The coupling constant averaged exchange–correlation energy density

ABSTRACT

The exchange–correlation energy, central to density-functional theory, may be represented in terms of the coupling constant averaged (CCA) exchange–correlation energy density. We present an approach to calculate the CCA energy density using accurate ab initio methods and its application to simple atomic systems. This function provides a link between intrinsically non-local, many-body electronic structure methods and simple local and semi-local density-functional approximations (DFAs). The CCA energy density is resolved into separate exchange and correlation terms and the features of each compared with those of quantities commonly used to construct DFAs. In particular, the more complex structure of the correlation energy density is found to exhibit features that align well with those present in the Laplacian of the density, suggesting its role as a key variable to be used in the construction of improved semi-local correlation functionals. The accurate results presented in this work are also compared with those provided by the Laplacian-dependent Becke–Roussel model for the exchange energy.     

Theoretical predictions about ENDOR of biradicals in liquid solution

Starting from the equation of motion for the density matrix, ENDOR spectra are computed for a biradical for the first time. The model biradical carries two electronic spins S = 1/2 and two nuclear spins I = 1/2. The relaxation operator is calculated ab initio for three distinct relaxation mechanisms. These mechanisms are the modulation of the isotropic exchange interaction, the hyperfine tensor and the zero-field splitting tensor. The dependence of the ENDOR effect on the amplitudes of the radiofrequency and microwave fields, on the strength of the zero-field splitting tensor, and on the correlation times of the correlation functions is investigated.     

Electromagnetic fluctuations in the dielectric slab resonator

Electromagnetic fluctuations between two parallel (distanceL) infinite extended and perfectly conducting plates are studied. The space between the plates may be homogeneously filled with an isotropic dielectric and magnetic medium. For small values ofLT (T=temperature) the influence of the imaginary part of the dielectric function on the spectral correlations of the radiation field is discussed.The local spectral energy density is calculated. It is shown that the energy density isr-independent for media without dispersion. In this case ther-dependent part of the trace of the electric correlation tensor cancels with the analogous part of the magnetic correlation tensor.For the empty slab the complete spatial and temporal correlation tensors are derived. Two representations suitable for small and large values ofLT are discussed. These representations are expansions arround the 2-dimensional radiation field, i.e. no modes with wave vectors perpendicular to the plates are excited and the half space limit, respectively. Curves of the relative deviation of the electric correlation functions from the infinite isotropic space limit and curves of the degree of anisotropy of the radiation field as functions of the distance to the metallic boundary are displayed.     

Density functionals for nondynamical correlation constructed from an upper bound to the exact exchange energy density

ABSTRACT

Hyper-generalised-gradient approximations (hGGAs) for the exact exchange-correlation functional are increasingly popular in density functional theory. HGGAs model nondynamical correlation using a flexible local combination of exact (Hartree–Fock, HF) exchange and approximate exchange. We present a simplified ‘Rung 3.5’ upper bound to the HF exchange energy density, the essential ingredient of hGGAs. We also present a nonempirical generalised gradient approximation for this upper bound. Both upper bounds go to zero in the high-density and density tail limits, facilitating the construction of hGGAs that recover HF exchange in these limits. The ‘Rung 3.5’ construction enables facile evaluation of analytic derivatives and calculations in periodic boundary conditions. Extensive numerical tests show that the upper bounds capture the critical difference between HF and approximate exchange, showing these ingredients' promise for building simple hGGAs. The tests also indicate a need for more sophisticated semi-local upper bounds.     

Valence band structure and density of states effective mass model of biaxial tensile strained silicon based on k·p theory

After constructing a stress and strain model, the valence bands of in-plane biaxial tensile strained Si is calculated by k·p method. In the paper we calculate the accurate anisotropy valance bands and the splitting energy between light and heavy hole bands. The results show that the valance bands are highly distorted, and the anisotropy is more obvious. To obtain the density of states (DOS) effective mass, which is a very important parameter for device modeling, a DOS effective mass model of biaxial tensile strained Si is constructed based on the valance band calculation. This model can be directly used in the device model of metal-oxide semiconductor field effect transistor (MOSFET). It also a provides valuable reference for biaxial tensile strained silicon MOSFET design.     

