The Influence of the Exchange-Correlation Functional on the Non-Interacting Kinetic Energy and Its Implications for Orbital-Free Density Functional Approximations

In this work it is shown that the kinetic energy and the exchange-correlation energy are mutual dependent on each other.This aspect is first derived in an orbital-free context.It is shown that the total Fermi potential depends on the density only,the individual parts,the Pauli kinetic energy and the exchange-correlation energy,however,are orbital dependent and as such mutually influence each other.The numerical investigation is performed for the orbital-based non-interacting Kohn-Sham system in order to avoid additional effects due to further approximations of the kinetic energy.The numerical influence of the exchange-correlation functional on the non-interacting kinetic energy is shown to be of the orderof a few Hartrees.For chemical purposes,however,the energetic performance as a function of the nuclear coordinates is much more important than total energies.Therefore,the effect on the bond dissociation curve was studied exemplarily for the carbon monoxide.The data reveals that,the mutual influence between the exchange-correlation functional and the kinetic energy has a significant influence on bond dissociation energies and bond distances.Therefore,the effect of the exchange-correlation treatment must be considered in the design of orbital-free density functional approximations for the kinetic energy.

Assignment of terahertz vibrational modes of L-glutamine using density functional theory within generalized-gradient approximation

The crystal structure of L-glutamine is stabilized by a three-dimensional network of intermolecular hydrogen bonds.We utilize plane-wave density functional theory lattice-dynamics calculations within the generalized-gradient approximation（GGA）, Perdew–Burke–Ernzerhof（PBE）, PBE for solids（PBEsol）, PBE with Wu–Cohen exchange（WC）, and dispersion-corrected PBE, to investigate the effect of these intermolecular contacts on the absorption spectra of glutamine in the terahertz frequency range. Among these calculations, the solid-state simulated results obtained using the WC method exhibit a good agreement with the measured absorption spectra, and the absorption features are assigned with the help of WC. This indicates that the vibrational modes of glutamine were related to the combination of intramolecular and intermolecular motions, the intramolecular modes were dominated by rocking or torsion involving functional groups; the intermolecular modes mainly result from the translational motions of individual molecules, and the rocking of the hydrogenbonded functional groups.

Bridge density functional approximation for non-uniform hard core repulsive Yukawa fluid

In this work, a bridge density functional approximation （BDFA） （J. Chem. Phys. 112, 8079 （2000）） for a nonuniform hard-sphere fluid is extended to a non-uniform hard-core repulsive Yukawa （HCRY） fluid. It is found that the choice of a bulk bridge functional approximation is crucial for both a uniform HCRY fluid and a non-uniform HCRY fluid. A new bridge functional approximation is proposed, which can accurately predict the radial distribution function of the bulk HCRY fluid. With the new bridge functional approximation and its associated bulk second order direct correlation function as input, the BDFA can be used to well calculate the density profile of the HCRY fluid subjected to the influence of varying external fields, and the theoretical predictions are in good agreement with the corresponding simulation data. The calculated results indicate that the present BDFA captures quantitatively the phenomena such as the coexistence of solid-like high density phase and low density gas phase, and the adsorption properties of the HCRY fluid, which qualitatively differ from those of the fluids combining both hard-core repulsion and an attractive tail.

Specification of Density Functional Approximation by Radial Distribution Function of Bulk Fluid

A systematic methodology is proposed to deal with the weighted density approximation version of clas-sical density functional theory by employing the knowledge of radial distribution function of bulk fluid. The presentmethodology results from the concept of universality of the free energy density functional combined with the test particlemethod. It is shown that the new method is very accurate for the predictions of density distribution ofa hard sphere fluidat different confining geometries. The physical foundation of the present methodology is also applied to the quantumdensity functional theory.

