Note on the Hall effect in ice

The magnetic field dependence of the polarization correlation function is investigated. It is shown that the Hall effect is extremely small and probably inobservable because of the lattice anti-polarization produced by the motion of ionic defects and because of the incoherent motion of Bjerrum defects.     

若干经济数学模型的研究与应用

本文论述了近些年我们在投入产出模型、广告最优随机控制模型、最佳营销管理模型以及时间序列—马尔可夫链组合预测模型等方面所做的研究工作,同时也论及国内外在上述几方面的研究状况．     

Lanthanide Identity Governs Guest-Induced Dimerization in LnIII[15-MC N(L-pheHA)-5])3+ Metallacrowns

Series of lanthanide-containing metallic coordination complexes are frequently presented as structurally analogous, due to the similar chemical and coordinative properties of the lanthanides. In the case of chiral (Ln^III[15-MC _N(L-pheHA)-5])³⁺ metallacrowns (MCs), which are well established supramolecular hosts, the formation of dimers templated by a dicarboxylate guest (muconate) in solution of neutral pH is herein shown to have a unique dependence on the identity of the MC's central lanthanide. Calorimetric data and nuclear magnetic resonance diffusion studies demonstrate that MCs containing larger or smaller lanthanides as the central metal only form monomeric host-guest complexes whereas analogues with intermediate lanthanides (for example, Eu, Gd, Dy) participate in formation of dimeric host-guest-host compartments. The driving force for the dimerization event across the series is thought to be a competition between formation of highly stable MCs (larger lanthanides) and optimally linked bridging guests (smaller lanthanides).     

Efficient Imine Formation by Oxidative Coupling at Low Temperature Catalyzed by High-Surface-Area Mesoporous CeO2 with Exceptional Redox Property

High-surface-area mesoporous CeO₂ (hsmCeO₂) was prepared by a facile organic-template-induced homogeneous precipitation process and showed excellent catalytic activity in imine synthesis in the absence of base from primary alcohols and amines in air atmosphere at low temperature. For comparison, ordinary CeO₂ and hsmCeO₂ after different thermal treatments were also investigated. XRD, N₂ physisorption, UV-Raman, H₂ temperature-programmed reduction, O₂ temperature-programmed desorption, EPR spectroscopy, and X-ray photoelectron spectroscopy were used to unravel the structural and redox properties. The hsmCeO₂ calcined at 400 °C shows the highest specific surface area (158 m² g⁻¹), the highest fraction of surface coordinatively unsaturated Ce³⁺ ions (18.2 %), and the highest concentration of reactive oxygen vacancies (2.4×10¹⁵ spins g⁻¹). In the model reaction of oxidative coupling of benzyl alcohol and aniline, such an exceptional redox property of the hsmCeO₂ catalyst can boost benzylideneaniline formation (2.75 and 5.55 mmol h⁻¹ based on >99 % yield at 60 and 80 °C, respectively) in air with no base additives. It can also work effectively at a temperature of 30 °C and in gram-scale synthesis. These are among the best results for all benchmark ceria catalysts in the literature. Moreover, the hsmCeO₂ catalyst shows a wide scope towards primary alcohols and amines with good to excellent yield of imines. The influence of reaction parameters, the reusability of the catalyst, and the reaction mechanism were investigated.     

Temperature Dependence of 1H Paramagnetic Chemical Shifts in Actinide Complexes,Beyond Bleaney's Theory: The AnVIO22+–Dipicolinic Acid Complexes (An=Np,Pu) as an Example

Actinide +VI complexes ( = , and ) with dipicolinic acid derivatives were synthesized and characterized by powder XRD, SQUID magnetometry and NMR spectroscopy. In addition, and complexes were described by first principles CAS based and two-component spin-restricted DFT methods. The analysis of the ¹H paramagnetic NMR chemical shifts for all protons of the ligands according to the X-rays structures shows that the Fermi contact contribution is negligible in agreement with spin density determined by unrestricted DFT. The magnetic susceptibility tensor is determined by combining SQUID, pNMR shifts and Evans’ method. The SO-RASPT2 results fit well the experimental magnetic susceptibility and pNMR chemical shifts. The role of the counterions in the solid phase is pointed out; their presence impacts the magnetic properties of the complex. The temperature dependence of the pNMR chemical shifts has a strong contribution, contrarily to Bleaney's theory for lanthanide complexes. The fitting of the temperature dependence of the pNMR chemical shifts and SQUID magnetic susceptibility by a two-Kramers-doublet model for the complex and a non-Kramers-doublet model for the complex allows for the experimental evaluation of energy gaps and magnetic moments of the paramagnetic center.     

Derivation of Lanthanide Series Crystal Field Parameters From First Principles

Two series of lanthanide complexes have been chosen to analyze trends in the magnetic properties and crystal field parameters (CFPs) along the two series: The highly symmetric LnZn₁₆(picHA)₁₆ series (Ln=Tb, Dy, Ho, Er, Yb; picHA=picolinohydroxamic acid) and the [Ln(dpa)₃](C₃H₅N₂)₃ ⋅ 3H₂O series (Ln=Ce–Yb; dpa=2,6-dipicolinic acid) with approximate three-fold symmetry. The first series presents a compressed coordination sphere of eight oxygen atoms whereas in the second series, the coordination sphere consists of an elongated coordination sphere formed of six oxygen atoms. The CFPs have been deduced from ab initio calculations using two methods: The AILFT (ab initio ligand field theory) method, in which the parameters are determined at the orbital level, and the ITO (irreducible tensor operator) decomposition, in which the problems are treated at the many-electron level. It has been found that the CFPs are transferable from one derivative to another, within a given series, as a first approximation. The sign of the second-order parameter differs in the two series, reflecting the different environments. It has been found that the use of the strength parameter S allows for an easy comparison between complexes. Furthermore, in both series, the parameters have been found to decrease in magnitude along the series, and this decrease is attributed to covalent effects.     

