Collocation by singular splines

Splines determined by the kernel of the differential operator are known to be useful to solve the singular boundary value problems of the form . One of the most successful methods is the collocation method based on special Chebyshev splines. We investigate the construction of the associated B-splines based on knot-insertion algorithms for their evaluation, and their application in collocation at generalized Gaussian points. Specially, we show how to obtain these points as eigenvalues of a symmetric tridiagonal matrix of order k. This research was supported by Grant 037-1193086-2771, by the Ministry of science, education and sports of the Republic of Croatia.     

杂双核(H)Rh-Cr配合物中乙烯插入RhI—H键反应的密度泛函研究

采用密度泛函理论B3LYP方法研究了配体和配位数对乙烯插入杂双核(CO)₄Cr(m-PH₂)₂RhH(L_n) (L＝CO或PH₃, n＝1或2)配合物中Rh—H键反应的影响. 计算结果表明, 六配位乙烯复合物中乙烯与铑之间轨道相互作用主要为乙烯到铑中心的s供体相互作用; 而五配位乙烯复合物中乙烯与铑中心间相互作用涉及乙烯到铑中心的s供体相互作用和铑到乙烯的p反馈作用. PH₃配体在热力学上不利于该反应. 处于氢配体对位的膦配体能加速乙烯插入反应. 乙烯插入的五配位反应途径占优势. Cr(CO)₄部分的引入降低了乙烯插入反应的活化能.     

Photoinduced Fe-Cp bond cleavage and insertion reactions of strained silicon- and sulphur-bridged [1]ferrocenophanes in the presence of transition-metal carbonyls

The photochemical reactions of the moderately strained sila[1]ferrocenophane [Fe(eta-C(5)H(4))(2)SiPh(2)] (1) and the highly strained thia[1]ferrocenophane [Fe(eta-C(5)H(4))(2)S] (8) with transition-metal carbonyls ([Fe(CO)(5)], [Fe(2)(CO)(9)] and [Co(2)(CO)(8)]) have been studied. The use of metal carbonyls has allowed the products of photochemically induced Fe-cyclopentadienyl (Cp) bond cleavage reactions in the [1]ferrocenophanes to be trapped as stable, characterisable products. During the course of these studies the synthesis of 8 from [Fe(eta-C(5)H(4)Li)(2)TMEDA] (TMEDA=N,N,N',N'-tetramethylethylenediamine) and S(SO(2)Ph)(2) has been significantly improved by a change of reaction solvent and temperature. Photochemical reaction of 1 with excess [Fe(CO)(5)] in THF gave the dinuclear complex [Fe(2)(CO)(2)(mu-CO)(2)(eta-C(5)H(4))(2)SiPh(2)] (9). The analogous photolytic reaction of 8 with [Fe(CO)(5)] in THF gave cyclic dimer [Fe(eta-C(5)H(4))(2)S](2) (10) and [Fe(2)(CO)(2)(mu-CO)(2)(eta-C(5)H(4))(2)S] (11), with the former being the major product. Photolysis of 1 with [Co(2)(CO)(8)] afforded the remarkable tetrametallic dimer [(CO)(2)Co(eta-C(5)H(4))SiPh(2)(eta-C(5)H(4))Fe(CO)(2)](2) (13). The corresponding photochemical reaction of 8 with [Co(2)(CO)(8)] gave a trimetallic insertion product in high conversion, [Co(CO)(4)(CO)(2)Fe(eta-C(5)H(4))S(eta-C(5)H(4))Co(CO)(2)] (14). These reactivity studies show that UV light promotes Fe-Cp bond cleavage reactions of both of the [1]ferrocenophanes 1 and 8. We have found that, whereas the less strained sila[1]ferrocenophane 1 requires photoactivation for Fe-Cp bond insertions to occur, the highly strained thia[1]ferrocenophane 8 undergoes both irradiative and non-irradiative insertions, although the latter occur at a slower rate. Our results suggest that such photoinduced bond cleavage reactions may be general and applicable to other related strained organometallic rings with pi-hydrocarbon ligands.     

离子注入对插入损耗和隔离度影响的研究

基于一个典型的013 μm绝缘体上硅,射频开关电路工艺流程,分析了离子掺杂工艺流程对射频开关导通电阻Ron和关断电容Coff的影响。通过N型MOS管的浅掺杂注入后热退火温度和N型MOS管浅掺杂能量的分批实验,证实了退火温度可影响射频开关的导通电阻和关断电容。进一步实验结果显示,浅掺杂注入的砷（As）和磷（P）注入的剂量是主导因素,各自对导通电阻和关断电容值的影响均为线性且趋势相反,为基于013 μm SOI的射频开关性能的优化提供了依据。     

Probing gas adsorption in MOFs using an efficient ab initio widom insertion Monte Carlo method

We propose a novel biased Widom insertion method that can efficiently compute the Henry coefficient, K_H, of gas molecules inside porous materials exhibiting strong adsorption sites by employing purely DFT calculations. This is achieved by partitioning the simulation volume into strongly and weakly adsorbing regions and selectively biasing the Widom insertion moves into the former region. We show that only few thousands of single point energy calculations are necessary to achieve accurate statistics compared to many hundreds of thousands or millions of such calculations in conventional random insertions. The methodology is used to compute the Henry coefficient for CO₂, N₂, CH₄, and C₂H₂ in M‐MOF‐74(M = Zn and Mg), yielding good agreement with published experimental data. Our results demonstrate that the DFT binding energy and the heat of adsorption are not accurate enough indicators to rank the guest adsorption properties at the Henry regime. © 2016 Wiley Periodicals, Inc.     

