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.

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.

Metric Basis of Four-Dimensional Klein Bottle

The Metric of a graph plays an essential role in the arrangement of different dimensional structures and finding their basis in various terms.The metric dimension of a graph is the selection of the minimum possible number of vertices so that each vertex of the graph is distinctively defined by its vector of distances to the set of selected vertices.This set of selected vertices is known as the metric basis of a graph.In applied mathematics or computer science,the topic of metric basis is considered as locating number or locating set,and it has applications in robot navigation and finding a beacon set of a computer network.Due to the vast applications of this concept in computer science,optimization problems,and also in chemistry enormous research has been conducted.To extend this research to a four-dimensional structure,we studied the metric basis of the Klein bottle and proved that the Klein bottle has a constant metric dimension for the variation of all its parameters.Although the metric basis is variying in 3 and 4 values when the values of its parameter change,it remains constant and unchanged concerning its order or number of vertices.The methodology of determining the metric basis or locating set is based on the distances of a graph.Therefore,we proved the main theorems in distance forms.

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.

Accurate equilibrium inversion barrier of ammonia by extrapolation to the one-electron basis set limit

A scheme based on treating uniform singlet-pair and triplet-pair interactions is suggested to extrapolate electron correlation energy of ammonia, calculated at two basis-set levels of ab initio theory in the infinite one-electron basis-set limit. The dual-level method is tested on the extrapolation of the full correlation in coupled-cluster singles and doubles and in the case also a noniterative perturbative correction for connected triple energies for the C3v and D3h structures of ammonia, with correlation-consistent basis sets of the type cc-pVXZ （X = D, T, Q, 5, 6） and aug-cc-pVXZ （X = D, T, Q, 5）. For testing and comparison purposes, the energies reported by Klopper [J. Comput. Chem. 22 1306 （2001）] have been taken. From a corresponding extrapolation of CCSD（T）/AVXZ energies for X = 4, 5, we obtain total inversion barriers of 1833.87 cm-1/1832.33 cm^-1 for the two/three-parameter extrapolation rules, which are in good agreement with other theoretical extrapolation and empirical values in the literature.

On the Accuracy of the Complete Basis Set Extrapolation for Anionic Systems: A Case Study of the Electron Affinity of Methane

Recent experimental evidence suggests again the existence of the metastable methane anion in plasma swarms. In order to test the reliability of the complete basis set (CBS) extrapolation scheme with augmented correlation-consistent basis sets for anionic molecules, we study the evolution of the electron affinity of methane with benchmark ab initio calculations with aug-cc basis sets up to aug-cc-pV6Z + diffuse. Geometry optimizations and vibrational analysis were done at the MP2 level. The electron affinity (EA) was calculated at the MP2 and CCSD(T) levels with and without frozen core and including the extrapolations to the CBS limit. Using the aug-cc-pVnZ basis sets it is found that two non-decreasing CCSD(T) CBS limits exist for the EA (0.29 and 0.53 eV) obtained with the n = 3, 4, 5 and n = 4, 5, 6 series, respectively. A new scheme is proposed which can be generalized for very accurate quantum chemical description of molecular anions: the standard aug-cc-pVnZ basis sets can be supplemented with extra-diffuse orbitals using a simple even-tempered scheme. This yields a reliable CBS extrapolation method to develop a (discrete approximation of a) continuum anionic state near ionization, viz., one that closely matches the energy of the corresponding neutral state. These results show that CH4 has no stable anions of 2A1 symmetry, implying that plasma swarms with anionic methane consist of metastable rather than stable methane anions.

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.

Basis Sets Dependency in Constructing Spectroscopy-Accuracy Ab Initio Global Electric Dipole Moment Functions

Recently,more attention have been paid on the construction of dipole moment functions(DMF)using theoretical methods.However,the computational methods to construct DMFs are not validated as much as those for potential energy surfaces do.In this letter,using Ar…He as an example,we tested how spectroscopyaccuracy DMFs can be constructed using ab initio methods.We especially focused on the basis set dependency in this scenario,i.e.,the convergence of DMF with the sizes of basis sets,basis set superposition error,and mid-bond functions.We also tested the explicitly correlated method,which converges with smaller basis sets than the conventional methods do.This work can serve as a pictorial sample of all these computational technologies behaving in the context of constructing DMFs.

Basis Set Extrapolation for the High Resolution Spectroscopy

Valence and all electron correlation energies of a large set of atoms and molecules with structural motifs from amino acids and peptides at their equilibrium as well as non-equilibrium geometries are calculated at the levels of MP2, RI-MP2, and CCSD （T） with Dunnings sequential correlation consistent basis sets. A two point basis set extrapolation scheme for correlation energies to the complete basis set limit based on only DZ （double-zeta） and TZ （triple-zeta） results is presented and analyzed. We show that this basis set extrapolation scheme reduces the computational cost by two to three orders of magnitude to obtain the same accuracy as simpler extrapolations from higher order basis set computations.