The 1:1 resonance in Hamiltonian systems

Two-degree-of-freedom Hamiltonian systems with an elliptic equilibrium at the origin are characterised by the frequencies of the linearisation. Considering the frequencies as parameters, the system undergoes a bifurcation when the frequencies pass through a resonance. These bifurcations are well understood for most resonances $k:l$, but not the semisimple cases $1:1$ and $1:?1$. A two-degree-of-freedom Hamiltonian system can be approximated to any order by an integrable normal form. The reason is that the normal form of a Hamiltonian system has an additional integral due to the normal form symmetry. The latter is intimately related to the ratio of the frequencies. For a rational frequency ratio this leads to $S^1$-symmetric systems. The question we wish to address is about the co-dimension of such a system in $1:1$ resonance with respect to left-right-equivalence, where the right action is $S^1$-equivariant. The result is a co-dimension five unfolding of the central singularity. Two of the unfolding parameters are moduli and the remaining non-modal parameters are the ones found in the linear unfolding of this system.     

Vertically Grown Few-Layer MoS2 Nanosheets on Hierarchical Carbon Nanocages for Pseudocapacitive Lithium Storage with Ultrahigh-Rate Capability and Long-Term Recyclability

Molybdenum disulfide (MoS₂) is an intensively studied anode material for lithium-ion batteries (LIBs) owing to its high theoretical capacity, but it is still confronted by severe challenges of unsatisfactory rate capability and cycle life. Herein, few-layer MoS₂ nanosheets, vertically grown on hierarchical carbon nanocages (hCNC) by a facile hydrothermal method, introduce pseudocapacitive lithium storage owing to the highly exposed MoS₂ basal planes, enhanced conductivity, and facilitated electrolyte access arising from good hybridization with hCNC. Thus, the optimized MoS₂/hCNC exhibits reversible capacities of 1670 mAh g⁻¹ at 0.1 A g⁻¹ after 50 cycles, 621 mAh g⁻¹ at 5.0 A g⁻¹ after 500 cycles, and 196 mAh g⁻¹ at 50 A g⁻¹ after 2500 cycles, which are among the best for MoS₂-based anode materials. The specific power and specific energy, which can reach 16.1 kW and 252.8 Wh after 3000 cycles, respectively, indicate great potential in high-power and long-life LIBs. These findings suggest a promising strategy for exploring advanced anode materials with high reversible capacity, high-rate capability, and long-term recyclability.     

One Way Traffic: Base-to-Backbone Hole Transfer in Nucleoside Phosphorodithioate

The directionality of the hole-transfer processes between DNA backbone and base was investigated by using phosphorodithioate [P(S⁻)=S] components. ESR spectroscopy in homogeneous frozen aqueous solutions and pulse radiolysis in aqueous solution at ambient temperature confirmed initial formation of G^.+-P(S⁻)=S. The ionization potential of G-P(S⁻)=S was calculated to be slightly lower than that of guanine in 5′-dGMP. Subsequent thermally activated hole transfer from G^.+ to P(S⁻)=S led to dithiyl radical (P-2S^.) formation on the μs timescale. In parallel, ESR spectroscopy, pulse radiolysis, and density functional theory (DFT) calculations confirmed P-2S^. formation in an abasic phosphorodithioate model compound. ESR investigations at low temperatures and higher G-P(S⁻)=S concentrations showed a bimolecular conversion of P-2S^. to the σ²-σ*¹-bonded dimer anion radical [-P-2S 2S-P-]⁻ [ΔG (150 K, DFT)=−7.2 kcal mol⁻¹]. However, [-P-2S 2S-P-]⁻ formation was not observed by pulse radiolysis [ΔG° (298 K, DFT)=−1.4 kcal mol⁻¹]. Neither P-2S^. nor [-P-2S 2S-P-]⁻ oxidized guanine base; only base-to-backbone hole transfer occurs in phosphorodithioate.     

Two Types of σ-Allenyl Complexes from Reactions of Silylenes and Germylenes with Chromium Fischer Alkynyl(alkoxy)carbenes

The reactivity of amidinatotetrylenes of the type E(tBu₂bzm)R¹ (E=Si, Ge; tBu₂bzm=N,N′-bis(tertbutyl)benzamidinate; R¹=alkyl or aryl) with the chromium Fischer alkynylcarbene complexes [Cr{C(OEt)C₂R²}(CO)₅] (R²=Ph; ferrocenyl, Fc) has been studied. At room temperature, two different reaction pathways have been identified: (a) attack of the amidinatotetrylene to the alkynyl C² atom (γ-attack), which leads to σ-allenyl complexes in which the original C_carbene atom maintains its attachment to the Cr(CO)₅ and OEt groups (compounds 3 ), and (b) attack of the amidinatotetrylene to the C_carbene atom (α-attack), which ends in σ-allenyl complexes in which the original C_carbene atom is not attached to the metal atom and has been inserted into an E−N bond of the amidinatotetrylene forming an E-C-N-C-N five-membered ring (compounds 4 ). It has been found that compounds 3 are thermodynamically less stable than their corresponding 4 isomers and that some of the former (E=Ge; R¹=CH₂SiMe₃) can be transformed into the latter upon heating. At high temperatures (>70 °C) the reactions involving bulky amidinatotetrylenes (R¹=Mes, tBu) end in the carbene-substitution products [Cr{E(tBu₂bzm)R¹}(CO)₅].