All-electron basis sets for H to Xe specific for ZORA calculations:Applications in atoms and molecules

A segmented basis set of quadruple zeta valence quality plus polarization functions(QZP)for H through Xe was developed to be used in conjunction with the ZORA Hamiltonian.This set was augmented with diffuse functions to describe electrons farther away from the nuclei adequately.Using the ZORA-CCSD(T)/QZP-ZORA theoretical model,atomic ionization energies and bond lengths,harmonic vibrational frequencies,and atomization energies of some molecules were calculated.The addition of core-valence corrections has been shown to improve the agreement between theoretical and experimental results for molecular properties.For atomization energies,a similar observation emerges when considering spin-orbit couplings.With the augmented QZP-ZORA set,static mean dipole polarizabilities of a set of atoms were calculated and compared with previously published recommended and experimental values.Performance evaluations of the ZORA and Douglas–Kroll–Hess Hamiltonians were made for each property studied.

A DFT/ECP-Small Basis Set Modelling of Cisplatin: Molecular Structure and Vibrational Spectrum

A DFT conformational and vibrational analysis of a single molecule of cisplatin (cis-[Pt(NH3)2Cl2]) was performed by means of PW91 functional and LANL08 ECP basis set for the Pt atom. 3-21G and 3-21G* Basis sets were used for the remaining atoms. All the initially chosen conformations were found to converge to the global minimum conformation of C2v symmetry with H atoms lying in the coordination plane and pointing to the Cl atoms. The computational results were compared with the newest experimental structural data and with the vibrational spectroscopic data for cisplatin, obtained by other workers. The chosen level of theory was found to describe satisfactory the molecular structure (r. m. s. of the relative deviations ≤ 6%) and the harmonic vibrational frequencies (r. m. s. of the relative deviations ≤ 5%) of cisplatin.

All-electron ZORA triple zeta basis sets for the elements Cs-La and Hf-Rn

Segmented all-electron basis set of triple zeta valence quality plus polarization functions(TZP)for the elements of the fifth row to be used together with the zero-order regular approximation(ZORA)is carefully constructed.To correctly describe electrons distant from atomic nuclei,the basis set is augmented with diffuse functions giving rise to a set designated as ATZP-ZORA.At the ZORA-B3LYP theoretical level,these sets are used to calculate the ionization energy and mean dipole polarizability of some atoms,bond length,dissociation energy,and harmonic vibrational frequency of diatomic molecules.Then,these results are compared with the theoretical and experimental data found in the literature.Even considering that our sets are relatively compact,they are sufficiently accurate and reliable to perform property calculations involving simultaneously electrons from the inner shell and outer shell.The performances of the ZORA and second-order Douglas-Kroll-Hess Hamiltonians are evaluated and the results are also discussed.

Topology and Shape Optimization of 2-D and 3-D Micro-ArchitecturedThermoelastic Metamaterials Using a Parametric Level Set Method

2-D and 3-D micro-architectured multiphase thermoelastic metamaterials are designed and analyzed using a parametric level set method for topology optimization and the finite element method.An asymptotic homogenization approach is employed to obtain the effective thermoelastic properties of the multiphase metamaterials.Theε-constraint multi-objective optimization method is adopted in the formulation.The coefficient of thermal expansion(CTE)and Poisson’s ratio(PR)are chosen as two objective functions,with the CTE optimized and the PR treated as a constraint.The optimization problems are solved by using the method of moving asymptotes.Effective isotropic and anisotropic CTEs and stiffness constants are obtained for the topologically optimized metamaterials with prescribed values of PR under the constraints of specified effective bulk modulus,volume fractions and material symmetry.Two solid materials along with one additional void phase are involved in each of the 2-D and 3-D optimal design examples.The numerical results reveal that the newly proposed approach can integrate shape and topology optimizations and lead to optimal microstructures with distinct topological boundaries.The current method can topologically optimize metamaterials with a positive,negative or zero CTE and a positive,negative or zero Poisson’s ratio.

Structural Investigation of Technetium-Diphosphonate Complex 99mTc-MDP

Density functional theory method has been employed to investigate the structures of the prototypical technetium-labeled diphosphonate complex 99mTc-MDP, where MDP represents methylenediphosphonic acid. A total of 14 trial structures were generated by allowing for the geometric, conformational, charge, and spin isomerism. Based on the optimized structures and calculated energies at the B3LYP/LANL2DZ level, two stable isomers were determined for the title complex. And they were further studied systematically in comparison with the experimental structure. The basis sets 6-31G＊（LANL2DZ for Tc）, 6-31G＊（cc-pVDZ-pp for Tc）, and DGDZVP have also been employed in combination with the B3LYP functional to study the basis set effect on the geometries of isomers. The optimized structures agree well with the available experimental data, and the bond lengths are more sensitive to the basis set than the bond angles. The charge distributions were studied by the Mulliken population analysis and natural bond orbital analysis. The results reflect a significant ligand-to-metal electron donation.

