Charge self-consistent dynamical mean field theory calculations incombination with linear combination of numerical atomic orbitalsframework based density functional theory

We present a formalism of charge self-consistent dynamical mean field theory(DMFT)in combination with densityfunctional theory(DFT)within the linear combination of numerical atomic orbitals(LCNAO)framework.We implementedthe charge self-consistent DFT+DMFT formalism by interfacing a full-potential all-electron DFT code with threehybridization expansion-based continuous-time quantum Monte Carlo impurity solvers.The benchmarks on several 3d,4fand 5f strongly correlated electron systems validated our formalism and implementation.Furthermore,within the LCANOframework,our formalism is general and the code architecture is extensible,so it can work as a bridge merging differentLCNAO DFT packages and impurity solvers to do charge self-consistent DFT+DMFT calculations.

Calculation of microscopic nuclear level densities based on covariant density functional theory

In this study,a microscopic method for calculating the nuclear level density(NLD)based on the covariant density functional theory(CDFT)is developed.The particle-hole state density is calculated by a combinatorial method using single-particle level schemes obtained from the CDFT,and the level densities are then obtained by considering collective effects such as vibration and rotation.Our results are compared with those of other NLD models,including phenomenological,microstatisti-cal and nonrelativistic Hartree–Fock–Bogoliubov combinatorial models.This comparison suggests that the general trends among these models are essentially the same,except for some deviations among the different NLD models.In addition,the NLDs obtained using the CDFT combinatorial method with normalization are compared with experimental data,including the observed cumulative number of levels at low excitation energies and the measured NLDs.The CDFT combinatorial method yields results that are in reasonable agreement with the existing experimental data.

Thermodynamic Properties for Polybrominated Dibenzothiophenes by Density Functional Theory

The thermodynamic properties of 135 polybrominated dibenzothiophenes （PBDTs） in the gaseous state at 298.15 K and 1.013×10^5 Pa, are calculated using the density functional theory （the B3LYP/6-311G^＊＊） with Gaussian 03. Based on these data, the isodesmic reacflons are designed to calculate the standard enthalpy of formation （△fH^θ） and the standard Gibbs energy of formation （△fG^θ） of PBDTs. The relations of these thermodynamic parameters with the number and positionof bromine subsfituents （NPBS） are discussed, and it is found that there exist good correlations between othermody namic parameters （including heat capacity at constant volume, entropy, enthaipy, free energy, △fH^θ, △fG^θ） and NPBS. Thoe relative stability order of PBDT congeners is proposed theoretically based on the relative magnitude of their △fG^θ. In addition, the values of molar heat capacities at constant pressure （Cp,m） for PBDT c ongelaers are calculated.

Density Functional Theory Study on the Adsorption of Dioxygen on Small Pt-Pd Clusters

The electronic and physical properties of PtmPdn （m＋n≤5） metal clusters and their interactions with dioxygen have been studied by using hybrid density functional B3LYP method. The total energies, atomization energies, vibration frequencies, and charge distributions were reported. The Pt-Pt bridge site modified by Pd atoms was found to be the most active site for the dissociation of dioxygen, which was mainly due to the change of electronic structures of the Pt atoms in bimetallic Pt-Pd clusters.

Hydrogen storage in BC_3 composite single-walled nanotube:a combined density functional theory and Monte Carlo investigation

This paper applies a density functional theory （DFT） and grand canonical Monte Carlo simulations （GCMC） to investigate the physisorptions of molecular hydrogen in single-walled BC3 nanotubes and carbon nanotubes. The DFT calculations may provide useful information about the nature of hydrogen adsorption and physisorption energies in selected adsorption sites of these two nanotubes. Furthermore, the GCMC simulations can reproduce their storage capacity by calculating the weight percentage of the adsorbed molecular hydrogen under different conditions. The present results have shown that with both computational methods, the hydrogen storage capacity of BC3 nanotubes is superior to that of carbon nanotubes. The reasons causing different behaviour of hydrogen storage in these two nanotubes are explained by using their contour plots of electron density and charge-density difference.

