Exploiting Strained Rings in Chelation Guided C−H Functionalization: Integration of C−H Activation with Ring Cleavage

Strained ring systems are regarded as privileged coupling partners in directed C?H bond functionalization and have emerged as a potential research area in organic synthesis. The inherent ring strain in these systems acts as a driving force, allowing the facile construction of diversified structural scaffolds via integrating C?H activation and ring‐scission. The mechanistic underpinnings allows the implementation of a plethora of C?H bonds across plentiful organic substrates, including the less reactive alkyl ones. Considering the synthetic space, this area will foster developments of novel synthetic methods in chelation guided C?H functionalization. This review will focus on recent developments in transition‐metal catalyzed chelation assisted concomitant C?H activation and ring scission of strained rings to attain molecular complexity.     

Comparison of diluted antiferromagnetic Ising models on frustrated lattices in a magnetic field

We study diluted antiferromagnetic Ising models on triangular and kagome lattices in a magnetic field, using the replica-exchange Monte Carlo method. We observe seven and five plateaus in the magnetization curve of the diluted antiferromagnetic Ising model on the triangular and kagome lattices, respectively, when a magnetic field is applied. These observations contrast with the two plateaus observed in the pure model. The origin of multiple plateaus is investigated by considering the spin configuration of triangles in the diluted models. We compare these results with those of a diluted antiferromagnetic Ising model on the three-dimensional pyrochlore lattice in a magnetic field pointing in the [111] direction, sometimes referred to as the “kagome-ice” problem. We discuss the similarity and dissimilarity of the magnetization curves of the “kagome-ice” state and the two-dimensional kagome lattice.     

Facile construction of three-membered rings via benzyne-promoted Darzens-type reaction of tertiary amines

A range of tertiary amines having electron-withdrawing groups were activated in situ by benzyne, generated from 2-(trimethylsilyl)phenyl triflate and a fluoride source, and participated in the Darzens-type reaction with carbonyl compounds, imines, and vinyl ketones to afford structurally diverse epoxides, aziridines, and cyclopropanes, respectively, in moderate to excellent yields with high trans-selectivity. The reaction involves in situ formation of unstrained ammonium ylides from tertiary amines and benzyne, proceeds in the absence of transition metals and strong bases, and tolerates a wide variety of functional groups.     

Criticality in the randomness-induced second-order phase transition of the triangular Ising antiferromagnet with nearest- and next-nearest-neighbor interactions

Using a Wang-Landau entropic sampling scheme, we investigate the effects of quenched bond randomness on a particular case of a triangular Ising model with nearest- (J_nn) and next-nearest-neighbor (J_nnn) antiferromagnetic interactions. We consider the case R=J_nnn/J_nn=1, for which the pure model is known to have a columnar ground state where rows of nearest-neighbor spins up and down alternate and undergo a weak first-order phase transition from the ordered to the paramagnetic state. With the introduction of quenched bond randomness we observe the effects signaling the expected conversion of the first-order phase transition to a second-order phase transition and using the Lee-Kosterlitz method, we quantitatively verify this conversion. The emerging, under random bonds, continuous transition shows a strongly saturating specific heat behavior, corresponding to a negative exponent α, and belongs to a new distinctive universality class with ν=1.135(11), γ/ν=1.744(9), and β/ν=0.124(8). Thus, our results for the critical exponents support an extensive but weak universality and the emerged continuous transition has the same magnetic critical exponent (but a different thermal critical exponent) as a wide variety of two-dimensional (2d) systems without and with quenched disorder.     

二维介观环中持续电流的梯度无序效应

基于紧束缚模型,考虑无序的梯度衰减,研究了无序-有序二维介观环体系中无序梯度及结构尺寸等因素对持续电流的影响.在表面无序区无梯度衰减时,持续电流随无序度的变化先减小后增大,观察到类弹道和局域性的转变.当存在梯度衰减时,无序区部分区域无序度相应减小,对有序区产生较强散射,典型电流比没有无序衰减时偏小.有趣的是,当无序度指数衰减时,上述类弹道和局域性的转变却消失了,揭示了介观实验中能否观察到该转变与无序的梯度分布密切相关.此外,计算表明表面无序渗透的深度和环的宽度对持续电流也有重要影响,呈现奇异的量子尺寸效应.这不同于以前的理论预言. 关键词： 介观环 梯度无序 持续电流     

