电子结构计算的数值方法与理论

第一原理电子结构计算已成为探索与研究物质机理、理解与预测材料性质的重要手段和工具.虽然第一原理电子结构计算取得了巨大的成功,但是如何利用高性能计算机又快又好地计算大规模体系,如何从数学角度理解电子结构模型的合理性与计算的可靠性和有效性,依然充满各种挑战.基于密度泛函理论的第一原理电子结构计算的核心数学模型为Kohn-Sham方程或相应的Kohn-Sham能量泛函极小问题.近年来,人们分别从非线性算子特征值问题的高效离散及Kohn-Sham能量泛函极小问题的最优化方法设计两个方面对电子结构计算的高效算法设计及分析展开了诸多研究.本文重点介绍我们小组在电子结构计算的方法与理论方面的一些进展,同时简单介绍该领域存在的困难与挑战.     

双曲型方程的质量集中有限元法

用有限元法求解波动方程有许多工作,在此不多加阐述,本文针对线性双曲型方程采用质量集中有限元法,该方法产生于用特定的数值积分公式计算普通有限元法中的内积积分,这种方法具有较好的数值稳定性。     

Synthesis of ratiometric fluorescent nanoparticles for sensing oxygen

A facile reprecipitation-encapsulation method is used for the preparation of ratiometric fluorescent nanoparticles (NPs) for sensing intracellular oxygen. The surface of the NPs is modified in-situ with poly-L-lysine, which renders good biocompatibility and enables easy internalization into living cells. The sensor NPs contain a red fluorescent probe whose fluorescence is sensitive to oxygen with a quenching response of 77 % on going from nitrogen saturation to oxygen saturation, and a reference dye giving a green signal that acts as an oxygen-independent reference. The ratio of the two emissions serves as the analytical information and is sensitive to dissolved oxygen in the 0–43?ppm concentration range. When incorporated into cells, the ratio of the signals increases by 400?% on going from oxygen-saturated to oxygen-free environment.

Multi-valued solutions to Hessian equations

In this paper, we use the Perron method to prove the existence of bounded multi-valued viscosity solutions to Hessian equations and interior Lipschitz continuity of the multi-valued solutions.     

Tuning the transport properties of a (C60)2 bridge with electron and hole dopings

The tuning effects of substitutional B and N dopings on the electron transport properties of a C(60) dimer bridge [(C(60))(2)] are investigated by nonequilibrium Green's functions in combination with density functional theory. It is found that, unlike C(60), the equilibrium conductance of (C(60))(2) is very small. However, it can be controlled by electron (N) doping or hole (B) doping, which shifts the molecular energy levels so that the LUMOs or HOMOs align well with the Fermi level and results in LUMO-mediated transport or HOMO-mediated transport. The conductance increases accordingly with a certain number of N or B atoms doped in the C(60)s. Interestingly, when one C(60) is doped with N atoms and the other is doped with B atoms, new transport behaviors arise and rectification is achieved due to the special alignment of the energy levels of the individual C(60)s with the Fermi level. It suggests that cluster or molecule assembling can often realize specific functions which are not available by single molecules and should be taken into consideration in the design of molecular devices.     

Ab initio electron transport study of carbon and boron-nitrogen nanowires

We report first-principles calculations on the electrical transport properties of two kinds of one-dimensional nanowires: (a) a carbon nanowire (CNW) with alternating single and triple bonds and (b) a boron-nitrogen nanowire (BNNW) with equidistant bonds. We demonstrate the similarity and difference between the carbon nanowire and its boron-nitrogen analogue in the molecular orbital and transport properties, and then explore the potential innovations. The effects of molecular orbitals and nanowire-electrode coupling on the transport properties are analyzed. The cases of the nanowires sandwiched between both nanoscale and bulk electrodes are considered. It suggests that the characteristics of the transmission spectra and the current-voltage characteristics (I-V curves) are determined both by the electrodes and by the molecule as well as their coupling. In particular, the negative differential resistance (NDR) phenomenon is more apparent when the nanowires are positioned between two nanoscale electrodes. The tuning of the transport properties is also probed through the changes of nanowire-electrode separation and the inclusion of a gate voltage. These lead to dramatic variations in the equilibrium conductance, which can be understood from the shift and alignment of the molecular orbital relative to the Fermi level of the electrodes. In the analysis of the effects of nanowire-electrode separation, it shows that the equilibrium conductance has the same variation behavior as that of the projected density of states (PDOS) for CNW, while the localized molecular orbitals of BNNW result in its conductance varies differently from its PDOS. The different molecular orbital characteristics near the Fermi level of these two kinds of nanowires underlie their different transport properties.     

一种新型铒镱共掺碲硅酸盐玻璃的光谱性质及荧光俘获效应研究

用高温熔制法制备了系列Er^3＋／Yb^3＋共掺碲硅酸盐玻璃样品，测试和分析了玻璃样品的吸收光谱、荧光光谱、上转换发光光谱及热稳定性。结果表明：这种玻璃具有较宽的荧光半高宽、较大的受激发射截面，较好的热稳定性。970nm泵浦下该系列玻璃在可见光525，546和658nm这3处存在明显的上转换现象，它们分别由Er^3＋离子^2H11/2→^4 I15/2，4S3/2→^4 I15/2和^4 F9/2→^4 I15/2辐射跃迁产生。另外，测试和讨论了在不同样品厚度下玻璃的光谱特性，如荧光光谱、荧光寿命和上转换发光光谱等。结果表明，荧光俘获效应对Er^3＋离子1．5μm波段荧光及上转换发光都有着较大的影响，并随着玻璃厚度的增加而增大，导致测量值与实际值产生较大的偏差。     

不同反相色谱系统保留值方程系数的换算

在统计热力学基础之上，运用数学方法导出了不同反相色谱系统中保留值方程系数换算公式如下：ａ′＝ｋ１＋ｋ２ａ＋ｋ３ｘＡ氢ｃ′＝ｊ１＋ｊ２ｃ＋ｊ３ｘＡ氢采用正构烷烃、卤代苯、烷基苯、氯代酚等类型化合物的实验数据，验证了上述公式。本文为不同反相色谱体系保留值的换算奠定了基础。     

Fe-MCM-41 with highly ordered mesoporous structure and high Fe content: synthesis and application in heterogeneous catalytic wet oxidation of phenol

Raman spectroscopy has been successfully employed in order to investigate the formation of β-cyclodextrin host–guest inclusion molecular complexes with several different azo-dye structures. The Raman pattern of the carbohydrate framework results negligible when neared to the magnificent intensity of the highly polarisable guest systems and a complete and feasible comparison of the spectral features between the free and the complexed situation of the guest molecule is allowed. In general, with respect to the free guest state, it was found within the complex that a hampering of Raman intensity displays, accompanied by a levelling directed variation of the relative peak intensities, and peculiar Raman peak broadening with shifts occur, relatable to the host–guest settling of inclusive intermolecular interactions. Supportively to the other commonly established characterising methods, or in valid alternative, Raman technique has proved astoundingly useful under the perspective of the diagnostic evaluation of cyclodextrin host–guest molecular inclusion for azo-dyes and, more generally, for a highly polarisable guest structure. It features sample non-destructivity, handiness, fastness and sensitive reproducibility, occasionally providing useful suggestions about the complexation topology.