Hybrid FEM-BEM for simulation of electromagnetic response

A finite element method with boundary element method (FEM-BEM) is presented for computing electromagnetic induction. The features of an edge element method including the volume and surface edge element method are investigated in depth. Surface basis functions of edge elements to an arbitrary shape of target are derived according to the geometrical property of basis functions and applied to discretize the surface integral equation for 3-D general targets. The proposed model is presented to compute resonant frequencies and surface current of underground unexplored ordnance (UXO), and then the electromagnetic responses of single target with different frequencies and positions of sensor are simulated and results are validated by experiments.

THE MESHLESS VIRTUAL BOUNDARY METHOD AND ITS APPLICATIONS TO 2D ELASTICITY PROBLEMS

A novel numerical method for eliminating the singular integral and boundary effect is processed. In the proposed method, the virtual boundaries corresponding to the numbers of the true boundary arguments are chosen to be as simple as possible. An indirect radial basis function network （IRBFN） constructed by functions resulting from the indeterminate integral is used to construct the approaching virtual source functions distributed along the virtual boundaries. By using the linear superposition method, the governing equations presented in the boundaries integral equations （BIE） can be established while the fundamental solutions to the problems are introduced. The singular value decomposition （SVD） method is used to solve the governing equations since an optimal solution in the least squares sense to the system equations is available. In addition, no elements are required, and the boundary conditions can be imposed easily because of the Kronecker delta function properties of the approaching functions. Three classical 2D elasticity problems have been examined to verify the performance of the method proposed. The results show that this method has faster convergence and higher accuracy than the conventional boundary type numerical methods.

Predefined Exponential Basis Set for Half-Bounded Multi Domain Spectral Method

A non-orthogonal predefined exponential basis set is used to handle half-bounded domains in multi domain spectral method (MDSM). This approach works extremely well for real-valued semi-infinite differential problems. It spans simultaneously wide range of exponential decay rates with multi scaling and does not suffer from zero crossing. These two conditions are necessary for many physical problems. For comparison, the method is used to solve different problems and compared with analytical and published results. The comparison exhibits the strengths and accuracy of the presented basis set.

THE THEORETICAL STUDY OF ADSORPTION OF METAL IONS ON CHITOSAN

The interactions between metal ions such as Zn2+, Pb2+, Mn2+, Hg2+, Cd2+, Ni2+ and chitosan have been investigated using the model cluster model method and density functional method. Full optimization and frequency analysis of all cluster models have been performed employing B3LYP hybrid method at 3-21G basis set level except metal ions which were invoked to use effective core potential (ECP) method. The energy changes, and the main structural parameters have been obtained during the theoretical study of the adsorption of metal ions on the chitosan. The calculations showed that the coordination modes of metal ions with chitosan models were different, the geometries of Mn2+, Zn2+, Cd2+, Hg2+, Pb2+ ions coordinated with two nitrogen atoms and two oxygen atoms were distorted tetrahedral, while the square planar structure of Ni2+ coordinated two nitrogen atoms and two oxygen atoms was observed. The heat of reaction between six metal ions and chitosan models showed the order: Mn2+ >Ni2+ >Zn2+ >Pb2+ >Hg2+ >Cd2+, this suggested that the coordination strength of Mn2+ >Ni2+ >Zn2+ >Pb2+ >Hg2+ >Cd2+.

Ground state energy of He isoelectronic sequence treated variationally via Hylleraas-like wavefunction

In this study, the energy for the ground state of helium and a few helium-like ions （Z=1-6） is computed variationally by using a Hylleraas-like wavefunction. A four-parameters wavefunction, satisfying boundary conditions for coalescence points, is combined with a Hylleraas-like basis set which explicitly incorporates r12 interelectronic distance. The main contribution of this work is the introduction of modified correlation terms leading to the definition of integral transforms which provide the calculation of expectation value of energy to be done analytically over single-particle coordinates instead of Hylleraas coordinates.

