Pure tetrahedral quadruple systems with index two

An oriented tetrahedron defined on four vertices is a set of four cyclic triples with the property that any ordered pair of vertices is contained in exactly one of the cyclic triples. A tetrahedral quadruple system of order $n$ with index $\lambda$, denoted by ${\text{TQS}}_{\lambda }\left(n\right)$, is a pair $\left(X,\mathrm{?}\right)$, where $X$ is an $n$‐set and $\mathrm{?}$ is a set of oriented tetrahedra (blocks) such that every cyclic triple on $X$ is contained in exactly $\lambda$ members of $\mathrm{?}$. A ${\text{TQS}}_{\lambda }\left(n\right)$ is pure if there do not exist two blocks with the same vertex set. When $\lambda =1$, the spectrum of a pure TQS $\left(n\right)$ has been completely determined by Ji. In this paper, we show that there exists a pure ${\text{TQS}}_2\left(n\right)$ if and only if $n\equiv 1,2\left(\mathrm{mod}3\right)$ and $n\ge 7$. A corollary is that a simple ${\text{QS}}_4\left(n\right)$ also exists if and only if $n\equiv 1,2\left(\mathrm{mod}3\right)$ and $n\ge 7$.     

Zerovalent Rhodium and Iridium Silatranes Featuring Two‐Center,Three‐Electron Polar σ Bonds

Species with 2‐center, 3‐electron (2c/3e^?) σ bonds are of interest owing to their fascinating electronic structures and potential for interesting reactivity patterns. Report here is the synthesis and characterization of a pair of zerovalent (d⁹) trigonal pyramidal Rh and Ir complexes that feature 2c/3e^? σ bonds to the Si atom of a tripodal tris(phosphine)silatrane ligand. X‐ray diffraction, continuous wave and pulse electron paramagnetic resonance, density‐functional theory calculations, and reactivity studies have been used to characterize these electronically distinctive compounds. The data available highlight a 2c/3e^? bonding framework with a σ*‐SOMO of metal 4‐ or 5d_z² parentage that is partially stabilized by significant mixing with Si (3p_z) and metal (5‐ or 6p_z) orbitals. Metal‐ligand covalency thus buffers the expected destabilization of transition‐metal (TM)‐silyl σ*‐orbitals by d–p mixing, affording well‐characterized examples of TM–main group, and hence polar, 2c/3e^? σ “half‐bonds”.     

Iridium-Catalyzed Enantioselective Hydrogenation of Oxocarbenium Ions: A Case of Ionic Hydrogenation

Ionic hydrogenation has not been extensively explored, but is advantageous for challenging substrates such as unsaturated intermediates. Reported here is an iridium-catalyzed hydrogenation of oxocarbenium ions to afford chiral isochromans with high enantioselectivities. A variety of functionalities are compatible with this catalytic system. In the presence of a catalytic amount of the Brønsted acid HCl, an α-chloroether is generated in situ and subsequentially reduced. Kinetic studies suggest first-order kinetics in the substrate and half-order kinetics in the catalyst. A positive nonlinear effect, together with the half kinetic order, revealed a dimerization of the catalyst. Possible reaction pathways based on the monomeric iridium catalyst were proposed and DFT computational studies revealed an ionic hydrogenation pathway. Chloride abstraction and the cleavage of dihydrogen occur in the same step.     

Crystal Structure of LiRh-type IrZn Determined by Powder X-ray and Selected Area Electron Diffraction

The LiRh-type crystal structure of the equiatomic intermetallic compound IrZn turns out to be a competitor to the otherwise energetically favored CsCl-type structures of congeneric transition metal zinc phases, thus enlightening the structural impact of element-specific factors beyond the Hume-Rothery concept.     

从混合态构造相应的系统-热库纠缠纯态的新方法

在量子统计学和低温物理学中,常用密度算符(或混合态)来表示物理系综.本文旨在提出一个新方法能将混合态转化为系统与热库相纠缠的量子纯态,这样做不但可以彰显环境对系统的影响,探寻新的物理态,尤其是纠缠态,而且能将求系综平均的复杂计算转化为较为简洁的求纯态平均.我们的新方法是将相干态和有序算符内的积分理论结合起来,就可直接将混合态扩充为自由度加倍的纯态.     

纯奇点范畴中的Buchweitz定理

我们定义纯奇点范畴D_(psg)~b(R)为有界纯导出范畴D_(pur)~b(R)与纯投射模构成的有界同伦范畴K~b(■)的Verdier商,得到了纯奇点范畴D_(psg)~b(R)三角等价于相对纯投射模的Gorenstein范畴的稳定范畴■的一个充分必要条件.同时,还给出三角等价D_(psg)~b(R)≌D_(psg)~b(S)的充分条件,这里R和S都是环.     

Activating Inert,Nonprecious Perovskites with Iridium Dopants for Efficient Oxygen Evolution Reaction under Acidic Conditions

Simultaneous realization of improved activity, enhanced stability, and reduced cost remains a desirable yet challenging goal in the search of oxygen evolution electrocatalysts in acid. Herein we report iridium‐containing strontium titanates (Ir‐STO) as active and stable, low‐iridium perovskite electrocatalysts for the oxygen evolution reaction (OER) in acid. The Ir‐STO contains 57 wt % less iridium relative to the benchmark catalyst IrO₂, but it exhibits more than 10 times higher catalytic activity for OER. It is shown to be among the most efficient iridium‐based oxide electrocatalysts for OER in acid. Theoretical results reveal that the incorporation of iridium dopants in the STO matrix activates the intrinsically inert titanium sites, strengthening the surface oxygen adsorption on titanium sites and thereby giving nonprecious titanium catalytic sites that have activities close to or even better than iridium sites.     

Iridium-catalyzed asymmetric hydrogenation of β-keto esters with new phenethylamine-derived tridentate P,N,N-ligands

A new class of phenethylamine-derived tridentate P,N,N-ligands has been successfully developed. These ligands exhibited good performance in the Ir-catalyzed asymmetric hydrogenation of β-keto esters, affording the corresponding β-hydroxy esters in moderate to good enantioselectivities.