General Relativistic Shock Waves that Extend the Oppenheimer-Snyder Model

In earlier work we constructed a class of spherically symmetric, fluid dynamical shock waves that satisfy the Einstein equations of general relativity. These shock waves extend the celebrated Oppenheimer-Snyder result to the case of non-zero pressure. Our shock waves are determined by a system of ordinary differential equations that describe the matching of a Friedmann-Robertson-Walker metric (a cosmological model for the expanding universe) to an Oppenheimer-Tolman metric (a model for the interior of a star) across a shock interface. In this paper we derive an alternate version of these ordinary differential equations, which are used to demonstrate that our theory generates a large class of physically meaningful (Lax-admissible) outgoing shock waves that model blast waves in a general relativistic setting. We also obtain formulas for the shock speed and other important quantities that evolve according to the equations. The resulting formulas are important for the numerical simulation of these solutions. (Accepted January 19, 1996)     

Isolation of Elusive HAsAsH in a Crystalline Diuranium(IV) Complex

The HAsAsH molecule has hitherto only been proposed tentatively as a short‐lived species generated in electrochemical or microwave‐plasma experiments. After two centuries of inconclusive or disproven claims of HAsAsH formation in the condensed phase, we report the isolation and structural authentication of HAsAsH in the diuranium(IV) complex [{U(Tren^TIPS)}₂(μ‐η²:η²‐As₂H₂)] ( 3 , Tren^TIPS=N(CH₂CH₂NSiPrⁱ₃)₃; Prⁱ=CH(CH₃)₂). Complex 3 was prepared by deprotonation and oxidative homocoupling of an arsenide precursor. Characterization and computational data are consistent with back‐bonding‐type interactions from uranium to the HAsAsH π*‐orbital. This experimentally confirms the theoretically predicted excellent π‐acceptor character of HAsAsH, and is tantamount to full reduction to the diarsane‐1,2‐diide form.     

Regioselectivity of the Claisen rearrangement in meta-allyloxy aryl ketones: an experimental and computational study, and application in the synthesis of (R)-(-)-pestalotheol D

A study of the regioselectivity of the Claisen rearrangement of meta-allyloxy aryl ketones showed that the electron-withdrawing carbonyl group has a major influence and strongly directs rearrangement to the more hindered ortho position. However, when the ketone is part of a ring structure, its electronic effect can be negated by conversion into its triisopropylsilyl enol ether, which dramatically reverses the regiochemistry of the Claisen rearrangement. DFT calculations suggest that the effect is electronic although there is also a steric effect of the bulky silyl group. This strategy for influencing the regiochemical outcome of the Claisen rearrangement was then employed in a short synthesis of the furo[2,3-g]chromene, (-)-pestalotheol D, that confirms the absolute stereochemistry of the natural product.     

Redox non-innocence of thioether crowns: spectroelectrochemistry and electronic structure of formal nickel(III) complexes of aza-thioether macrocycles

The Ni^II complexes [Ni([9]aneNS₂‐CH₃)₂]²⁺ ([9]aneNS₂‐CH₃=N‐methyl‐1‐aza‐4,7‐dithiacyclononane), [Ni(bis[9]aneNS₂‐C₂H₄)]²⁺ (bis[9]aneNS₂‐C₂H₄=1,2‐bis‐(1‐aza‐4,7‐dithiacyclononylethane) and [Ni([9]aneS₃)₂]²⁺ ([9]aneS₃=1,4,7‐trithiacyclononane) have been prepared and can be electrochemically and chemically oxidized to give the formal Ni^III products, which have been characterized by X‐ray crystallography, UV/Vis and multi‐frequency EPR spectroscopy. The single‐crystal X‐ray structure of [Ni^III([9]aneNS₂‐CH₃)₂](ClO₄)₆?(H₅O₂)₃ reveals an octahedral co‐ordination at the Ni centre, while the crystal structure of [Ni^III(bis[9]aneNS₂‐C₂H₄)](ClO₄)₆?(H₃O)₃? 3H₂O exhibits a more distorted co‐ordination. In the homoleptic analogue, [Ni^III([9]aneS₃)₂](ClO₄)₃, structurally characterized at 30 K, the Ni? S distances [2.249(6), 2.251(5) and 2.437(2) Å] are consistent with a Jahn–Teller distorted octahedral stereochemistry. [Ni([9]aneNS₂‐CH₃)₂](PF₆)₂ shows a one‐electron oxidation process in MeCN (0.2 M NBu₄PF₆, 293 K) at E_1/2=+1.10 V versus Fc⁺/Fc assigned to a formal Ni^III/Ni^II couple. [Ni(bis[9]aneNS₂‐C₂H₄)](PF₆)₂ exhibits a one‐electron oxidation process at E_1/2=+0.98 V and a reduction process at E_1/2=?1.25 V assigned to Ni^II/Ni^III and Ni^II/Ni^I couples, respectively. The multi‐frequency X‐, L‐, S‐, K‐band EPR spectra of the 3+ cations and their 86.2 % ⁶¹Ni‐enriched analogues were simulated. Treatment of the spin Hamiltonian parameters by perturbation theory reveals that the SOMO has 50.6 %, 42.8 % and 37.2 % Ni character in [Ni([9]aneNS₂‐CH₃)₂]³⁺, [Ni(bis[9]aneNS₂‐C₂H₄)]³⁺ and [Ni([9]aneS₃)₂]³⁺, respectively, consistent with DFT calculations, and reflecting delocalisation of charge onto the S‐thioether centres. EPR spectra for [⁶¹Ni([9]aneS₃)₂]³⁺ are consistent with a dynamic Jahn–Teller distortion in this compound.     