Understanding the Relativistic Generalization of Density Functional Theory (DFT) and Completing It in Practice

In 2014, 50 years following the introduction of density functional theory (DFT), a rigorous understanding of it was published [AIP Advances, 4, 127,104 (2014)]. This understanding includes two features that complete the theory in practice, inasmuch as they are necessary for its correct application in electronic structure calculations;this understanding elucidates what appears to have been the crucial misunderstanding for 50 years, namely, the confusion between a stationary solution, attainable with most basis sets, following self-consistent iterations, with the ground state solution. The latter is obtained by a calculation that employs the well-defined optimal basis set for the system. The aim of this work is to review the above understanding and to extend it to the relativistic generalization of density functional theory by Rajagopal and Callaway [Phys. Rev. B7, 1912 (1973)]. This extension straightforwardly follows similar steps taken in the non-relativistic case, with the four-component current density, in the former, replacing the electronic charge density, in the latter. This new understanding, which completes relativistic DFT in practice, is expected to be needed for the study of heavy atoms and of materials (from molecules to solids) containing them—as is the case for some high temperature superconductors.

Statistical Gauge Theory for Relativistic Finite Density Problems

A relativistic quantum field theory is presented for finite density problems based on the principle of locality. It is shown that, in addition to the conventional ones, a local approach to the relativistic quantum field theories at both zero and finite densities consistent with the violation of Bell-like inequalities should contain and provide solutions to at least three additional problems, namely, i) the statistical gauge invariance; ii) the dark components of the local observables; and iii) the fermion statistical blocking effects, based upon an asymptotic nonthermal ensemble. An application to models is presented to show the importance of the discussions.

Adaptive phase field modelling of crack propagation in orthotropic functionally graded materials

In this work,we extend the recently proposed adaptive phase field method to model fracture in orthotropic functionally graded materials(FGMs).A recovery type error indicator combined with quadtree decomposition is employed for adaptive mesh refinement.The proposed approach is capable of capturing the fracture process with a localized mesh refinement that provides notable gains in computational efficiency.The implementation is validated against experimental data and other numerical experiments on orthotropic materials with different material orientations.The results reveal an increase in the stiffness and the maximum force with increasing material orientation angle.The study is then extended to the analysis of orthotropic FGMs.It is observed that,if the gradation in fracture properties is neglected,the material gradient plays a secondary role,with the fracture behaviour being dominated by the orthotropy of the material.However,when the toughness increases along the crack propagation path,a substantial gain in fracture resistance is observed.

Lattice Models of Finite Fields

Finite fields form an important chapter in abstract algebra, and mathematics in general, yet the traditional expositions, part of Abstract Algebra courses, focus on the axiomatic presentation, while Ramification Theory in Algebraic Number Theory, making a suited topic for their applications, is usually a separated course. We aim to provide a geometric and intuitive model for finite fields, involving algebraic numbers, in order to make them accessible and interesting to a much larger audience, and bridging the above mentioned gap. Such lattice models of finite fields provide a good basis for later developing their study in a more concrete way, including decomposition of primes in number fields, Frobenius elements, and Frobenius lifts, allowing to approach more advanced topics, such as Artin reciprocity law and Weil Conjectures, while keeping the exposition to the concrete level of familiar number systems. Examples are provided, intended for an undergraduate audience in the first place.

A study of U-isotope ground state properties with covariant energy density functional

In this study,we systematically analyzed the ground state of uranium isotopes from 225 to 240.In our calculations,we used the covariant energy density functional of density-dependent meson exchange interaction(DDME2)with separable pairing interaction(TMR).Using the multiple deformation constraint,we calculated the potential energy surface(PES)of the uranium isotopes for both even-even and even-odd nuclei with quadrupole and octupole deformation.Based on our calculation and upon comparing the experimental data and Hartree-Fock-Bogoliubov calculations with Gogny D1S calculation data,the ground state of uranium isotopes with reflection-asymmetric deformation was found to be preferred.

Waves induced by a submerged moving dipole in a two-layer fluidof finite depth

The waves induced by a moving dipole in a two-fluid system are analytically and experimentally investigated. The velocity potential of a dipole moving horizontally in the lower layer of a two-layer fluid with finite depth is derived by superposing Greens functions of sources (or sinks). The far-field waves are studied by using the method of stationary phase. The effects of two resulting modes, i.e. the surface- and internal-wave modes, on both the surface divergence field and the interfacial elevation are analyzed. A laboratory study on the internal waves generated by a moving sphere in a two-layer fluid is conducted in a towing tank under the same conditions as in the theoretical approach. The qualitative consistency between the present theory and the laboratory study is examined and confirmed.