How to Extend the Bridge Density Functional Approximation to the Confined Non-hard Sphere Fluid

一个理论方法被建议扩大桥密度为到不一致的 Lennard-Jones (LJ ) 液体的不一致的难范围液体的功能的近似(BDFA ) 。为 LJ 液体的 DFT 途径简单，在大量共存阶段精确的份量上和外部地参数。特别， DFT 途径仅仅直接需要第二份订单是的共存体积液体的关联功能(DCF ) 输入，并且对 subcritical 温度区域因此适用。现在的理论方法能被认为是热力学的不安理论，它不在免费精力的水平，但是在 2000the 秒顺序 DCF 的水平在是的一个不一致的对应物。

Exchange-Correlation Functional Comparison of Electronic Energies in Atoms Using a Grid Basis

Calculation of total energies of the electronic ground states of atoms forms the basis for the frozen-core pseudopotentials used in atomistic calculations of much larger scale. Reference values for these energies provide a benchmark for the validation of new software to calculate such potentials. In addition, basic atomic-scale electronic properties such as the (first) ionization energy provide a simple check on the approximation used in the calculation method. We present a comparison of the total energies and ionization energies of atoms Z = 1 - 92 calculated in density functional theory with several levels of exchange-correlation functional and the Hartree-Fock method, comparing ionization energies to experiment. We also investigate the role of relativistic treatment on these energies.

APPROXIMATION RATES OF ERROR DISTRIBUTION OF DOUBLE KERNEL ESTIMATES OF CONDITIONAL DENSITY

In this paper, the normal approximation rate and the random weighting approximation rate of error distribution of the kernel estimator of conditional density function f(y|x) are studied. The results may be used to construct the confidence interval of f(y|x) .

Accurate Description of Catalytic Selectivity:Challenges and Opportunities for the Development of Density Functional Approximations

An accurate description of catalytic selectivity poses an enormous challenge for theoretical simulations.Due to the absence of a well-defined benchmark set on the catalytic selectivity,the performance of even the widely used density functional approximations(DFAs)is yet to be validated.This work reports a test set based on the selective hydrogenation ofα,β-unsaturated aldehydes catalyzed by ruthenium(Ru)hydride complexes.Special attention is paid to benchmark the regioselectivity of aldehydes to either unsaturated alcohols or saturated aldehydes.Accurate reference data were calculated by the massive parallel implementation of the coupled-cluster single,double,and perturbative triple excitations[CCSD(T)]approach,based completely on set limits.Furthermore,we performed the microkinetic simulation based on the CCSD(T)energy profiles,serving the most direct criteria for the performance of DFAs on catalytic selectivity of hydrogenation reactions.Using this test set,we uncovered the intrinsic difficulty of semilocal and hybrid functionals for such a purpose.In the context of the XYG3-type double hybrid(xDH)framework,we showed that this particular challenge could be addressed by the top rung functionals only when the many-body nondynamic correlation effect was accounted for adequately.A recently proposed xDH,namely scsRPA,showed unprecedented accuracy with only 5%error on average.The predicted kinetic selectivity by scsRPA is in close agreement with the reference value,revealing a unique versatility of the top rung DFAs for a reliable description of catalytic selectivity of hydrogenation reactions.

3C-SiC中嬗变原子(Mg、Be、Al)对He间隙原子迁移行为影响的第一性原理研究

辐照条件下固体嬗变原子对立方碳化硅(3C-SiC)基体内氦泡形成过程中的作用尚不明确。本文基于密度泛函理论研究了Mg、Be、Al这三种固体嬗变原子对He间隙原子在3C-SiC基体内的形成能以及迁移行为的影响。计算发现,He原子在3C-SiC基体中主要稳定于由Si或C原子组成的四面体间隙中,且易于在相邻间隙间迁移。当嬗变原子浓度从0增至5%(物质的量分数)时,碳四面体间隙位点的He原子形成能先是骤降、然后随着固体原子浓度的增大而线性改变,而硅四面体间隙位点的He原子形成能则是和固体原子浓度呈多次函数关系。同时,三种固体原子也使He原子的迁移势垒和扩散系数发生明显改变,He原子从C原子间隙迁移到Si原子间隙的迁移势垒随着固体原子浓度的升高而线性降低、扩散系数逐渐增大;从Si原子间隙迁移到C原子间隙的迁移势垒与浓度呈多次函数关系,扩散系数与势垒曲线反相关。无论哪种路径和掺杂浓度,固体原子的加入都促进了He原子的迁移,这为气泡的成核生长提供了有利条件。

Compton profiles of NiO and TiO_2 obtained from first principles GWA spectral function

