单边条件下的 Taylor平均逼近

本文中 ,我们对函数加适当的条件 ,从而改进了 Taylor平均逼近的阶.     

Simulation of molecular and electronic structure of polyhydrogenated (n,0)-tubulenes and their analogs intercalated with lithium

Molecular and electronic structure of four polyhydrogenated (n,0)-tubulenes, namely, [−C₂₄H₄−] _m (1), two isomers of composition [−C₂₈H₄−] _m (2 and3), and [−C₃₂H₄−] _m (4) withn benzene rings in the cross section (n=6, 7, 7, and 8, respectively), was simulated atm>1 (m is the number of repeating fragemnts). It was assumed that hydrogen atoms are attached to all carbon atoms lying on the two most distant elements of the cylinders of the corresponding tubulenes. The energy band structures of macromolecules1–4 and their Li-intercalated analogs [−C₂₄H₄Li−] _m (5) [−C₂₈H₄Li−] _m (two isomers,6 and7), and [−C₃₂H₄Li−] _m (8), containing one Li atom per repeating unit at each center, were obtained in the EHT approximation by the crystal orbital method. Geometric parameters of repeating units of structures1–8 were found after MNDO/PM3 optimization of the energies of hydrocarbon molecules C₇₂H₂₄, C₈₄H₂₆ (two geometric isomers), and C₉₆H₂₈, containing three repeating units of corresponding tubulenes1–4 each. The conductivity types of polyhydrogenated tubulenes1–4 are the same as those of their precursors, (6,0)-, (7,0)-, and (8,0)-tubulenes. Dispersion curves of systems5–8 are much the same as those of macromolecules1–4; however, electron energy spectra of5–8 possess metallic conductivity type and the positions of Fermi levels for these systems are higher than for compounds1–4. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 11, pp. 2061–2067, November, 1999.     

About the compatibility between ansatzes and constraints for a local formulation of orbital‐free density functional theory

Functional properties that are exact for the Hohenberg–Kohn functional may turn into mutually exclusive constraints at a given level of ansatz. This is exemplarily shown for the local density approximation. Nevertheless, it is possible to reach exactly the Kohn–Sham data from an orbital‐free density functional framework based on simple one‐point functionals by starting from the Levy–Perdew–Sahni formulation. The energy value is obtained from the density‐potential pair, and therefore does not refer to the functional dependence of the potential expression. Consequently, the potential expression can be obtained from any suitable model and is not required to follow proper scaling behavior.     

Theoretical investigation of the weak interactions of rare gas atoms with silver clusters by resonance Raman spectroscopy modeling

The interactions of rare gas atoms (Rg = Ar, Kr, and Xe) with small neutral and cationic silver clusters have been investigated by density functional methods and the effect of these weak interactions on the resonance Raman spectra of the complexes has been evaluated. The resonance Raman technique that depends on the properties of ground and excited state, seems deeply sensitive to the weak rare gas–metal cluster interactions, and the use of inert gases has been proven to be an excellent approach to recognize the ability of this technique to detect extremely weak interactions. In this work, for , and complexes the IR, normal and resonance Raman spectra have been calculated and the effect of rare gas–cluster stretching vibration ( ) on the pattern and the relative intensities of different spectra have been investigated. The resonance Raman spectra for the weakly interacted complexes (with the interaction energies less than ?2.0 kcal/mol) exhibit the vibration with the detectable intensity that its intensity increases by going from Ag₆–Ar to Ag₆–Xe complex. Moreover, the resonance Raman spectra (based on the excited state gradient approximation) for high intensity nearly degenerate excited states, proved the effect of accumulation of the excited state charge density on the relative intensity of vibration.     

