Arylation of styrene derivatives using aryliron complexes [CpFe(CO)2Ar] revealed by density functional theory calculations: Fe(II)-assisted group exchange through Fe-C bond cleavage and Fe-X bond formation

The detailed mechanism for arylation of styrene or its α-CF₃ substituted analog using aryliron complex [CpFe(CO)₂Ar] was studied using density functional theory calculations. Results of calculations show that the arylation mechanism mainly involves three steps: (1) a ligand exchange process between a CO and styrene or its derivative; (2) migration of Ar group from Fe to β-C of styrene; (3) β-H (or β-F) elimination and dissociation of the stilbene derivative from the CpFeHCO (or CpFeFCO) moiety. Both of Steps (2) and (3) experience a similar four-memberred cyclic transition state. The d_π-p_π interaction stabilizes the CC π coordinated complexes and the agostic interaction plays an important role in stabilizing intermediates and promoting elimination of the β-H (or β-F if available). For arylation of the α-CF3 substituted styrene, our calculations clarified that the dissociation of ethylene derivatives to give PF (product for β-F elimination) is kinetically and thermodynamically more favorable than to give PH (product for β-H elimination), which is the determined step for the selectivity of the final products.     

Synthesis, crystal structure and optical properties of the new lead fluoride borate—Pb2BO3F

A new compound, Pb₂BO₃F, has been grown by high temperature solution method from the PbO–PbF₂–B₂O₃ system for the first time. The crystal structure of this compound has been identified by single crystal X-ray diffraction analysis. It crystallizes in the hexagonal system, space group P6₃/m (No. 176) with unit-cell parameters a=7.2460(3) Å, c=14.5521(17) Å, Z=6, V=661.69(9) ų. Its structure was solved by the direct methods and refined to R₁=0.0163 and wR₂=0.0367. The structure of Pb₂BO₃F consists of the distorted PbO₃F₂ groups and BO₃ triangles, which are all symmetric with each other in the gestalt structure to the extent that the Pb₂BO₃F compound crystallizes in the symmetric space group. The powder X-ray diffraction pattern of the Pb₂BO₃F has been measured. The BO₃ functional groups presented in the sample were identified by FTIR spectrum. The DTA curve of Pb₂BO₃F suggests that Pb₂BO₃F melts congruently at 448 °C.     

On-chip pre-concentration and complexation of [¹⁸F]fluoride ions via regenerable anion exchange particles for radiochemical synthesis of Positron Emission Tomography tracers

Microfluidic approaches have demonstrated a relevant impact on radiochemical reactions involving Positron Emission Tomography (PET) nuclides, due to shorter reaction times and smaller precursor quantities. However, little attention has been given to the integration of the initial pre-concentration and drying of radioactive [(18)F]fluoride ions, required for the labeling of radiotracer compounds. In this work we report the design, fabrication and implementation of a glass microfluidic device filled with recyclable anion exchange particles for the repeated recovery of [(18)F] and [(19)F]fluoride ions. The device was first tested with non radioactive [(19)F]fluoride ions and it was shown to repeatedly trap and elute >95% fluoride over 40 successive experimental runs with no decrease in efficiency. The same device was then tested for the trapping and release of [(18)F]fluoride ions over 20 experiments with no measurable decrease in performance. Finally, the [(18)F]fluoride ions were eluted as a K(18)F/K2.2.2 complex, dried by repeated dissolution in acetonitrile and evaporation of residual water, and reacted with ethyl ditosylate (EtDT) leading to the desired product ([(18)F]fluoroethyltosylate) with 96 ± 3% yield (RCY). The overall time needed for conditioning, trapping, elution and regeneration was less than 6 min. This approach will be of great benefit towards an integrated platform able to perform faster and safer radiochemical synthesis on the micro-scale.     

LiVPO4F电子结构及电化学性质的第一性原理研究

采用密度泛函理论(DFT)结合投影缀加波(PAW)方法,对LiVPO₄F的晶体结构,电子结构和电化学属性进行了研究。从理论上获得了脱Li前后具体的晶格参数的变化。通过对其态密度的计算,发现在放电过程中,V在化合物中呈现离子态,发生+3/+4价态的转变,电子转移主要发生在V原子上;而P原子的状态比较稳定,并不发生大的电子的转移,磷酸根的空间结构也变化不大。同时LiVPO₄F的禁带宽度仅为1.63 eV,说明其在一定情况下具有良好的导电性,有利于放电过程中电子的输运。LiVPO₄F是铁磁相,磁矩为2μ_B,而VPO₄F为反铁磁相。此外,通过计算获得了LiVPO₄F的平均嵌锂电压为4.0 eV。     

Random attractors for stochastic lattice dynamical systems in weighted spaces

In this paper, we first provide some sufficient conditions for the existence of global compact random attractors for general random dynamical systems in weighted space (p?1) of infinite sequences. Then we consider the existence of global compact random attractors in weighted space for stochastic lattice dynamical systems with random coupled coefficients and multiplicative/additive white noises. Our results recover many existing ones on the existence of global random attractors for stochastic lattice dynamical systems with multiplicative/additive white noises in regular l² space of infinite sequences.     

On the number of limit cycles in small perturbations of a class of hyper-elliptic Hamiltonian systems with one nilpotent saddle

In this paper, we make a complete study on small perturbations of Hamiltonian vector field with a hyper-elliptic Hamiltonian of degree five, which is a Liénard system of the form x^′=y, y^′=Q₁(x)+εyQ₂(x) with Q₁ and Q₂ polynomials of degree respectively 4 and 3. It is shown that this system can undergo degenerated Hopf bifurcation and Poincaré bifurcation, which emerges at most three limit cycles in the plane for sufficiently small positive ε. And the limit cycles can encompass only an equilibrium inside, i.e. the configuration (3,0) of limit cycles can appear for some values of parameters, where (3,0) stands for three limit cycles surrounding an equilibrium and no limit cycles surrounding two equilibria.     

On a divisor problem related to the Epstein zeta-function, II

Recently by using the theory of modular forms and the Riemann zeta-function, Lü improved the estimates for the error term in a divisor problem related to the Epstein zeta-function established by Sankaranarayanan. In this short note, we are able to further sharpen some results of Sankaranarayanan and of Lü, and to establish corresponding Ω-estimates.     

Higher power moments of the Riesz mean error term of symmetric square L-function

Let be the error term of the Riesz mean of the symmetric square L-function. We give the higher power moments of and show that if there exists a real number A₀:=A₀(ρ)>3 such that , then we can derive asymptotic formulas for , 3?h<A₀, h∈N. Particularly, we get asymptotic formulas for , h=3,4,5 unconditionally.     

Borne uniforme pour les homothéties dans l?image de Galois associée aux courbes elliptiques

Let K be a fixed number field and GK its absolute Galois group. We give a bound C(K), depending only on the degree, the class number and the discriminant of K, such that for any elliptic curve E defined over K and any prime number p strictly larger than C(K), the image of the representation of GK attached to the p-torsion points of E contains a subgroup of homotheties of index smaller than 12.     

Certain values of Hecke L-functions and generalized hypergeometric functions

We compare two calculations due to Bloch and the author of the regulator of an elliptic curve with complex multiplication which is a quotient of a Fermat curve, and express the special value of its L-function at s=0 in terms of special values of generalized hypergeometric functions.