The nature of unsupported uranium-ruthenium bonds: a combined experimental and theoretical study

Four new uranium-ruthenium complexes, [(Tren(TMS))URu(η(5)-C(5)H(5))(CO)(2)] (9), [(Tren(DMSB))URu(η(5)-C(5)H(5))(CO)(2)] (10), [(Ts(Tolyl))(THF)URu(η(5)-C(5)H(5))(CO)(2)] (11), and [(Ts(Xylyl))(THF)URu(η(5)-C(5)H(5))(CO)(2)] (12) [Tren(TMS)=N(CH(2)CH(2)NSiMe(3))(3); Tren(DMSB)=N(CH(2)CH(2)NSiMe(2)tBu)(3)]; Ts(Tolyl)=HC(SiMe(2)NC(6)H(4)-4-Me)(3); Ts(Xylyl)=HC(SiMe(2)NC(6)H(3)-3,5-Me(2))(3)], were prepared by a salt-elimination strategy. Structural, spectroscopic, and computational analyses of 9-12 shows: i) the formation of unsupported uranium-ruthenium bonds with no isocarbonyl linkages in the solid state; ii) ruthenium-carbonyl backbonding in the [Ru(η(5)-C(5)H(5))(CO)(2)](-) ions that is tempered by polarization of charge within the ruthenium fragments towards uranium; iii) closed-shell uranium-ruthenium interactions that can be classified as predominantly ionic with little covalent character. Comparison of the calculated U-Ru bond interaction energies (BIEs) of 9-12 with the BIE of [(η(5)-C(5)H(5))(3)URu(η(5)-C(5)H(5))(CO)(2)], for which an experimentally determined U-Ru bond disruption enthalpy (BDE) has been reported, suggests BDEs of approximately 150 kJ mol(-1) for 9-12.     

Characterization and dynamics of substituted ruthenacyclobutanes relevant to the olefin cross-metathesis reaction

The reaction of the phosphonium alkylidene [(H(2)IMes)RuCl(2)=CHP(Cy)(3))](+) BF(4)(-) with propene, 1-butene, and 1-hexene at -45 °C affords various substituted, metathesis-active ruthenacycles. These metallacycles were found to equilibrate over extended reaction times in response to decreases in ethylene concentrations, which favored increased populations of α-monosubstituted and α,α'-disubstituted (both cis and trans) ruthenacycles. On an NMR time scale, rapid chemical exchange was found to preferentially occur between the β-hydrogens of the cis and trans stereoisomers prior to olefin exchange. Exchange on an NMR time scale was also observed between the α- and β-methylene groups of the monosubstituted ruthenacycle (H(2)IMes)Cl(2)Ru(CHRCH(2)CH(2)) (R = CH(3), CH(2)CH(3), (CH(2))(3)CH(3)). EXSY NMR experiments at -87 °C were used to determine the activation energies for both of these exchange processes. In addition, new methods have been developed for the direct preparation of metathesis-active ruthenacyclobutanes via the protonolysis of dichloro(1,3-bis(2,4,6-trimethylphenyl)-2-imidazolidinylidene)(benzylidene) bis(pyridine)ruthenium(II) and its 3-bromopyridine analogue. Using either trifluoroacetic acid or silica-bound toluenesulfonic acid as the proton source, the ethylene-derived ruthenacyclobutane (H(2)IMes)Cl(2)Ru(CH(2)CH(2)CH(2)) was observed in up to 98% yield via NMR at -40 °C. On the basis of these studies, mechanisms accounting for the positional and stereochemical exchange within ruthenacyclobutanes are proposed, as well as the implications of these dynamics toward olefin metathesis catalyst and reaction design are described.     