Tensor of internal stresses in polycrystalline grains with complex bending

Processes that occur upon the straining of a polycrystal are studied. Components of the internal stress tensor were determined. Changes in the bending and torsion stresses in the crystal lattice of a strained polycrystal are analyzed. A correlation between changes in the internal stress tensor components and the fraction of material with complex bending is established.     

(001)面任意方向单轴应变硅材料能带结构

首先计算了(001)晶面单轴应变张量,在此基础上采用结合形变势理论的K ·P微扰法建立了在(001)晶面内受任意方向的单轴压/张应力作用时,应变硅材料的能带结构与应力(类型、大小)及晶向的关系模型,进而分析了不同单轴应力(类型、大小)及晶向对应变硅材料导带带边、价带带边、导带分裂能、价带分裂能、禁带宽度的影响.研究结果可为单轴应变硅器件应力及晶向的选择设计提供理论依据. 关键词： 单轴应变硅 K ·P法 能带结构     

应变Si电子电导有效质量模型

采用K·P微扰法建立了应变Si导带能谷由纵、横向有效质量表征的E-k关系,并在此基础上,研究分析了(001),(101),(111)晶面应变Si电子的电导有效质量与应力、能谷分裂能及晶向的关系.结果表明,弛豫Si_1-xGe_x材料(001)面生长的应变Si沿[100],[010]晶向的电子电导有效质量和弛豫Si_1-xGe_x材料(101)面生长的应变Si 关键词： 应变Si K·P法 电导有效质量     

Binding energy calculations for metal aggregates

Within the framework of the local density functional formalism the binding energies of atoms in metallic aggregates are computed. The calculations are based on the following approach: The total charge density is approximated by the superposition of the charge densities of the respective free atoms. The kinetic energy is obtained by a modified Thomas-Fermi-Weizsäcker expression, and the exchange/correlation energy is determined by theX -approximation. As a first example of application we have calculated the adsorption energies of Cu and Pd on tungsten and the formation energy of a vacancy in pure copper and in copper with Ge impurities. The results are in fair agreement with the respective experimental data.     

Investigation of the magnetic properties and magnetic structure parameters of nanocrystalline Fe<Subscript>79</Subscript>Zr<Subscript>10</Subscript>N<Subscript>11</Subscript> films

The magnetic properties (magnetization curve, ferromagnetic resonance spectrum) of nanocrystalline Fe₇₉Zr₁₀N₁₁ films obtained by RF magnetron sputtering with subsequent annealing were studied experimentally, along with the fundamental magnetic constants of these films (saturation magnetization M _S, local magnetic anisotropy energy K, and the exchange coupling constant A). The magnetic properties are discussed within the random magnetic model, which determines the correlation of the magnetic properties with the fundamental magnetic constants and nanostructure parameters (grain size, magnetic anisotropy, and correlation radius R _C). The exchange correlation length 2R _L for the film magnetic microstructure was determined by correlation magnetometry.     

The stress tensor of an atomistic system

We prove that the stress tensor conservation equation expressing the local equilibrium condition of a body results from the invariance of its partition function under canonical point transformations. From this result the expression of the stress tensor of a general atomistic system (with short range interactions) in terms of its microscopic degrees of freedom can be obtained. The derivation, which can be extended to encompass the quantum mechanical case, works in the canonical as well as the micro-canonical ensemble and is valid for systems endowed with arbitrary boundary conditions. As an interesting by-product of our general approach, we are able to positively answer the old question concerning the uniqueness of the stress tensor expression.     

A Stress Tensor for Anti-de Sitter Gravity

We propose a procedure for computing the boundary stress tensor associated with a gravitating system in asymptotically anti-de Sitter space. Our definition is free of ambiguities encountered by previous attempts, and correctly reproduces the masses and angular momenta of various spacetimes. Via the AdS/CFT correspondence, our classical result is interpretable as the expectation value of the stress tensor in a quantum conformal field theory. We demonstrate that the conformal anomalies in two and four dimensions are recovered. The two dimensional stress tensor transforms with a Schwarzian derivative and the expected central charge. We also find a nonzero ground state energy for global AdS₅, and show that it exactly matches the Casimir energy of the dual super Yang–Mills theory on S ³×R. Received: 20 April 1999 / Accepted: 8 July 1999     

Axiomatic renormalization of the stress tensor of a conformally invariant field in conformally flat spacetimes

Using only the general properties which the renormalized stress-energy tensor T_μν should satisfy—and not relying on any assumptions associated with specific renormalization techniques—we derive the expression for T_μν for conformally invariant fields in conformally flat spacetimes of two and four dimensions. In two dimensions, these arguments rederive the Davies-Fulling-Unruh expression for the stress tensor of a scalar field; in four dimensions the results agree with those of Brown and Cassidy, except that we exclude the local curvature term depending on fourth-order derivatives of the metric. The dynamics of a k = 0 Robertson-Walker universe filled with radiation of the conformally invariant field is investigated and it is found that the equations cease to admit a solution when the Planck density is reached.     