Predicting ion selectivity in water purification by capacitive deionization: Electric double layer models

Ion-selective water treatment is needed to address emerging problems in an energy- and cost-efficient manner. Capacitive deionization (CDI) is a membraneless water treatment technology, which relies on storing ions in charged electric double layers (EDLs) of micropores. CDI has shown remarkable selectivity, with local density approximations (LDAs) showing some success in guiding selective separations. However, many underlying processes are represented by lumped fitting parameters in LDA models, hindering further progress. Atomistic models help unravel selectivity mechanisms, but are difficult to integrate with cell-level CDI theory. Here, we review and extend LDA models for CDI, highlight a knowledge gap in connecting between LDA and atomistic models for CDI, and emphasize and build upon analogies between micropore EDLs and nanofiltration membranes.     

Monitoring the Thiol/Thiophenol Molecule-Modulated Plasmon-Mediated Silver Oxidation with Dark-Field Optical Microscopy

Surface plasmon can trigger or accelerate many photochemical reactions, especially useful in energy and environmental industries. Recently, molecular adsorption has proven effective in modulating plasmon-mediated photochemistry, however the realized chemical reactions are limited and the underlying mechanism is still unclear. Herein, by using in situ dark-field optical microscopy, the plasmon-mediated oxidative etching of silver nanoparticles (Ag NPs), a typical hot-hole-driven reaction, is monitored continuously and quantitatively. The presence of thiol or thiophenol molecules is found essential in the silver oxidation. In addition, the rate of silver oxidation is modulated by the choice of different thiol or thiophenol molecules. Compared with the molecules having electron donating groups, the ones having electron accepting groups accelerate the silver oxidation dramatically. The thiol/thiophenol modulation is attributed to the modulation of the charge separation between the Ag NPs and the adsorbed thiol or thiophenol molecules. This work demonstrates the great potential of molecular adsorption in modulating the plasmon-mediated photochemistry, which will pave a new way for developing highly efficient plasmonic photocatalysts.     

Incommensurate Phase in Λ-cobalt (III) Sepulchrate Trinitrate Governed by Highly Competitive N−H⋅⋅⋅O and C−H⋅⋅⋅O Hydrogen Bond Networks**

Phase transitions in molecular crystals are often determined by intermolecular interactions. The cage complex of [Co(C₁₂H₃₀N₈)]³⁺ ⋅ 3 NO₃⁻ is reported to undergo a disorder-order phase transition at T_c1 ≈133 K upon cooling. Temperature-dependent neutron and synchrotron diffraction experiments revealed satellite reflections in addition to main reflections in the diffraction patterns below T_c1. The modulation wave vector varies as function of temperature and locks in at T_c3≈98 K. Here, we demonstrate that the crystal symmetry lowers from hexagonal to monoclinic in the incommensurately modulated phases in T_c1<T<T_c3. Distinctive levels of competitions: trade-off between longer N−H⋅⋅⋅O and shorter C−H⋅⋅⋅O hydrogen bonds; steric constraints to dense C−H⋅⋅⋅O bonds give rise to pronounced modulation of the basic structure. Severely frustrated crystal packing in the incommensurate phase is precursor to optimal balance of intermolecular interactions in the lock-in phase.     

Continuous Porous Aromatic Framework Membranes with Modifiable Sites for Optimized Gas Separation

Continuous microporous membranes are widely studied for gas separation, due to their low energy premium and strong molecular specificity. Porous aromatic frameworks (PAFs) with their exceptional stability and structural flexibility are suited to a wide range of separations. Main-stream PAF-based membranes are usually prepared with polymeric matrices, but their discrete entities and boundary defects weaken their selectivity and permeability. The synthesis of continuous PAF membranes is still a major challenge because PAFs are insoluble. Herein, we successfully synthesized a continuous PAF membrane for gas separation. Both pore size and chemistry of the PAF membrane were modified by ion-exchange, resulting in good selectivity and permeance for the gas mixtures H₂/N₂ and CO₂/N₂. The membrane with Br^? as a counter ion in the framework exhibited a H₂/N₂ selectivity of 72.7 with a H₂ permeance of 51844 gas permeation units (GPU). When the counter ions were replaced by BF₄^?, the membrane showed a CO₂ permeance of 23058 GPU, and an optimized CO₂/N₂ selectivity of 60.0. Our results show that continuous PAF membranes with modifiable pores are promising for various gas separation situations.