A Characterization of Cosmological Time Functions

A characterization of time functions on a spacetime is made by using theMöbius equation. It is shown that a time function characterized in this wayyields past timelike geodesic incompleteness and local Lorentzian warpedproduct decomposition of spacetime, provided that the stress-energy tensoris a fluid. Also, by imposing additional assumptions on the stress-energytensor and global analytic structure of the spacetime, more restrictivedecompositions closer to Robertson–Walker spacetimes are obtained.     

Non-gravitating scalars and spacetime compactification

We discuss role of partially gravitating scalar fields, scalar fields whose energy–momentum tensors vanish for a subset of dimensions, in dynamical compactification of a given set of dimensions. We show that the resulting spacetime exhibits a factorizable geometry consisting of usual four-dimensional spacetime with full Poincaré invariance times a manifold of extra dimensions whose size and shape are determined by the scalar field dynamics. Depending on the strength of its coupling to the curvature scalar, the vacuum expectation value (VEV) of the scalar field may or may not vanish. When its VEV is zero the higher-dimensional spacetime is completely flat and there is no compactification effect at all. On the other hand, when its VEV is nonzero the extra dimensions get spontaneously compactified. The compactification process is such that a bulk cosmological constant is utilized for curving the extra dimensions.     

Novel Enantioselective Synthesis of Both Enantiomers of Furan‐2‐yl Amines and Amino Acids

A new enantioselective synthesis of furan‐2‐yl amines and amino acids is described, in which the key step is the oxazaborolidine‐catalyzed enantioselective reduction of O‐benzyl (E)‐ and (Z)‐furan‐2‐yl ketone oximes to the corresponding chiral amines. The chirality of the furan‐2‐yl amines is fully controlled by the appropriate choice of the geometrical isomer of the O‐benzyl oxime. Oxidation of the furan ring furnished amino acids in high yields.     

Use of tetrahydropyrimidinium salts for highly efficient palladium-catalyzed cross-coupling reactions of aryl bromides and chlorides

New, sterically demanding 1,3-dialkyl-3,4,5,6-tetrahydropyrimidinium salts (2) as NHC precursors have been synthesized and characterized. These salts, in combination with palladium acetate, provided active catalysts for the cross-coupling of aryl chlorides and bromides under mild conditions. The catalytic system was applied to the Heck, Suzuki and benzaldehyde (Kumada) coupling reactions. Catalyst activity was found to be influenced by the presence of a methoxy group on the ring of the p-position of benzyl substituent of the ligand precursor.     

Synthesis and structure of cyclopropano-annelated homosesquinorbornene derivatives containing pyramidalized double bonds: evidence for the sterical effect of a cyclopropyl group on the degree of C=C double-bond pyramidalization

[reaction: see text] endo- and exo-2,3,4,7-tetrahydro-1H-1,4-methanobenzocycloheptene-7-carboxylic acid ethyl esters have been synthesized, and their Diels-Alder cycloaddition reactions with maleic anhydride, dimethyl acetylenedicarboxylate and singlet oxygen have been investigated. The X-ray analysis of four adducts indicated the pyramidalization of the central double bond. Density functional theory calculations on the isolated products and model compounds showed excellent agreement between the experimental and theoretical determined butterfly angles. Furthermore, it has been shown that a cyclopropyl group fused to [2.2.2] system decreases significantly the degree of the pyramidalization which is attributed to the steric interactions between the cyclopropyl group and ethano bridge of the norbornene systems. Due to the instability of the bicyclic endoperoxides, their X-ray analysis could not be carried out. DFT calculations on model compounds showed increased bending in the case of the product obtained by the addition of singlet oxygen to endo-2,3,4,7-tetrahydro-1H-1,4-methanobenzocycloheptene-7-carboxylic acid ethyl ester.     

Enantioselective reduction of ketones with borane catalyzed by cyclic β- amino alcohols prepared from proline

New catalysts have been prepared from (S)- and (R)- proline and the asymmetric borane reduction of prochiral ketones using these catalysts has been studied. The secondary alcohols were obtained in 76–95% yield with 57– 96% enantiomeric excesses.     