Calculations of derivatives of porphin and porphyrazine with an annulated five-membered heteroaromatic ring using a modified INDO method

Quantum-chemical calculations for series of porphin (H₂P) and porphyrazine (H₂PA) derivatives whose molecules contain a 3,4-annulated five-membered heteroaromatic ring of pyrrole, furan, and thiophene as well as 1,2,5-triazole, 1,2,5-oxadiazole, and 1,2,5-thiadiazole have been carried out by the AM1 and INDO/Sm methods (m means “modified parametrization”). As follows from the unrestricted Hartree-Fock AM1 calculations, the ground state energy of the a isomer is lower than that of the b isomers for all compounds, the a and b isomers being NH isomers with the additional five-membered ring fused to a pyrrolenine or pyrrole ring, respectively. Condensation of the five-membered ring for the b isomers of the H₂P derivatives is shown to extend the main conjugation path from 18-membered to 21-membered cyclopolyene. However, the 18-membered cyclopolyene for the a isomers of the H₂P derivatives and 16-membered cyclopolyene for both isomers of the H₂PA derivatives prove to be isolated from the five-membered ring carrying six π-electrons. Based on INDO/Sm computations of electronic absorption spectra of the H₂P and H₂PA derivatives, it is shown that the Q_x level of the a isomers is sensitive to the nature of the annulated ring whereas the Q_y level is practically not shifted. On the contrary, the Q_x level of the b isomers is relatively insensitive to the nature of the annulated ring while the Q_y level decreases monotonously in the H₂P and H₂PA series, being the first excited state level for the majority of the derivatives (X is along the NH-HN axis; Y, perpendicular to it). The electronic absorption spectra at the border of the visible and near-UV regions are determined mainly by two high-intensity G → B_x and G → B_y transitions for the H₂P derivatives. However, four intense G → B_x, G → B_y, G → N_x, and G → N_y transitions are characteristic of the spectra of the H₂PA derivatives. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 75, No. 5, pp. 606–622, September–October, 2008.     

A laser cavity used as an etalon for interferometric control of its own field

A quantitative relationship between the cavity parameters and the angular structure of the emission scattered in a parallel-plane active cavity filled with an arbitrary set of optical elements has been determined. The multipath interference into the active cavity is demonstrated to have properties which differ radically from similar processes in the etalon—among other things the relatively low finesse of the cavity interference rings is independent of the mirror quality and is a function of the Fresnel number only. The use of the operating laser cavity as an etalon for precise control of its own mode wave parameters is discussed.     

Countable linear transformations are clean

It is shown that every linear transformation on a vector space of countable dimension is the sum of a unit and an idempotent.

     

Ferromagnetism in the Hubbard model: instability of the Nagaoka state on the triangular,honeycomb and kagome lattices

In order to analyse the lattice dependence of ferromagnetism in the two-dimensional Hubbard model we investigate the instability of the fully polarised ferromagnetic ground state (Nagaoka state) on the triangular, honeycomb and kagome lattices. We mainly focus on the local instability, applying single spin flip variational wave functions which include majority spin correlation effects. The question of global instability and phase separation is addressed in the framework of Hartree-Fock theory. We find a strong tendency towards Nagaoka ferromagnetism on the non-bipartite lattices (triangular, kagome) for more than half filling. For the triangular lattice we find the Nagaoka state to be unstable above a critical density of n = 1.887 at U = ∞, thereby significantly improving former variational results. For the kagome lattice the region where ferromagnetism prevails in the phase diagram widely exceeds the flat band regime. Our results even allow the stability of the Nagaoka state in a small region below half filling. In the case of the bipartite honeycomb lattice several disconnected regions are left for a possible Nagaoka ground state.     

Perturbative solution to order βɛ of the Percus-Yevick equation for triangular well potential forn=2

The radial distribution function for a fluid in which the molecules interactvia a triangular well potential is considered. Expanding the radial distribution function in pwoers of βɛ, where ɛ is the depth of the potential andβ=1/k _BT the first-order terms are calculated analytically using the Percus-Yevick theory in the Baxter’s formulation. The first-order terms in the direct correlation functionc(r) are also calculated. The first- and second-order terms in the free energy obtained from the energy equation of state are calculated and compared with other calculations. An erratum to this article is available at .