Rough set and radial basis function neural network based insulation data mining fault diagnosis for power transformer

Rough set (RS) and radial basis function neural network (RBFNN) based insulation data mining fault diagnosis for power transformer is proposed. On the one hand rough set is used as front of RBFNN to simplify the input of RBFNN and mine the rules. The mined rules whose “confidence” and “support” is higher than requirement are used to offer fault diagnosis service for power transformer directly. On the other hand the mining samples corresponding to the mined rule, whose “confidence and support” is lower than requirement, are used to be training samples set of RBFNN and these samples are clustered by rough set. The center of each clustering set is used to be center of radial basis function, i.e., as the hidden layer neuron. The RBFNN is structured with above base, which is used to diagnose the case that can not be diagnosed by mined simplified valuable rules based on rough set. The advantages and effectiveness of this method are verified by testing.

量子力学表示理论的一种实现

量子力学创立伊始,狄拉克就关注到了一般表示的问题,其后量子力学的发展又引入了福克态、相干态等表示。好的表示应能提供正交归一的完备基,同时又能给出问题的严格解析解或者允许方便地得到近似解,但这常常是做不到的。我们意识到此前得到的相干态正交化方法恰恰满足表示理论的一般性要求,且因为包含自由参数为构造归一化的完备正交基实际上提供了无限的选择,这样甚至在解决问题的过程中都可以灵活地选择不同的表示,从而带来计算量的大幅减小。通过对不同耦合强度下的近共振态Rabi模型最初10个能级的计算,并同关联的JC模型的结果相比较,验证了相干态正交化方法的有效性。

原子基态能量的高精度Roothaan-Hartree-Fock计算方法

量子力学中的Roothaan-Hartree-Fock(R-H-F)近似计算在原子、分子和材料电子结构计算中具有重要的意义,是其他高精度电子结构计算方法的基础.本工作根据开源网站Basis Set Exchange中丰富的基组资源,利用高斯型基组矩阵元具有解析表达式的特性,自行编写Roothaan-Hartree-Fock计算程序,可以较为方便的达到高精度的计算结果.同时本工作用不同大小的基组计算了多种原子和离子的基态能量,研究了He、Be、C2+等原子和离子在不同基组下的收敛特性.此外,基于自行编写的R-H-F程序计算得到He、Be、Ne的第一电离能,与实验对比最大误差不超过6.84%.

Optimized numerical density functional theory calculation of rotationally symmetric jellium model systems

In real space density functional theory calculations,the effective potential depends on the electron density,requiring self-consistent iterations,and numerous integrals at each step,making the process time-consuming.In our research,we propose an optimization method to expedite density functional theory(DFT)calculations for systems with large aspect ratios,such as metallic nanorods,nanowires,or scanning tunneling microscope tips.This method focuses on employing basis set to expand the electron density,Coulomb potential,and exchange-correlation potential.By precomputing integrals and caching redundant results,this expansion streamlines the integration process,significantly accelerating DFT computations.As a case study,we have applied this optimization to metallic nanorod systems of various radii and lengths,obtaining corresponding ground-state electron densities and potentials.

基于B3LYP/LanL2DZ和B3LYP/aug-cc-pVTZ方法计算铜络合物的铜同位素分馏

铜的氯络合物和硫氢络合物是铜在成矿流体中稳定存在并参与地球化学迁移的重要形式;文中利用量子化学方法B3LYP/LanL2DZ和B3LYP/aug-cc-pVTZ研究计算了Cu＋络合物（CuCl、[CuCl2]-、[CuCl3]2-、CuCl（H2O）（真空）、CuHS,0～600℃）和Cu2＋络合物（CuCl＋、CuCl2（真空）、CuOH＋、CuHS＋、Cu（HS）2,0～300℃）的简约配分函数比。然后对比前人的理论与计算成果,讨论了不同基组方法计算铜络合物的铜同位素分馏的适应性。计算结果表明：利用LanL2DZ得到的Cu＋氯络合物的分馏结果103lnβ65-63比应用其他方法计算的结果偏大;而基于LanL2DZ基组计算Cu2＋络合物的结果比aug-cc-pVTZ基组偏小。利用赝势基组LanL2DZ计算铜同位素分馏和实验结果偏差比较大,可能的原因是基于赝势基组LanL2DZ对上述络合物开展结构优化时,键长值比实验值偏大所致。因此,从理论计算上看,利用6-311＋G（d,p）基组可能更适合铜络合物的铜同位素分馏计算。虽然这些不同基组计算的结果存在差异,但与前人的实验结果相比,各种理论计算结果都在误差允许范围之内。鉴于此,在利用第一性原理计算同位素分馏系数时,如果计算条件允许,最好利用多种基组计算并作对比分析。