Implicit Shape Reconstruction of Unorganized Points Using PDE-Based Deformable 3D Manifolds

In this work we consider the problem of shape reconstruction from an unorganized data set which has many important applications in medical imaging, scientific computing, reverse engineering and geometric modelling. The reconstructed surface is obtained by continuously deforming an initial surface following the Partial Differential Equation (PDE)-based diffusion model derived by a minimal volume-like variational formulation. The evolution is driven both by the distance from the data set and by the curvature analytically computed by it. The distance function is computed by implicit local interpolants defined in terms of radial basis functions. Space discretization of the PDE model is obtained by finite co-volume schemes and semi-implicit approach is used in time/scale. The use of a level set method for the numerical computation of the surface reconstruction allows us to handle complex geometry and even changing topology,without the need of user-interaction. Numerical examples demonstrate the ability of the proposed method to produce high quality reconstructions. Moreover, we show the effectiveness of the new approach to solve hole filling problems and Boolean operations between different data sets.

数字平台型企业网络效应影响因素的组态研究——基于模糊集定性比较分析方法

在消费者主导的数字浪潮下,网络效应已成为数字平台型企业扩大市场规模的关键点,依靠网络效应建立用户价值优势成为最核心的竞争策略。本研究在数字经济这一全新背景下,从网络效应视角出发,根据调查问卷获取的数据,运用模糊集定性比较法分析其多影响因素间的组态关系,深入挖掘其前因条件间的有效组合和匹配(即协同)。研究发现:市场定位和价格因素二者之间的协同是网络效应激发过程中的核心条件。技术因素和社交因素二者间的协同是网络效应扩大过程中的核心条件。平台治理和技术因素间的协同关系是网络效应迭代过程中的核心条件。在此基础上,本研究提出了“激发—扩大—迭代”三条增强数字平台型企业网络效应的实现路径,为数字平台企业综合竞争力的提升和可持续发展提供了科学的参考。

基于多源数据融合的电子对抗效能评估

以电子对抗基地化演训任务为支撑,提出一种多源数据融合的效能评估方法。结合实兵对抗过程中各种类型数据,采用统计分析和专家评判建立指标模型,针对效能评估指标的权重确定问题,使用最小二乘法融合主客观信息进行组合赋权,通过加权聚合模型对作战效能进行综合评估,最后运用粗糙集开展电子对抗效能的影响因素分析。实例表明该方法能够通过聚合不同类别数据之间的互补优势,提高评估结果的可靠性,在电子对抗作战效能评估中具有一定实用性。

自制三通管、输血皮条改良注射器注水法在FURL中的应用

目的:探析自制三通管、输血皮条改良注射器注水法在输尿管软镜钬激光碎石术(FURL)中的应用效果。方法:选择2021年1月~2022年12月弋矶山医院收治的480例接受FURL治疗的泌尿系结石患者作为研究对象,按照住院号尾数单双数进行随机分组,双数为对照组(n=240),采用传统注射器注水法;单数为观察组(n=240),采用自制的三通管、输血皮条改良注射器注水法,对比两组患者并发症发生率、医生满意度、手术器械台术中潮湿率以及手术时间等指标。结果:观察组患者全身炎症反应综合征、尿路刺激征等并发症发生率均低于对照组患者(P<0.05)。观察组手术医生护理满意率(89.29%)高于对照组(60.71%),观察组器械台术中潮湿率(4.16%)低于对照组(91.67%)(P<0.05)。观察组中手术时间、平均注水量、平均住院费用均低于对照组,平均住院时间短于对照组(P<0.05)。结论:FURL术中使用自制三通管、输血皮条改良注射器注水法可降低术后并发症发生率,提高医生满意率,降低手术器械台潮湿率,缩短手术时间,减少术中注水量,降低患者住院费用,对提升患者整体治疗效果有着积极的作用。

Efficient Mapping of High Order Basis Sets for Unbounded Domains

Many physical problems involve unbounded domains where the physical quantities vanish at infinities.Numerically,this has been handled using different techniques such as domain truncation,approximations using infinitely extended and vanishing basis sets,and mapping bounded basis sets using some coordinate transformations.Each technique has its own advantages and disadvantages.Yet,approximating simultaneously and efficiently a wide range of decaying rates has persisted as major challenge.Also,coordinate transformation,if not carefully implemented,can result in non-orthogonal mapped basis sets.In this work,we revisited this issue with an emphasize on designing appropriate transformations using sine series as basis set.The transformations maintain both the orthogonality and the efficiency.Furthermore,using simple basis set(sine function)help avoid the expensive numerical integrations.In the calculations,four types of physically recurring decaying behaviors are considered,which are:non-oscillating and oscillating exponential decays,and non-oscillating and oscillating algebraic decays.The results and the analyses show that properly designed high-order mapped basis sets can be efficient tools to handle challenging physical problems on unbounded domains.Decay rate ranges as large of 6 orders of magnitudes can be approximated efficiently and concurrently.

