Ancillary ligand effects : from zirconium(IV)-catalyzed homogeneous propylene polymerization to platinum(II)-mediated C-H bond activation

<p>A series of C_s- and C₁-symmetric doubly-linked ansa-metallocenes of the general formula {1,1'-SiMe₂-2,2'-E-('��⁵-C₅H₂-4-R¹)-(��⁵-C₅H-3',5'-(CHMe₂)₂)}ZrC₂ (E = SiMe₂ (1), SiPh₂ (2), SiMe₂ -SiMe₂ (3); R¹ = H, CHMe₂, C₅H₉, C₆H₁₁, C₆H₅) has been prepared. When activated by methylaluminoxane, these are active propylene polymerization catalysts. 1 and 2 produce syndiotactic polypropylenes, and 3 produces isotactic polypropylenes. Site epimerization is the major pathway for stereoerror formation for 1 and 2. In addition, the polymer chain has slightly stronger steric interaction with the diphenylsilylene linker than with the dimethylsilylene linker. This results in more frequent site epimerization and reduced syndiospecificity for 2 compared to 1. </p> <p>C₁-Symmetric ansa-zirconocenes [1,1 '-SiMe₂-(C₅H₄)-(3-R-C₅H₃)]ZrCl₂ (4), [1,1 '-SiMe₂-(C₅H₄)-(2,4-R₂-C₅H₂)]ZrCl₂ (5) and [1,1 '-SiMe₂-2,2 '-(SiMe₂-SiMe₂)-(C₅H₃)-( 4-R-C₅H₂)]ZrCl₂ (6) have been prepared to probe the origin of isospecificity in 3. While 4 and 3 produce polymers with similar isospecificity, 5 and 6 give mostly hemi-isotactic-like polymers. It is proposed that the facile site epimerization via an associative pathway allows rapid equilibration of the polymer chain between the isospecific and aspecific insertion sites. This results in more frequent insertion from the isospecific site, which has a lower kinetic barrier for chain propagation. On the other hand, site epimerization for 5 and 6 is slow. This leads to mostly alternating insertion from the isospecific and aspecific sites, and consequently, a hemi-isotactic-like polymers. In comparison, site epimerization is even slower for 3, but enchainment from the aspecific site has an extremely high kinetic barrier for monomer coordination. Therefore, enchainment occurs preferentially from the isospecific site to produce isotactic polymers. </p> <p>A series of cationic complexes [(ArN=CR-CR=NAr)PtMe(L)]⁺[BF₄]⁺ (Ar = aryl; R = H, CH₃; L = water, trifluoroethanol) has been prepared. They react smoothly with benzene at approximately room temperature in trifluoroethanol solvent to yield methane and the corresponding phenyl Pt(II) cations, via Pt(IV)-methyl-phenyl-hydride intermediates. The reaction products of methyl-substituted benzenes suggest an inherent reactivity preference for aromatic over benzylic C-H bond activation, which can however be overridden by steric effects. For the reaction of benzene with cationic Pt(II) complexes, in which the diimine ligands bear 3,5-disubstituted aryl groups at the nitrogen atoms, the rate-determining step is C-H bond activation. For the more sterically crowded analogs with 2,6-dimethyl-substituted aryl groups, benzene coordination becomes rate-determining. The more electron-rich the ligand, as reflected by the CO stretching frequency in the IR spectrum of the corresponding cationic carbonyl complex, the faster the rate of C-H bond activation. This finding, however, does not reflect the actual C-H bond activation process, but rather reflects only the relative ease of solvent molecules displacing water molecules to initiate the reaction. That is, the change in rates is mostly due to a ground state effect. Several lines of evidence suggest that associative substitution pathways operate to get the hydrocarbon substrate into, and out of, the coordination sphere; i.e., that benzene substitution proceeds by a solvent- (TFE-) assisted associative pathway. </p>

Reactions of oxygen containing ligands in the coordination sphere of permethylhafnocene and permethyltantalocene