Studies on transannulation reactions across a nine-membered ring: the synthesis of natural product-like structures

A series of diverse natural product-like structures have been synthesised by the use of a number of novel transannulation reactions across a cyclononene ring. Transannular cyclisations through oxygen functionality have generated a number of bicyclo[5.3.1]systems containing bridged cyclic ethers and bicyclo[5.2.2]lactones, as well as a tetrahydrofuran-containing bridged analogue of hexacyclinic acid. An unprecedented Br?nsted acid mediated transannular cyclisation between proximal carbons generated bicyclo[4.3.0]nonanes which form the core of the pinguisane and austrodorane families of sesquiterpenoids. In all cases the key factor that determined the mode of reactivity was the conformation of the nine-membered ring and the distance between the reacting centres.     

Halide, amide, cationic, manganese carbonylate, and oxide derivatives of triamidosilylamine uranium complexes

Treatment of the complex [U(Tren(TMS))(Cl)(THF)] [1, Tren(TMS) = N(CH(2)CH(2)NSiMe(3))(3)] with Me(3)SiI at room temperature afforded known crystalline [U(Tren(TMS))(I)(THF)] (2), which is reported as a new polymorph. Sublimation of 2 at 160 °C and 10(-6) mmHg afforded the solvent-free dimer complex [{U(Tren(TMS))(μ-I)}(2)] (3), which crystallizes in two polymorphic forms. During routine preparations of 1, an additional complex identified as [U(Cl)(5)(THF)][Li(THF)(4)] (4) was isolated in very low yield due to the presence of a slight excess of [U(Cl)(4)(THF)(3)] in one batch. Reaction of 1 with one equivalent of lithium dicyclohexylamide or bis(trimethylsilyl)amide gave the corresponding amide complexes [U(Tren(TMS))(NR(2))] (5, R = cyclohexyl; 6, R = trimethylsilyl), which both afforded the cationic, separated ion pair complex [U(Tren(TMS))(THF)(2)][BPh(4)] (7) following treatment of the respective amides with Et(3)NH·BPh(4). The analogous reaction of 5 with Et(3)NH·BAr(f)(4) [Ar(f) = C(6)H(3)-3,5-(CF(3))(2)] afforded, following addition of 1 to give a crystallizable compound, the cationic, separated ion pair complex [{U(Tren(TMS))(THF)}(2)(μ-Cl)][BAr(f)(4)] (8). Reaction of 7 with K[Mn(CO)(5)] or 5 or 6 with [HMn(CO)(5)] in THF afforded [U(Tren(TMS))(THF)(μ-OC)Mn(CO)(4)] (9); when these reactions were repeated in the presence of 1,2-dimethoxyethane (DME), the separated ion pair [U(Tren(TMS))(DME)][Mn(CO)(5)] (10) was isolated instead. Reaction of 5 with [HMn(CO)(5)] in toluene afforded [{U(Tren(TMS))(μ-OC)(2)Mn(CO)(3)}(2)] (11). Similarly, reaction of the cyclometalated complex [U{N(CH(2)CH(2)NSiMe(2)Bu(t))(2)(CH(2)CH(2)NSiMeBu(t)CH(2))}] with [HMn(CO)(5)] gave [{U(Tren(DMSB))(μ-OC)(2)Mn(CO)(3)}(2)] [12, Tren(DMSB) = N(CH(2)CH(2)NSiMe(2)Bu(t))(3)]. Attempts to prepare the manganocene derivative [U(Tren(TMS))MnCp(2)] from 7 and K[MnCp(2)] were unsuccessful and resulted in formation of [{U(Tren(TMS))}(2)(μ-O)] (13) and [MnCp(2)]. Complexes 3-13 have been characterized by X-ray crystallography, (1)H NMR spectroscopy, FTIR spectroscopy, Evans method magnetic moment, and CHN microanalyses.     

Synthesis and characterisation of complexes of the 2,6-diphenoxyphenyl ligand

The use of the 2,6-diphenoxyphenyl ligand has facilitated the stabilisation of lithium, silane and stannane complexes. The ortho-metallation reaction between 1,3-(PhO)₂C₆H₄ and ⁿBuLi yields 2,6-(PhO)₂C₆H₃Li (1); the crystallographically characterised dimer [2,6-(PhO)₂C₆H₃Li(OEt₂)]₂ ([1.Et₂O]₂) can be obtained by the crystallisation of 1 from diethyl ether. The reaction between 1 and Me₃ECl gives rise to the structurally authenticated complexes 2,6-(PhO)₂C₆H₃EMe₃ [E = Si, 2; E = Sn, 3].     

Highly porous and robust scandium-based metal-organic frameworks for hydrogen storage

The metal-organic frameworks NOTT-400 and NOTT-401, based on a binuclear [Sc(2)(μ(2)-OH)(O(2)CR)(4)] building block, have been synthesised and characterised; the desolvated framework NOTT-401a shows a BET surface area of 1514 m(2) g(-1) with a total H(2) uptake of 4.44 wt% at 77 K and 20 bar.