Selective one-pot synthesis of substituted pyrrole-3-phosphonates from α-cyanomethyl-β-ketoesters

A one-step synthesis of 5-alkoxypyrrole-3-phosphonates is presented starting from suitable α-cyanomethyl-β-ketophosphonates. The key step in the synthesis involves a one-pot addition and heteroannulation sequence. The zinc perchlorate-catalyzed addition of alcohols to the nitrile carbon of α-cyanomethyl-β-ketophosphonates followed by annulation furnished 5-alkoxypyrrole-3-phosphonates. The addition-annulation process is carried out in the presence of water and 4,5-dihydro-5-oxo-1H-pyrrole-3-phosphonates (pyrrolinones) are obtained in good yields.     

Eta6-mesityl,eta1-imidazolinylidene-carbene-ruthenium(II) complexes: catalytic activity of their allenylidene derivatives in alkene metathesis and cycloisomerisation reactions

The reaction of electron-rich carbene-precursor olefins containing two imidazolinylidene moieties [(2,4,6-Me(3)C(6)H(2)CH(2))NCH(2)CH(2)N(R)Cdbond;](2) (2a: R=CH(2)CH(2)OMe, 2 b R=CH(2)Mes), bearing at least one 2,4,6-trimethylbenzyl (R=CH(2)Mes) group on the nitrogen atom, with [RuCl(2)(arene)](2) (arene=p-cymene, hexamethylbenzene) selectively leads to two types of complexes. The cleavage of the chloride bridges occurs first to yield the expected (carbene) (arene)ruthenium(II) complex 3. Then a further arene displacement reaction takes place to give the chelated eta(6)-mesityl,eta(1)-carbene-ruthenium complexes 4 and 5. An analogous eta(6)-arene,eta(1)-carbene complex with a benzimidazole frame 6 was isolated from an in situ reaction between [RuCl(2)(p-cymene)](2), the corresponding benzimidazolium salt and cesium carbonate. On heating, the RuCl(2)(imidazolinylidene) (p-cymene) complex 8, with p-methoxybenzyl pendent groups attached to the N atoms, leads to intramolecular p-cymene displacement and to the chelated eta(6)-arene,eta(1)-carbene complex 9. On reaction with AgOTf and the propargylic alcohol HCtbond;CCPh(2)OH, compounds 4-6 were transformed into the corresponding ruthenium allenylidene intermediates (4-->10, 5-->11, 6-->12). The in situ generated intermediates 10-12 were found to be active and selective catalysts for ring-closing metathesis (RCM) or cycloisomerisation reactions depending on the nature of the 1,6-dienes. Two complexes [RuCl(2)[eta(1)-CN(CH(2)C(6)H(2)Me(3)-2,4,6)CH(2)CH(2)N- (CH(2)CH(2)OMe)](C(6)Me(6))] 3 with a monodentate carbene ligand and [RuCl(2)[eta(1)-CN[CH(2)(eta(6)-C(6)H(2)Me(3)-2,4,6)]CH(2)CH(2)N-(CH(2)C(6)H(2)Me(3)-2,4,6)]] 5 with a chelating carbene-arene ligand were characterised by X-ray crystallography.     

A new and efficient chemoenzymatic route to both enantiomers of 4-hydroxycyclohex-2-en-1-one

[reaction: see text] A chemoenzymatic synthesis of both enantiomers of the pharmacologically interesting 4-hydroxycyclohex-2-en-1-one in three steps starting from 3-methoxycyclohex-2-en-1-one is described. Manganese(III) acetate-mediated acetoxylation followed by enzyme-mediated hydrolysis of alpha-acetoxy enone affords acetoxy enone 3 and hydroxy enone 4 with high enantiomeric excesses and in good yields. The reduction of the acetoxy and hydroxy enones furnished both enantiomers of 4-hydroxycyclohex-2-en-1-one in high enantiomeric excess.     

Synthesis of a bipyridine-derived achiral thiourea trifluoromethanesulfonic acid salt and its application as an additive in organocatalytic asymmetric reactions

The host–guest complex of a proline–thiourea bipyridine trifluoromethanesulfonic acid salt can catalyze organocatalytic asymmetric reactions such as aldol, Michael, and Mannich in polar protic medium with high stereoselectivities. The privileged bipyridine backbone and the thiourea motif are essential to the activity and enantioselectivity through hydrogen bonding interactions.