Density and temperature reconstruction of a flame-induced distorted flow field based on background-oriented schlieren(BOS) technique

An experimental system based on the background-oriented schlieren（BOS） technique is built to reconstruct the density and temperature distribution of a flame-induced distorted flow field which has a density gradient. The cross-correlation algorithm with sub-pixel accuracy is introduced and used to calculate the background-element displacement of a disturbed image and a fourth-order difference scheme is also developed to solve the Poisson equation. An experiment for a disturbed flow field caused by a burning candle is performed to validate the built BOS system and the results indicate that density and temperature distribution of the disturbed flow field can be reconstructed accurately. A notable conclusion is that in order to make the reconstructed results have a satisfactory accuracy, the inquiry step length should be less than the size of the interrogation window.

Joint probability density function of the stochastic responses of nonlinear structures

The joint probability density fimction （PDF） of different structural responses is a very important topic in the stochastic response analysis of nonlinear structures. In this paper, the probability density evolution method, which is successfully developed to capture the instantaneous PDF of an arbitrary single response of interest, is extended to evaluate the joint PDF of any two responses. A two-dimensional partial differential equation in terms of the joint PDF is established. The strategy of selecting representative points via the number theoretical method and sieved by a hyper-ellipsoid is outlined. A two-dimensional difference scheme is developed. The free vibration of an SDOF system is examined to verify the proposed method, and a flame structure exhibiting hysteresis subjected to stochastic ground motion is investigated. It is pointed out that the correlation of different responses results from the fact that randomness of different responses comes from the same set of basic random parameters involved. In other words, the essence of the probabilistic correlation is a physical correlation.

Probability Density Analysis of Nonlinear Random Ship Rolling

Ship rolling in random waves is a complicated nonlinear motion that contributes substantially to ship instability and capsizing.The finite element method(FEM)is employed in this paper to solve the Fokker Planck(FP)equations numerically for homoclinic and heteroclinic ship rolling under random waves described as periodic and Gaussian white noise excitations.The transient joint probability density functions(PDFs)and marginal PDFs of the rolling responses are also obtained.The effects of stimulation strength on ship rolling are further investigated from a probabilistic standpoint.The homoclinic ship rolling has two rolling states,the connection between the two peaks of the PDF is observed when the periodic excitation amplitude or the noise intensity is large,and the PDF is remarkably distributed in phase space.These phenomena increase the possibility of a random jump in ship motion states and the uncertainty of ship rolling,and the ship may lose stability due to unforeseeable facts or conditions.Meanwhile,only one rolling state is observed when the ship is in heteroclinic rolling.As the periodic excitation amplitude grows,the PDF concentration increases and drifts away from the beginning location,suggesting that the ship rolling substantially changes in a cycle and its stability is low.The PDF becomes increasingly uniform and covers a large region as the noise intensity increases,reducing the certainty of ship rolling and navigation safety.The current numerical solutions and analyses may be applied to evaluate the stability of a rolling ship in irregular waves and capsize mechanisms.

Numerical modeling calculation for the spatial distribution characteristics of horizontal field transfer functions

Applying 3-dimension finite difference method, the distribution characteristics of horizontal field transfer functions for rectangular conductor have been computed, and the law of distribution for Re-part and Im-part has been given. The influences of source field period, the conductivity, the buried depth and the length of the conductor on the transfer functions were studied. The extrema of transfer functions appear at the center, the four corners and around the edges of conductor, and move with the edges. This feature demonstrates that around the edges are best places for transfer functions' observation.

白铅矿(PbCO_(3))和菱锌矿(ZnCO_(3))硫化机理的DFT研究

采用密度泛函理论(DFT)比较研究白铅矿(PbCO_(3))和菱锌矿(ZnCO_(3))硫化机理的差异。通过在PbCO_(3)/ZnCO_(3)表面构建Pb-S/Zn-S层来模拟硫化结构。层距和Mulliken电荷的结果表明,PbCO_(3)上形成稳定的Pb-S层,而ZnCO_(3)上形成的Zn-S层不稳定。由于Pb-S层具有高的共价性,而Zn-S层具有高的离子性,因此,硫化-黄药法对PbCO_(3)浮选有效,对ZnCO_(3)浮选无效。为了回收ZnCO_(3),需要强离子性捕收剂,因此,硫化-胺法在ZnCO_(3)浮选中应用较广。PbCO_(3)和ZnCO_(3)表面硫化层结构和浮选行为差异主要是由于金属离子(Pb^(2+)和Zn^(2+))和配体(O配体和S配体)极化率的不同以及Zn^(2+)3d^(10)轨道的惰性造成的。