基于fsQCA和NCA的农村电商增收效应模型分析

为有效利用和优化农村电商增收的综合作用及其内在机制,从组态视角深入探讨分析农村电商增收效应的复杂影响机制。构建政府投入、基础设施、人力资本、发展质量及发展规模5个前因变量和1个经济效益结果变量的模型,综合运用熵值法、模糊集定性比较分析(Fuzzy-Set Qualitative Comparative Analysis,fsQCA)法及必要条件分析(Necessary Condition Analysis,NCA)法,对全国28个省(自治区、直辖市)的数据进行深入分析。研究结果表明:在影响农村电商增收效应的要素中,发展规模和发展质量对增收效应具有显著的正向推动作用;加强基础设施和人力资本的投入、提高发展质量及扩大发展规模,能够共同提高农村电商增收效应。

卟吩结构的理论方法和基组效应

用考虑电子相关的 MP2和 2种 DFT方法 ,在不同的基组下对卟吩结构全优化 .结果表明 ,当使用 MP2 / 3- 2 1 G方法时 ,仅考虑 2 0个最外层占据轨道的电子相关 ,即可较好地描述卟吩的对称结构 ;而 BPL/ 3- 2 1 G和 B3LYP/ 3- 2 1 G方法也能正确描述其对称结构 ;其中后者更接近实验值 ,说明用同时考虑定域和非定域相关的 B3LYP方法 ,比仅考虑定域相关的 BPL方法有较高的计算精度 .更大的基组对卟吩结构的描述并无大的改进 .

1961年以来海河流域干旱时空变化特征分析

以干旱易发区海河流域为例,利用流域内及其周边地区58个气象站点1961—2010年逐日气象观测数据,结合累积相对湿润度指数和模糊集对评价法,考虑了干旱的累积效应以及评价标准等级边界的模糊性和评价因子的时程分配,分析了海河流域干旱时空变化特征。结果表明:①近50年来流域主要干旱类型为中旱和重旱,平均面积分别约为7.30万km2和7.78万km2,重旱面积呈现出显著的增加趋势;②近25年来,重旱易发区范围表现出扩张的态势,1985—2010年重旱易发区面积达到14.9万km2,为1961—1985年的1.6倍。

利用PPR新方法建立草地产量增长模型及生态成因机理研究

利用新型的投影寻踪回归 ( PPR)统计方法 ,对新疆天山北坡蒿属荒漠草地上观测的 3a草地产量和其它 6个相关生态因子数据 ,进行了多元回归统计分析和 PPR分析 ,建立了 PPR新型牧草增长模型 ,并进而做了产量生态成因机理分析和理论解释。研究结果表明 ,在一般年份下 ,干草产量在不同年代不同季节均随降水量的分配状况而发生有规律的变化 ,产量分配呈现双峰模式 ;在降水量、积温和光照时数 3个影响产量形成和高低的生态因子中 ,尤以降水量影响最明显 ,是主导生态因子 ,但牧草生长发育状况和增长类型则是水热因子、质地、牧草生态习性和种类组成共同作用的结果 ;在建立草地产量增长模型和成因机理分析过程中 ,充分运用 PPR统计方法成功地克服了非正态非线性高维数据点稀疏所造成的“维数祸根”和自动排除了无关因子及人为因素的干扰 ,提高了建模的精度和效能 ,并给出各自变量因子对建模贡献率大小的效果 ,科学地揭示了用其它多元回归统计方法 ,所难以发现的数据内在的结构特征和规律性。进而 ,运用建立的PPR模型 ,较好地估测和拟合实测产量值 ,使模型估产精度达 90 %以上 ,并通过了效果检验和给出了贡献率统计分析。在6个自变量因子中 ,对牧草产量增长量贡献值最大的是生长时期 ( T) ,其次为土壤含水量 (

水合硅酸分子电子结构的从头算与基组效应研究

应用能量梯度技术 ,在从头算自洽场分子轨道的水平上 ,借助于最小基和扩展基中的 7种基组 ,优化得到了水合硅酸分子的平衡态几何构型 ,并与成键参数的实验值进行了比较 ,从而确定了以 6 31G基组进行几何构型优化最为合适 .对基态能量 (S0 )进行了自洽场 (RHF)、组态相互作用(CI)、M ller Plesset(MP2、MP4 )的计算 ,并利用CI法计算了水合硅酸分子体系的第 1激发态 (S1、T1)能量 ,其结果表明 ,以 6 31G 基组结合MP4计算出的系统能量最低 .通过对自洽场从头算基组效应的分析 ,确定水合硅酸分子系统的计算模式为 :以 6 31G基组为优化几何构型 ,然后利用 6 31G 基组计算能量 ,并利用MP4进行相关能量校正 。