Chromatic polynomials and whitney's broken circuits

The theorem of Hassler Whitney, which gives the chromatic polynomial of a graph in terms of “broken circuits,” is used to derive a new formula for the coefficients of chromatic polynomials.     

Palladium-catalyzed 1,4-acetoxy-trifluoroacetoxylation of 1,3-dienes

Palladium-catalyzed oxidation of conjugated dienes in acetic acid containing CF₃COOH/LiOOCCF₃ results in the formation of 1-acetoxy-4-trifluoroacetoxy-2-alkenes.     

Solvent-free methylthiomethyllithium [LiCH2SMe]infinity: solid state structure and thermal decomposition

Solvent-free [LiCH2SMe]infinity forms a layer structure consisting of four- (Li2C2), five- (Li2CS2), and six-membered (Li2C2S2) rings in the solid state; the compound violently explodes upon heating to T=160+/-5 degrees C under an argon atmosphere.     

Chemistry of the phenoxathiins and isosterically related heterocycles. XVIII. The synthesis, 1H- and 13C-NMR Spectroscopy of benzo[b]-1,4,9-triazaphenoxathiin

The first synthesis of a triazaphenoxathiin system, benzo[b]-1,4,9-triazaphenoxathiin, is reported. Attempts directed toward the total assignment of the ¹³C-nmr spectrum of the title compound failed to produce an unequivocal assignment. The carbons of the benzo-portion of the molecule could not be unequivocally assigned at 25.2 MHz but were subgrouped into permutable pairs of resonances on the basis of relaxation times, a result of the antisotropic reorientation of the molecule. Further attempts to complete the ¹³C-nmr assignment at 100 MHz by selective on-resonance decouplings in the 400 MHz ¹H-nmr spectrum were also unsuccessful because of similarities in the chemical shifts of the benzo-protons. Complete ¹H-nmr chemical shifts and homo-nuclear spin-coupling constants were obtained using the PANIC program.     

The reaction of 2,4-diamino-6-piperidinopyrimidine 3-oxide with acid anhydrides

2,4-Diamino-6-piperidinopyrimidine 3-oxide reacts preferentially with acid anhydrides at the 4-amino group. The structures of amide products are readily assigned by the position of the 5-H.     

Stereospecific palladium-catalyzed 1,4-acetoxychlorination of 1,3-dienes

Palladium-catalyzed oxidation of 1,3-dienes in acetic acid in the presence of LiCl and LiOAc produces 1-acetoxy-4-chloro-2-alkenes in high selectivity. The 1,4-adducts were stereo- and regioselectively functionalized.     

The time-symmetric initial value problem for a homogeneous,anisotropic, empty,closed universe,using Regge calculus

Models for a homogeneous, anisotropic, empty, closed universe at a particular moment of time are constructed from sets of empty tetrahedra. It is shown using Regge calculus that only two such models have a moment of time symmetry.On leave from Girton College, Cambridge CB3 OJG, and Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge CB3 9EW, England.     

Bulky 4-phosphacyclohexanones: diastereoselective complexations, orthometallations and unprecedented [3.1.1]metallabicycles

The 4-phosphacyclohexanones, 2,2,6,6-tetramethyl-1-phenyl-4-phosphorinanone (La), 1,2,6-triphenyl-4-phosphorinanone ((Ph)Lb), 1-cyclohexyl-2,6-diphenyl-4-phosphorinanone ((Cy)Lb) and 1-tert-butyl-2,6-diphenyl-4-phosphorinanone ((Bu)Lb) have been made by modifications of literature methods. Phosphines (R)Lb are each formed as mixtures of meso- and rac-diastereoisomers. Isomerically pure rac-(Ph)Lb, rac-(Cy)Lb and meso-(Bu)Lb can be isolated by recrystallisation from MeCN. Heating mixtures of isomers of (R)Lb with TsOH leads to isomerisations to give predominantly the meso-(R)Lb. The complex trans-[PdCl2(La)2] (1) is readily made from [PdCl2(NCPh)2] but the analogous platinum complex 2 has not been detected and instead, cyclometallation at the 3-position (alpha to the ketone) in the phosphacycle occurs to give trans-[PtCl(La)(La-3H)] (3) (where La-3H = La deprotonated at the 3-position) featuring a [3.1.1]metallabicycle as confirmed by X-ray crystallography. The analogous palladabicycle 4 has been detected upon treatment of 1 with Et3N in refluxing toluene. The type of complex formed by (R)Lb depends on which diastereoisomer (meso or rac) is involved. rac-(Ph)Lb (a mixture of R,R- and S,S-enantiomers, labelled alpha and beta) forms trans-[MCl2(rac-(Ph)Lb)2], M = Pd (5) or Pt (6), as mixtures of diastereoisomers (alphaalpha/betabeta and alphabeta forms). The structure of alphaalpha-6 has been determined by X-ray crystallography. Ligand competition experiments monitored by 31P NMR showed that Pd(II) and Pt(II) have a significant preference to bind rac-(Ph)Lb over meso-(Ph)Lb. meso-(Bu)Lb reacts with [PtCl2(NCBu(t))2] under ambient conditions to give the binuclear complex [Pt2Cl2(meso-(Bu)Lb-2'H)2] (7) where orthometallation has occurred on one of the exocyclic phenyl substituents as confirmed by X-ray crystallography. rac-(Bu)Lb reacts with [PtCl2(NCBu(t))2] to give a mononuclear cyclometallated species assigned the structure trans-[PtCl(rac-(Bu)Lb-2'H)((Bu)Lb)] (8) on the basis of its 31P NMR spectrum. rac-(Cy)Lb reacts with [PtCl2(NCBu(t))2] in refluxing toluene to give trans-[PtCl2(rac-(Cy)Lb)2] (9) and the crystal structure of alphabeta-9 has been determined.