 5 and 6 reveal bicyclic structures which formally involve the entrapment of the monomers (t)BuN(H)MCl(2) by a four-membered BN(2)M ring (M = Ga, In). The synthesis and X-ray structure of Cl(2)Ga[mu-N(H)(t)Bu](2)GaCl(2) are also reported.     

Cubic and spirocyclic radicals containing a tetraimidophosphate dianion [P(NR)3(NR')]*2-

The reaction of Cl(3)PNSiMe(3) with 3 equiv of LiHNR (R = (i)Pr, Cy, (t)Bu, Ad) in diethyl ether produces the corresponding tris(amino)(imino)phosphoranes (RNH)(3)PNSiMe(3) (1a, R = (i)Pr; 1b, R = Cy; 1c, R = (t)Bu; 1d, R = Ad); subsequent reactions of 1b-d with (n)BuLi yield the trilithiated tetraimidophosphates {Li(3)[P(NR)(3)(NSiMe(3))]} (2a, R = Cy; 2b, R = (t)Bu; 2c, R = Ad). The reaction of [((t)BuNH)(4)P]Cl with 1 equiv of (n)BuLi results in the isolation of ((t)BuNH)(3)PN(t)Bu (1e); treatment of 1e with additional (n)BuLi generates the symmetrical tetraimidophosphate {Li(3)[P(N(t)Bu)(4)]} (2d). Compounds 1 and 2 have been characterized by multinuclear ((1)H, (13)C, and (31)P) NMR spectroscopy; X-ray structures of 1b,c were also obtained. Oxidations of 2a-c with iodine, bromine, or sulfuryl chloride produces transient radicals in the case of 2a or stable radicals of the formula {Li(2)[P(NR)(3)(NSiMe(3))]LiX.3THF}* (X = Cl, Br, I; R = (t)Bu, Ad). The stable radicals exhibit C(3) symmetry and are thought to exist in a cubic arrangement, with the monomeric LiX unit bonded to the neutral radical {Li(2)[P(NR)(3)(NSiMe(3))]}* to complete the Li(3)N(3)PX cube. Reactions of solvent-separated ion pair {[Li(THF)(4)]{Li(THF)(2)[(mu-N(t)Bu)(2)P(mu-N(t)Bu)(2)]Li(THF)(2)} (6) with I(2) or SO(2)Cl(2) produce the persistent spirocyclic radical {(THF)(2)Li(mu-N(t)Bu)(2)P(mu-N(t)Bu)Li(THF)(2)}* (10a); all radicals have been characterized by a combination of variable concentration EPR experiments and DFT calculations.     

Preparation and structural characterization of (Me(3)SiNSN)(2)Se, a new synthon for sulfur-selenium nitrides

The reaction of (Me(3)SiN)(2)S with SeCl(2) (2:1 ratio) in CH(2)Cl(2) at -70 degrees C provides a route to the novel mixed selenium-sulfur-nitrogen compound (Me(3)SiNSN)(2)Se (1). Crystals of 1 are monoclinic and belong the space group P2(1)/c, with a = 7.236(1) A, b = 19.260(4) A, c = 11.436(2) A, beta = 92.05(3) degrees, V = 1592.7(5) A(3), Z = 4, and T = -155(2) degrees C. The NSNSeNSN chain in 1 consists of Se-N single bonds (1.844(3) A) and S=N double bonds (1.521(3)-1.548(3) A) with syn and anti geometry at the N=S=N units. The N-Se-N bond angle is 91.8(1) degrees. The EI mass spectrum shows a molecular ion with good agreement between the observed and calculated isotopic distributions. The (14)N NMR spectrum exhibits two resonances at -65 and -77 ppm. Both (13)C and (77)Se NMR spectra show single resonances at 0.83 and 1433 ppm, respectively. The reaction of 1 with an equimolar amount of SeCl(2) produces 1,5-Se(2)S(2)N(4) (2) in a good yield, and that of (Me(3)SiNSN)(2)S with SCl(2) affords S(4)N(4) (3), but the reactions of (Me(3)SiNSN)(2)Se with SCl(2) and (Me(3)SiNSN)(2)S with SeCl(2) result in the formation of a mixture of 2 and 3. A likely reaction pathway involves the intermediate formation of E(2)N(2) fragments (E = S, Se).     

