Incomplete idempotent Schröder quasigroups and related packing designs

Summary In this paper it is proved that, for any positive integern 2, 3 (mod 4),n 7, there exists an incomplete idempotent Schröder quasigroup with one hole of size two IISQ(n, 2) except forn = 10. It is also proved that for any positive integern 0, 1 (mod 4), there exists an idempotent Schröder quasigroup ISQ(n) except forn = 5 and 9. These results completely determine the spectrum of ISQ(n) and provide an application to the packing of a class of edge-coloured block designs.Research supported by NSERC grant A-5320.Research supported by NSFC grant 19231060-2.     

Ditungsten Siloxide Hydrides, [(silox)(2)WH(n)()](2) (n = 1, 2; silox = (t)BuSiO), and Related Complexes

The addition of 4.0 equiv of Na(silox) to Na[W(2)Cl(7)(THF)(5)] afforded (silox)(2)ClW&tbd1;WCl(silox)(2) (1, 65%). Treatment of 1 with 2.0 equiv of MeMgBr in Et(2)O provided (silox)(2)MeW&tbd1;WMe(silox)(2) (2, 81%). In the presence of 1 atm of H(2), reduction of 1 with 2.0 equiv of Na/Hg in DME provided (silox)(2)HW&tbd1;WH(silox)(2) (3, 70%), characterized by a hydride resonance at delta 19.69 (J(WH) = 325 Hz, (1)H NMR). Exposure of 2 to 1 atm of H(2) yielded 3 and CH(4) via (silox)(2)HW&tbd1;WMe(silox)(2) (4); use of D(2) led to [(silox)(2)WD](2) (3-d(2)). Exposure of 3 to ethylene ( approximately 1 atm, 25 degrees C) in hexanes generated (silox)(2)EtW&tbd1;WEt(silox)(2) (5), but solutions of 5 reverted to 3 and free C(2)H(4) upon standing. NMR spectral data are consistent with a sterically locked, gauche, C(2) symmetry for 1-5. Thermolysis of 3 at 100 degrees C (4 h) resulted in partial conversion to (silox)(2)HW&tbd1;W(OSi(t)Bu(2)CMe(2)CH(2))(silox) (6a, approximately 60%) and free H(2), while extended thermolysis with degassing (5 d, 70 degrees C) produced a second cyclometalated rotational isomer, 6b (6a:6b approximately 3:1). When left at 25 degrees C (4 h) in sealed NMR tubes, 6 and free H(2) regenerated 3. Reduction of 1 with 2.0 equiv of Na/Hg in DME also afforded 6a (25%). When 3 was exposed to approximately 3 atm of H(2), equilibrium amounts of [(silox)(2)WH(2)](2) (7) were observed by (1)H NMR spectroscopy (3 + H(2) right harpoon over left harpoon 7; 25.9-88.7 degrees C, DeltaH = -9.6(4) kcal/mol, DeltaS = -21(2) eu). Benzene solutions of 3 and 1-3 atm of D(2) revealed incorporation of deuterium into the silox ligands, presumably via intermediate 6. In sealed tubes containing [(silox)(2)WCl](2) (1) and dihydrogen (1-3 atm), (1)H NMR spectral evidence for [(silox)(2)WCl](2)(&mgr;-H)(2) (8) was obtained, suggesting that formation of 3 from 1 proceeded via reduction of 8. Alternatively, 3 may be formed from direct reduction of 1 to give [(silox)(2)W](2) (9), followed by H(2) addition. Hydride chemical shifts for 7 are temperature dependent, varying from delta 1.39 (-70 degrees C, toluene-d(8)), to delta 3.68 (90 degrees C). (29)Si{(1)H} NMR spectra revealed a similar temperature dependence of the silox (delta 12.43, -60 degrees C, to delta 13.64, 45 degrees C) resonances. These effects may arise from thermal population of a low-lying, deltadelta, paramagnetic excited state of D(2)(d)() [(silox)(2)W](2)(&mgr;-H)(4) (DeltaE approximately 2.1 kcal/mol, chi(7a) approximately 0.03), an explanation favored over thermal equilibration with an energetically similar but structurally distinct isomer (e.g., [(silox)(2)WH(2)](2)(&mgr;-H)(2), DeltaG degrees approximately 0.69 kcal/mol, chi(7b) approximately 0.25) on the basis of spectral arguments. Extended Hückel and ab initio molecular orbital calculations on model complexes [(H(3)SiO)(2)W](2)(&mgr;-H)(4) (staggered bridged 7a', EHMO), [(H(3)SiO)(2)WH(2)](2) (all-terminal 7b', EHMO), [(H(3)SiO)(2)W](2) (9', EHMO), (HO)(4)W(2)(H(4)) (staggered-bridged 7", ab initio), and (HO)(4)W(2)(H(4)) (bent-terminal 7, ab initio) generally support the explanation of a thermally accessible excited state and assign 7 a geometry intermediate between the all-terminal and staggered-bridged forms.     

Oxidative addition of dialkylphosphites to complexes of iridium(I) and rhodium(I)

The PH bond of dialkylphosphites (dimethylphosphite, 5,5-dimethyl-1,3-dioxa-2-phosphorinane and 4,4,5,5-tetramethyl-1,3-dioxa-2-phospholane) oxidatively adds to irClL₂(L = PPh₃, AsPh₃) and IrCl(PMe₂Ph)₃ generated in situ to give six-coordinate hydrido(dialkylphosphonato)iridium(III) complexes, e.g. IrHClL₂[{(MeO)₂-PO}₂H] and IrHCl(PMe₂Ph)₃[PO(OMe)₂]. Addition of triphenylphosphine to a solution containing [IrCl(C₈H₁₄)₂]₂ and dimethylphosphite in a 1:2 mol ratio gives a five-coordinate hydrido (dimethylphosphonato)iridium(III) complex IrHCl(PPh₃)₂{PO(OMe)₂}, from which six-coordinate pyridine and acetylacetonato complexes IrHCl(PPh₃)₂(C₅H₅N){PO(OMe)₂} and IrH(PPh₃)₂(acac){PO(OMe)₂} can be obtained. The ligand arrangements in the various complexes are inferred from IR, ¹H and ³¹P NMR data.     

Spongistatin synthetic studies. An efficient, second-generation construction of an advanced ABCD intermediate

[reaction: see text] A short, efficient, and stereocontrolled synthesis of (-)-4, an advanced ABCD subunit of the spongistatins, has been achieved. Central to the synthetic strategy is the multicomponent linchpin union of silyl dithianes with epoxides to access both the AB and CD fragments. Fragment coupling was then achieved via an efficient stereoselective aldol reaction. The linear sequence required 22 steps and proceeded in 4.0% overall yield.