<p>A series of terl-butylperoxide complexes of hafnium, Cp*₂Hf(R)(OOCMe₃) (Cp* = ((��⁵-C₅Me₅); R = Cl, H, CH₃, CH₂CH₃, CH₂CH₂CH₃, CH₂CH₂CH₂CH₃, CH₂CHMe₂, CH=CHCMe₃, C₆H₅, meta-C₆H₃(CH₂)2) and Cp*(��⁵-C₅(CH₃)₄CH₂CH₂CH₂)Hf(OOCMe₃), has been synthesized. One example has been structurally characterized, Cp*₂Hf(OOCMe₃)CH₂CH₃ crystallizes in space group P2₁/c, with a = 19.890(7)��, b = 8.746(4)��, c = 17.532(6)��, �� = 124.987(24)��, V = 2498(2)��³, Z = 4 and R_F = 0.054 (2222 reflections, I > 0). Despite the coordinative unsaturation of the hafnium center, the terl-butylperoxide ligand is coordinated in a mono-dentate ligand. The mode of decomposition of these species is highly dependent on the substituent R. For R = H, CH₂CH₃, CH₂CH₂CH₃, CH₂CH₂CH₂CH₃, CH₂CHMe₂ a clean first order conversion to Cp*₂Hf(OCMe₃)(OR) is observed (for R CH₂CH₃, ��H�� = 19.6 kcal���mol^-1, ��S�� = -13 e.u.). These results are discussed in terms of a two step mechanism involving ��²-coordination of the terl-butylperoxide ligand. Homolytic O-O bond cleavage is observed upon heating of Cp*₂Hf(OOCMe₃) R (R = C₆H₆, meta-C₆H₃(CH₃)₂). In the presence of excess 9,10-dihydroanthracene thermolysis of Cp*₂Hf(OOCMe₃)C₆H₆ cleanly affords Cp*₂Hf(C₆H₆)OH and HOCMe₃ (��H�� = 22.6 kcal���mol^-1, ��S�� = -9 e.u.). The O-O bond strength in these complexes is thus estimated to be 22 kcal���mol^-1.</p> <p>Cp*₂Ta(CH₂)H, Cp*₂Ta(CHC₆H₅)H, Cp*₂Ta(C₆H₄)H, Cp*₂Ta(CH₂=CH₂)H and Cp*₂Ta(CH₂=CHMe)H react, presumably through Cp*₂Ta-R intermediates, with H₂O to give Cp*₂Ta(O)H and alkane. Cp*₂Ta(O)H was structurally characterized: space group P2₁/n, a= 13.073(3)��, b = 19.337(4)��, c = 16.002(3)��, �� = 108.66(2)��, V = 3832(1)��³, Z = 8 and R_F = 0.0672 (6730 reflections). Reaction of terlbutylhydroperoxide with these same starting materials ultimately yields Cp*₂Ta(O)R and HOCMe₃. Cp*₂Ta(CH₂=CHR)OH species are proposed as intermediates in the olefin hydride reactions. Cp*₂Ta(O₂)R species can be generated from the reaction of the same starting materials and O₂. Lewis acids have been shown to promote oxygen insertion in these complexes.</p>

The global optimization of phase-incoherent signals

<p>The problem of global optimization of M phase-incoherent signals in N complex dimensions is formulated. Then, by using the geometric approach of Landau and Slepian, conditions for optimality are established for N = 2 and the optimal signal sets are determined for M = 2, 3, 4, 6, and 12.</p> <p>The method is the following: The signals are assumed to be equally probable and to have equal energy, and thus are represented by points ���_i, i = 1, 2, ���, M, on the unit sphere S₁ in C^N. If W_ik is the halfspace determined by ���_i and ���_k and containing ���_i, i.e. W_ik = {�����C^N:| ��� | �����, ���_k��|}, then the ��_i = ���/k���i W_ik, i = 1, 2, ���, M, the maximum likelihood decision regions, partition S₁. For additive complex Gaussian noise ��� and a received signal ��� = ���_ie^j�� + ���, where �� is uniformly distributed over [0, 2��], the probability of correct decoding is P_C = 1/��^N ���/��/0 r^2N-1e^-(r²+1)U(r)dr, where U(r) = 1/M M/��/i=1 ��_i ��/��� S₁ I₀(2r | �����, ���_i��|)d��(���), and r = �������.</p> <p>For N = 2, it is proved that U(r) ��� ��/C_�� I₀(2r|�����, ���_i��|)d��(���) ��� 2K/M. h(1/2K [M��(C_��)-��(S₁)]), where C_�� = {�����S₁:|�����, ���_i��| ��� ��}, K is the total number of boundaries of the net on S₁ determined by the decision regions, and h is the strictly increasing strictly convex function of ��(C_�����W), (where W is a halfspace not containing ���_i), given by h = ��/C_�����W I₀ (2r|�����, ���_i��|)d��(���). Conditions for equality are established and these give rise to the globally optimal signal sets for M = 2, 3, 4, 6, and 12. </p>