In this work,we first use momentum density studies to understand strongly correlated electron behavior,which is typically seen in transition metal oxides.We observe that correlated electron behavior as seen in bulk NiO is due to the Fermi break located in the middle of overlapping spectral functions obtained from a GW（G is Green’s function and W is the screened Coulomb interaction） approximation（GWA） calculation while in the case of TiO2 we can see that the origin of the constant momentum distribution in lower momenta is due to a pile up of spectra before the Fermi energy.These observations are then used to compare our calculated Compton profiles with previous experimental studies of Fukamachi and Limandri.Our calculations for NiO are observed to follow the same trend as the experimental profile but it is seen to have a wide difference in the case of TiO2 before the Fermi break.The ground state momentum densities differ significantly from the quasiparticle momentum density,thus stressing the importance of the quasiparticle wave function as the input for the study of charge density and the electron localization function.Finally we perform a calculation of the quasiparticle renormalization function,giving a quantitative description of the discontinuity of the GWA momentum density.

Local Galerkin Method for the Approximate Solutions to General FPK Equations

In this paper, the method proposed recently by the author for the solution of probability density function (PDF) of nonlinear stochastic systems is presented in detail and extended for more general problems of stochastic differential equations (SDE), therefore the Fokker Planck Kolmogorov (FPK) equation is expressed in general form with no limitation on the degree of nonlinearity of the SDE, the type of δ correlated excitations, the existence of multiplicative excitations, and the dimension of SDE or FPK equation. Examples are given and numerical results are provided for comparing with known exact solution to show the effectiveness of the method.

Gradient Density Estimation in Arbitrary Finite Dimensions Using the Method of Stationary Phase

We prove that the density function of the gradient of a sufficiently smooth function , obtained via a random variable transformation of a uniformly distributed random variable, is increasingly closely approximated by the normalized power spectrum of ?as the free parameter . The frequencies act as gradient histogram bins. The result is shown using the stationary phase approximation and standard integration techniques and requires proper ordering of limits. We highlight a relationship with the well-known characteristic function approach to density estimation, and detail why our result is distinct from this method. Our framework for computing the joint density of gradients is extremely fast and straightforward to implement requiring a single Fourier transform operation without explicitly computing the gradients.

Robust Frequency Estimation Under Additive Symmetric α-Stable Gaussian Mixture Noise

Here the estimating problem of a single sinusoidal signal in the additive symmetricα-stable Gaussian(ASαSG)noise is investigated.The ASαSG noise here is expressed as the additive of a Gaussian noise and a symmetricα-stable distributed variable.As the probability density function(PDF)of the ASαSG is complicated,traditional estimators cannot provide optimum estimates.Based on the Metropolis-Hastings(M-H)sampling scheme,a robust frequency estimator is proposed for ASαSG noise.Moreover,to accelerate the convergence rate of the developed algorithm,a new criterion of reconstructing the proposal covar-iance is derived,whose main idea is updating the proposal variance using several previous samples drawn in each iteration.The approximation PDF of the ASαSG noise,which is referred to the weighted sum of a Voigt function and a Gaussian PDF,is also employed to reduce the computational complexity.The computer simulations show that the performance of our method is better than the maximum likelihood and the lp-norm estimators.

基于近似零范数稀疏恢复的迭代解法的三维重力反演（英文）

重力反演是应用地球物理中一个经典的方法,可以获取地下空间的密度分布特征。本文研究了一种新的三维重力反演方法,以压缩感知中的稀疏恢复方法为基本原理。建立以零范数为约束的目标函数,采用近似零范数求解方法对目标函数进行迭代求解。以重力正演模型为基础进行反演方法研究,建立包含深度加权函数的零范数的目标函数,采用相应的最优化数学方法进行求解,得到稀疏的反演结果。同时,为了得到具有实际地质意义的反演结果,采用惩罚函数将反演密度值约束在具有实际地球物理和地质意义范围内。采用本文提出的反演方法得到的反演目标异常源具有较为清晰的边界、深度信息和剩余密度分布信息。本文利用理论模型实验来验证反演方法效果,并将得到的反演结果与设计的理论模型对比分析说明三维反演方法的有效性和可靠性。为了进一步说明本文采用的反演方法的可靠性,将其应用到美国德克萨斯州采集的实际重力数据反演,并将反演结果与前人研究结果和该地区的测井资料进行对比分析,盐丘的深度为4.2km与测井得到深度4.4km基本上是一致的,说明研究的反演方法具有实际应用价值。