基于神经网络的风电海缆弯曲限制器优化设计

我国海上风力发电已进入平价并网时代,行业中所有零部件设计都将面临优化设计的挑战。弯曲限制器广泛应用于风电缆保护中,其弯曲刚度与Mises峰值应力都是结构设计的关键指标。目前,弯曲限制器结构优化设计多基于经验和有限元分析迭代,该方法效率较低,并且多目标优化较困难。本文针对该问题提出一种基于神经网络的风电海缆弯曲限制器多目标优化方法。先在给定的设计域内,利用正交试验设计法和有限元分析获得的样本,构建RBF神经网络代理模型;再采用非支配排序遗传算法IⅡI(NSGA-IⅡI)对弯曲限制器进行多目标优化,得到了Pareto最优解集。本文为限弯器结构结构设计提供了一种可行的多目标优化方法。

Characteristic Properties of Perspective Sets for Finite Stochastic Decision

For a perspective set that is derived by finite consequences with probabilities, this paper introduces the conception of basis that is proved and the uniqueness of basis over a perspective set holds. These give the characteristic properties of perspective sets and finite consequences with probabilities. These properties are applied to the utility defined by the consequences.

地理信息科学一流本科专业核心课程体系设计与实践

随着地理学、测绘科学与技术、信息技术等学科的发展,地理信息科学(GIS)专业核心课程体系面临修订和完善的需求。如何设计适合本专业的课程体系,以及需要参考哪些因素,是亟待讨论的问题。本文在对比分析北京大学、南京大学和北京师范大学GIS专业核心课程体系基础上,详细讨论了武汉大学GIS专业核心课程体系的设计原则和实践过程,提出了影响课程体系设计的若干因素,包括学科支撑、社会需求、师资结构等,可为其他高校GIS专业课程体系设计提供有益借鉴。

平面波与高斯函数或样条函数复合基组

通过将平面波与高斯函数或者样条函数结合到一起,本文构建了一种新的复合基组.利用格拉姆-施密特正交化方法或者L?wdin正交化方法,对复合基组进行正交归一化.通过选择平面波函数中波矢的绝对值,选择性地求解某个能量区间内的本征态,将大型哈密顿矩阵的计算转变为多个小型矩阵的计算,以及通过减少电子势能平缓部分展开基矢数目,极大地加快了计算速度.以一维有限深势阱为例,通过与严格计算方法的对比,验证了本文复合基组能够在加速计算的情况下保证求解精度.同时,本文还研究了不同的参数设置对计算精度的影响,包括复合基矢的疏密度、高斯函数的宽值,以及样条函数不同区域占函数总宽度的比值等参数.最后该复合基组可以直接应用到对大尺寸纳米金属结构的等离激元数值计算当中.

Optimizing radial basis function neural network based on rough sets and affinity propagation clustering algorithm

A novel method based on rough sets (RS) and the affinity propagation (AP) clustering algorithm is developed to optimize a radial basis function neural network (RBFNN). First, attribute reduction (AR) based on RS theory, as a preprocessor of RBFNN, is presented to eliminate noise and redundant attributes of datasets while determining the number of neurons in the input layer of RBFNN. Second, an AP clustering algorithm is proposed to search for the centers and their widths without a priori knowledge about the number of clusters. These parameters are transferred to the RBF units of RBFNN as the centers and widths of the RBF function. Then the weights connecting the hidden layer and output layer are evaluated and adjusted using the least square method (LSM) according to the output of the RBF units and desired output. Experimental results show that the proposed method has a more powerful generalization capability than conventional methods for an RBFNN.

一种基于IDOA-RBF神经网络的正常流量过滤方法

针对全流量检测方式容易使安全检测设备出现性能瓶颈的问题,给出一种使用改进的野狗优化算法来优化径向基函数神经网络的正常流量过滤方法。首先,采用Singer混沌映射和搜索平衡策略对野狗优化算法进行改进;其次,用改进后的野狗优化算法优化RBF神经网络的输出权值,使用CSE-CIC-IDS2018数据集训练网络,构建正常流量过滤模型;最后,在网络流量进入安全检测设备前尽可能多地过滤掉其中正常流量,减轻安全检测设备的工作负担。实验结果表明:与现有的模型相比,IDOA-RBF神经网络的正常流量过滤模型在建模时间上有较大的改善,同时保持较高的识别精度,并且能在需要检测的流量中过滤掉72.9%的正常流量。