Conversion of the Native 24‐mer Ferritin Nanocage into Its Non‐Native 16‐mer Analogue by Insertion of Extra Amino Acid Residues

Protein assemblies with high symmetry are widely distributed in nature. Most efforts so far have focused on repurposing these protein assemblies, a strategy that is ultimately limited by the structures available. To overcome this limitation, methods for fabricating novel self‐assembling proteins have received intensive interest. Herein, by reengineering the key subunit interfaces of native 24‐mer protein cage with octahedral symmetry through amino acid residues insertion, we fabricated a 16‐mer lenticular nanocage whose structure is unique among all known protein cages. This newly non‐native protein can be used for encapsulation of bioactive compounds and exhibits high uptake efficiency by cancer cells. More importantly, the above strategy could be applied to other naturally occurring protein assemblies with high symmetry, leading to the generation of new proteins with unexplored functions.     

Stereo‐ and Regioselective Alkyne Hydrometallation with Gold(III) Hydrides

The hydroauration of internal and terminal alkynes by gold(III) hydride complexes [(C^N^C)AuH] was found to be mediated by radicals and proceeds by an unexpected binuclear outer‐sphere mechanism to cleanly form trans‐insertion products. Radical precursors such as azobisisobutyronitrile lead to a drastic rate enhancement. DFT calculations support the proposed radical mechanism, with very low activation barriers, and rule out mononuclear mechanistic alternatives. These alkyne hydroaurations are highly regio‐ and stereospecific for the formation of Z‐vinyl isomers, with Z/E ratios of >99:1 in most cases.     

Synthesis and Deprotonation of Aminophosphane Complexes: First K/N(H)R Phosphinidenoid Complexes and Access to a Complex with a P2N‐Ring Ligand

Synthesis of 1,1′‐bifunctional aminophosphane complexes 3 a–e was achieved by the reaction of Li/Cl phosphinidenoid complex 2 with various primary amines (R=Me, iPr, tBu, Cy, Ph). Deprotonation of complex 3 a (R=Me) with potassium hexamethyldisilazide yielded a mixture of K/NHMe phosphinidenoid complex 4 a and potassium phosphanylamido complex 4 a′ . Treatment of complex 3 c (R=tBu) and e (R=Ph) with KHMDS afforded the first examples of K/NHR phosphinidenoid complexes 4 c and e . The reaction of complex 3 c with 2 molar equivalents of KHMDS followed by PhPCl₂ afforded complexes 5 c,c′ , which possess a P₂N‐ring ligand. All complexes were characterized by NMR, IR, MS, and microanalysis, and additionally, complexes 3 b – e and 5 c′ were scrutinized by single‐crystal X‐ray crystallography.     

Switchable [3+2] and [4+2] Heteroannulation of Primary Propargylamines with Isonitriles to Imidazoles and 1,6‐Dihydropyrimidines: Catalyst Loading Enabled Reaction Divergence

Isonitrile 1 due to its carbene‐like reactivity serves generally as a one‐carbon synthon in a diverse set of organic transformations. We report in this article that the isocyano group can also act as a polarized triple bond to undergo, as a two‐atom synthon, heteroannulation with primary propargylamines 15 . In addition, we serendipitously discovered that the reaction pathways can be modulated by simply changing the catalyst loading. In the presence of 0.1 equiv of Yb(OTf)₃ or TfOH, the reaction between 1 and 15 afforded exclusively imidazoles 16 by a formal [3+2] cycloaddition. At a higher catalyst loading (Yb(OTf)₃ (0.4 equiv) or TfOH (0.5 equiv)) under otherwise identical conditions, the same reaction furnished 1,6‐dihydropyrimidines 17 in good to excellent yields by way of a formal [4+2] cycloaddition process. Mechanistic investigations indicated that both annulations went through an amidine intermediate resulting from the insertion of the isocyano group to the NH bond of the primary amine. Subsequent catalyst‐loading‐dependent 5‐exo‐dig or 6‐endo‐dig cyclization provided selectively the two heterocycles, respectively.     

Palladium‐Catalyzed Intramolecular Carbene Insertion into C(sp3)−H Bonds

A palladium‐catalyzed carbene insertion into C(sp³)?H bonds leading to pyrrolidines was developed. The coupling reaction can be catalyzed by both Pd⁰ and Pd^II, is regioselective, and shows a broad functional group tolerance. This reaction is the first example of palladium‐catalyzed C(sp³)?C(sp³) bond assembly starting from diazocarbonyl compounds. DFT calculations revealed that this direct C(sp³)?H bond functionalization reaction involves an unprecedented concerted metalation–deprotonation step.