Versatile Ligands for Palladium-Catalyzed Asymmetric Allylic Alkylation

Palladium complexes of the chiral diphosphanes 1 and 2 which possess a rigid backbone and a large bite angle catalyze the alkylation of allyl compounds with both high enantioselectivities and reaction rates, particularly with less sterically demanding substrates. 1 : R=Me, X=S; 2 : R=H, X=C(CH₃)₂.     

Concise synthesis of (S,S)-(+)-dehydrohomoancepsenolide

A concise total synthesis of the bis-butenolide 3 in optically active form is reported. Key steps are a zinc-mediated "three-component coupling" with formation of dienyne 9 which undergoes ring closing metathesis (RCM) on treatment with (PCy(3))(2)Cl(2)Ru=CHPh. Dimerization of the resulting butenolide 11 is then achieved via alkyne metathesis using (tBuO)(3)W&tbd1;CCMe(3) as the catalyst. A Lindlar reduction completes this synthesis which delivers product 3 in only five steps with an overall yield of 25%.     

Die Kristallstrukturen der Hexachlorometallate NH4[SbCl6], NH4[WCl6], [K(18‐Krone‐6)(CH2Cl2)]2[WCl6]·6CH2Cl2 und (PPh4)2[WCl6]·4CH3CN

Crystal Structures of the Hexachlorometalates NH₄[SbCl₆], NH₄[WCl₆], [K(18‐crown‐6)(CH₂Cl₂)]₂[WCl₆]·6CH₂Cl₂ and (PPh₄)₂[WCl₆]·4CH₃CN The crystal structures of the title compounds were determined by single crystal X‐ray methods. NH₄[SbCl₆] and NH₄[WCl₆] crystallize isotypically in the space group C2/c with four formula units per unit cell. The NH₄⁺ ions occupy a twofold crystallographic axis, whereas the metal atoms of the [MCl₆]^— ions occupy a centre of inversion. There exist weak interionic hydrogen bridges. [K(18‐crown‐6)(CH₂Cl₂)]₂[WCl₆]·6CH₂Cl₂ crystallizes in the orthorhombic space group R3¯/m with Z = 3. The compound forms centrosymmetric ion triples, in which the potassium ions are coordinated with a WCl₃ face each. In trans‐position to it the chlorine atom of a CH₂Cl₂ molecule is coordinated so that, together with the oxygen atoms of the crown ether, coordination number 10 is achieved. (PPh₄)₂[WCl₆]·4CH₃CN crystallizes in the monoclinic space group P2₁/c with Z = 4. This compound, too, forms centrosymmetric ion triples, in which in addition the acetonitrile molecules are connected with the [WCl₆]^2— ion via weak C—H···Cl contacts.     

Maximum principles for submanifolds of arbitrary codimension and bounded mean curvature

We construct quadratic forms on which are subharmonic on any n-dimensional minimal submanifold in and, more generally, on submanifolds of bounded mean curvature. This leads to nonexistence results for connected n-dimensional minimal submanifolds in as well as to necessary conditions for the existence of connected submanifolds of bounded mean curvature with arbitrary codimension. Furthermore we discuss a barrier principle for n-dimensional submanifolds in of bounded mean curvature.Received: 11 November 2003, Accepted: 29 January 2004, Published online: 2 April 2004Mathematics Subject Classification (2000): 35J60, 49Q05, 53C42     

A Bernstein result for energy minimizing hypersurfaces

We show that there are no entire, positive, stable solutions in ⁿ of the Euler equation corresponding to the singular variational integral ,>0, if+n<5.236.... Furthermore we prove a related result for smooth boundaries of least-energy |x _n+1||D _U | in ⁿ⁺¹.