高岭石表面水化机理及电场弱化其吸附性能的分子模拟

高岭石是泥岩黏土矿物组成中的主要成分之一,其水理特性对分析高岭石类黏土矿物遇水工程性质劣化的研究至关重要,通过密度泛函理论和分子动力学模拟研究了高岭石表面水化机理及电化学作用对高岭石表面吸附性能的影响。结果表明:水分子在高岭石(001)晶面吸附时水中的Hw、Ow原子与高岭石表面羟基的Hs、Os原子间形成了Hw-Os及Hs-Ow两种类型的氢键,并且Hw-Os氢键作用较强;水分子与高岭石(001)晶面之间形成的氢键作用导致高岭石(001)晶面具有较强的亲水性质;外加电场对体系中水分子的平衡构象及吸附形态产生显著影响,当体系无电场时,水分子通过氢键与高岭石(001)晶面结合紧密,随着电场强度不断增加,水分子逐渐从高岭石表面脱附,以氢原子朝上、氧原子朝下的“V”字型结构向体相中扩散,水分子的偶极矩沿电场方向排列;随着水-高岭石体系中电场强度的增加,吸附体系中的氢键作用逐渐被破坏,水分子脱附能力增强,高岭石表面对水分子的吸附性降低。

Density functional theory study on organic semiconductor for field effect transistors: Symmetrical and unsymmetrical porphyrazine derivatives with annulated 1,2,5-thiadiazole and 1,4-diamyloxybenzene moieties

Density functional theory (DFT) calculations were carried out to investigate the organic field effect transistor (OFET) performance of the symmetrical metal-free tetrakis (1,2,5-thiadiazole) porphyrazine (S4)PzH2 and tetrakis (1,4-diamyloxybenzene) (A4)PzH2 as well as the low-symmetry metal-free porphy- razine with annulated 1,2,5-thiadiazole and 1,4-diamyloxybenzene groups in the ratio 2:2 (cis) and 1:3, that is, (cis-S2A2)PzH2 and (SA3)PzH2, (S = 1,2,5-thiadiazole ring, A = annulated 1,4-diamyloxy-benzene ring, Pz = porphyrazine) in terms of the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energy, ionization energy (IE), electron affinity (EA), and their reorganization energy (λ) during the charge-transport process. On the basis of Marcus electron transfer theory, electronic couplings (V) and field effect transistor (FET) properties for the four compounds with known crystal structure have been calculated. The electron transfer mobility (μ -) is revealed to be 0.056 cm2·V-1·s-1 for (S4)PzH2. The hole transfer mobility (μ+) is 0.075, 0.098, and 8.20 cm2·V-1·s-1 for (cis-S2A2)PzH2, (SA3)PzH2, and (A4)PzH2, respectively. The present work represents the theoretical effort towards understanding the OFET properties of symmetrical and unsymmetrical porphyrazine derivatives with annulated 1,2,5-thiadiazole and 1,4-diamyloxybenzene.

外场作用下吡咯分子的物理性质研究

吡咯分子是重要的有机半导体材料,适用于微电子和光电等多个领域,成功地引领了一场新的技术革命.本文基于密度泛函理论,使用B3LYP/6-311++g(d,p)方法研究了在0-0.03 a.u.的电场强度作用下,吡咯分子的物理特性变化规律.发现随着电场的增大,分子逐渐沿x轴方向被压缩,分子的偶极矩在减小,总能量在减小.分子的最高占据分子轨道能量基本保持不变,最低未占据分子轨道能量在不断地下降,致使分子的能带隙不断减小,无法保证能带隙的稳定性,从而降低了半导体材料的使用寿命.通过含时密度泛函计算可以发现:在不同的电场下,吡咯分子均出现两个紫外吸收峰,其中两个C=C双键的π-π*跃迁占主要贡献.但随着电场强度的增大,其在跃迁中的占比越来越小.考察在0.02 a.u.的电场下,紫外吸收峰主要由第6、11、13、15等激发态决定.这为更好地研究和设计半导体材料提供了良好的理论依据.

An Efficient Real Space Method for Orbital-Free Density-Functional Theory

We consider the Thomas-Fermi-von Weizsacker energy functional,with the Wang-Teter correction,and present an efficient real space method for Orbital-Free Density Functional Theory.It is proved that the energy minimizer satisfies a second order quasilinear elliptic equation,even at the points where the electron density vanishes.This information is used to construct an efficient energy minimization method for the resulting constrained problem,based on the truncated Newton method for unconstrained optimization.The Wang-Teter kernel is analyzed,and its behavior in real space at short and far distances is determined.A second order accurate discretization of the energy is obtained using finite differences.The efficiency and accuracy of the method is illustrated with numerical simulations in an Aluminium FCC lattice.