结构可靠性分析的多项式数值逼近法

提出了工程结构可靠性分析的多项式数值逼近法。它是以多项式 {1 ,x,… ,xn}为基 ,利用功能函数高阶矩 ,通过计算功能函数的最佳逼近概率密度函数 ,然后用工程结构可靠性分析的一般式来计算结构失效概率的可靠性分析新方法。通过理论分布曲线的数值检验和结构构件失效概率的计算 。

敏感负荷电压凹陷敏感度的最佳平方逼近评估法

敏感负荷电压凹陷敏感度评估的关键在于电压耐受曲线随机分布规律的确定。文章以勒让德多项式为基函数,提出一种通过最佳平方逼近法确定敏感负荷电压凹陷敏感度特征参数随机分布的概率密度函数的方法,该方法无需主观假设,忠实于样本特征,具有原理简单、计算量小的特点。文中对概率密度函数的逼近算法、评估原理和过程进行了研究,以PC机为例,通过蒙特卡罗方法随机模拟样本,用所提出的方法进行评估,证明了所提出方法的准确性和适应性。

力学建模在变密度法中密度与刚度关系中的应用

将结构拓扑优化中的变密度人为过程视作材料纵横方向收缩的物理过程,并把此收缩量转化为密度与刚度关系的中间变量。利用一种有限元数值模型将三者建立离散的数据关系,再使用幂指近似函数建立密度与收缩量的解析关系,最后利用力学关系建立密度与刚度的解析关系。数值计算表明:本文方法概念明确、操作简捷、数据拟合效果好。

采煤机牵引部传动系统动态可靠性分析

考虑齿轮的时变啮合刚度、非线性侧隙等因素,根据3自由度齿轮集中质量模型,建立了采煤机牵引部的动力学整体模型,研究变速重载工况下系统的振动响应,获得了牵引部各位置的动态接触应力。考虑随机运动参数、结构参数与材料参数系统等的影响,基于鞍点逼近方法获得了系统功能函数的概率密度函数与概率分布函数,基于顺序统计量理论研究了载荷多次作用下牵引部传动系统的动态可靠性评价问题,计算结果表明:随着系统运转时间的增加,传动系统中齿轮接触应力分布均值增大且标准差减小;动态运转过程中,牵引系统首次运转是较为安全的,系统前期可靠性降低速度较快,后期可靠性递减速度较缓慢。

改进的高斯粒子概率假设密度滤波算法

高斯粒子概率假设密度滤波在预测和更新时需要进行粒子近似和重新采样,这在一定程度上降低了算法的精度和实时性.针对这一问题,提出一种改进的高斯粒子概率假设密度滤波算法,算法通过粒子的方式表示并传递目标的概率假设密度(PHD)预测值,然后直接利用这些表征PHD预测值的粒子进行更新,最后利用具有最大似然性的粒子将更新后的PHD表示为混合高斯形式.仿真实验表明,和高斯粒子概率假设密度滤波相比,改进算法的多目标误差距离减少了约30%,运行时间减少了约50%.

H_2在δ-Pu(100)表面吸附的第一原理研究

采用密度泛函理论结合平板周期性模型研究了H2在δ-Pu(100)表面的吸附行为.结果表明,H2在该表面最稳定的吸附方式为洞位垂直吸附,吸附能为0.183eV,距离表面最近的H原子与表面垂直距离为0.378nm.吸附的H2分子的键长增加、H—H键伸缩振动频率的红移都不明显.只有极少量电子从第1层的Pu原子流向H2分子,吸附引起的表面功函增加也不明显.这说明δ-Pu(100)面分子态H2的吸附属于较弱的物理吸附.讨论了离解吸附的热力学可能性,H2分子的吸附趋向于离解成2个原子态H的吸附,离解后的H原子优先吸附于洞位,此时吸附为较强的化学吸附.