A Ten‐membered Dimetallacycle with an [Ag···Ag]2+ Dication Bridged by Two P,N Ligands

The reaction of silver hexafluoridoantimonate with Ph₂PCH₂PPh₂NSiMe₃ ( 1 ) in dichloromethane produces the dimeric complex [Ag(μ‐Ph₂PCH₂PPh₂NSiMe₃)]₂[SbF₆]₂ ( 2 ), in which two heterobifunctional ligands 1 in the dication are N, P‐chelated in a head‐to‐tail fashion to a [Ag ··· Ag]²⁺ unit that exhibits an Ag ··· Ag contact of 2.8530(6) Å. Quantum theory of atoms‐in‐molecules (QTAIM) analysis of the bonding revealed an attractive interaction between the two silver atoms.     

Synthesis and X‐ray Structures of the Polycyclic Dimers {[PhB(μ‐NtBu)2AsN(tBu)H]LiI}2 and [PhB(μ‐NtBu)2AsN(tBu)Li]2

The metathesis of [PhB(μ‐NtBu)₂]AsCl and tBuN(H)Li in 1:1 molar ratio in diethyl ether produced the amido derivative [PhB(μ‐NtBu)₂AsN(tBu)H] ( 1 ) in good yield. The lithiation of 1 with one equivalent of nBuLi afforded the lithium salt [PhB(μ‐NtBu)₂AsN(tBu)Li] ( 2a ). Both 1 and 2a were characterized by multinuclear NMR spectroscopy. The crystal structure of 2a is comprised of a U‐shaped, centrosymmetric dimer in which the monomeric [PhB(μ‐NtBu)₂AsN(tBu)]^?Li⁺ units are linked by Li‐N interactions to give a six‐rung ladder. Oxidation of 2a with one‐half equivalent of I₂ in diethyl ether resulted in hydrogen abstraction from the solvent to give the dimeric lithium iodide adduct {[PhB(μ‐NtBu)₂AsN(tBu)H]LiI}₂ ( 1 ·LiI) with a central Li₂I₂ ring.     

Dynamics of matter-wave solitons in a ratchet potential

We study the dynamics of bright solitons formed in a Bose-Einstein condensate with attractive atomic interactions perturbed by a weak bichromatic optical lattice potential. The lattice depth is a biperiodic function of time with a zero mean, which realizes a flashing ratchet for matter-wave solitons. We find that the average velocity of a soliton and the soliton current induced by the ratchet depend on the number of atoms in the soliton. As a consequence, soliton transport can be induced through scattering of different solitons. In the regime when matter-wave solitons are narrow compared to the lattice period the dynamics is well described by the effective Hamiltonian theory.     

Coinage Metal Complexes of a Tellurium Diimide: cis→trans Isomerization and Metal–Metal Interactions

The different coordination behavior of the ligand tBuN=Te(μ-NtBu)₂Te=NtBu (L) towards Cu⁺ and Ag⁺ results from a cis→trans isomerization. The two Cu⁺ ions in [Cu₂L₃]²⁺ (shown schematically) bridge trans and cis isomers of the ligand, whereas the Ag⁺ ions in [Ag₂L₂]²⁺ link two trans ligands and exhibit a weak Ag⋅⋅⋅Ag interaction.     

Small Chvátal Rank

We propose a variant of the Chvátal-Gomory procedure that will produce a sufficient set of facet normals for the integer hulls of all polyhedra {x : A x ≤ b} as b varies. The number of steps needed is called the small Chvátal rank (SCR) of A. We characterize matrices for which SCR is zero via the notion of supernormality which generalizes unimodularity. SCR is studied in the context of the stable set problem in a graph, and we show that many of the well-known facet normals of the stable set polytope appear in at most two rounds of our procedure. Our results reveal a uniform hypercyclic structure behind the normals of many complicated facet inequalities in the literature for the stable set polytope. Lower bounds for SCR are derived both in general and for polytopes in the unit cube.     

Ratchet-induced matter-wave transport and soliton collisions in Bose-Einstein condensates

We study the dynamics of bright matter-wave solitons in a Bose-Einstein condensate with negative scattering length under the influence of a time-periodic ratchet potential. The potential is formed by a one-dimensional bichromatic optical lattice which flashes on and off so that the time average of its amplitude vanishes. Due to the broken space and time-reversal symmetries of the potential, the soliton is transported with a nonzero average velocity. By employing the non-dissipative mean-field model for the matter waves, we study the dependence of the transport velocity on the initial state of the soliton and show how the properties of the individual localized states affect the outcome of their collisions. A useful insight into the transport properties is provided by Hamiltonian theory for the mean field, which treats the extended matter-wave excitation as an effective classical particle.