Quantum Monte Carlo assessment of density functionals for π-electron molecules: ethylene and bifuran

ABSTRACT

We perform all-electron, pure-sampling quantum Monte Carlo (QMC) calculations on ethylene and bifuran molecules. The orbitals used for importance sampling with a single Slater determinant are generated from Hartree-Fock and density functional theory (DFT). Their fixed-node energy provides an upper bound to the exact energy. The best performing density functionals for ethylene are BP86 and M06, which account for 99% of the electron correlation energy. Sampling from the π-electron distribution with these orbitals yields a quadrupole moment comparable to coupled cluster CCSD(T) calculations. However, these, and all other density functionals, fail to agree with CCSD(T) while sampling from electron density in the plane of the molecule. For bifuran, as well as ethylene, a correlation is seen between the fixed-node energy and deviance of the QMC quadrupole moment estimates from those calculated by DFT. This suggests that proximity of DFT and QMC densities correlates with the quality of the exchange nodes of the DFT wave function for both systems.     

Membrane stress tensor in the presence of lipid density and composition inhomogeneities

We derive the expression of the stress tensor for one- and two-component lipid membranes with density and composition inhomogeneities. We first express the membrane stress tensor as a function of the free-energy density by means of the principle of virtual work. We then apply this general result to a monolayer model which is shown to be a local version of the area-difference elasticity (ADE) model. The resulting stress tensor expression generalizes the one associated with the Helfrich model, and can be specialized to obtain the one associated with the ADE model. Our stress tensor directly gives the force exchanged through a boundary in a monolayer with density and composition inhomogeneities. Besides, it yields the force density, which is also directly obtained in covariant formalism. We apply our results to study the forces induced in a membrane by a local perturbation.     

Electronic Structure of RCo2 (R = Y, Nd, Ho, Er)

The results of electronic structure studies of the YCo₂ performed in the framework of the density functional theory (DFT) are reported. We have applied both local spin density approximation (LSDA) and generalized gradient approximation (GGA) for the treatment of exchange and correlation effects. We have found the stable paramagnetic ground state (a _min/a _exp = 0.962) using LSDA. In addition, we have investigated the influence of the local R-4f moments in RCo₂ (R = Nd, Ho, Er) on the ferrimagnetic solution using a self-interaction corrected LSDA method.     

Note on the correlation energy of an electron gas

The residual ring diagram contribution which is due to the use of approximate eigenvalues and a momentum cutoff is evaluated and the terms of orderr _s in the correlation energy are given explicitly. The result is exact to orderr _s within neglect of the third order exchange contribution and improves the results of Du Bois, and Carr and Maradudin. The correlation energy plotted againstr _s connects rather smoothly to the low density results obtained recently by Stevens and Pokrant based on an entirely different variational method.This work was supported by the National Science Foundation     

Climbing the density functional ladder: nonempirical meta-generalized gradient approximation designed for molecules and solids

The electron density, its gradient, and the Kohn-Sham orbital kinetic energy density are the local ingredients of a meta-generalized gradient approximation (meta-GGA). We construct a meta-GGA density functional for the exchange-correlation energy that satisfies exact constraints without empirical parameters. The exchange and correlation terms respect two paradigms: one- or two-electron densities and slowly varying densities, and so describe both molecules and solids with high accuracy, as shown by extensive numerical tests. This functional completes the third rung of "Jacob's ladder" of approximations, above the local spin density and GGA rungs.     

单轴应变Si(001)任意晶向电子电导有效质量模型

单轴应变Si材料电子电导有效质量是理解其电子迁移率增强的关键因素之一, 对其深入研究具有重要的理论意义和实用价值. 本文从Schrödinger方程出发, 将应力场考虑进来, 建立了单轴应变Si材料导带E-k解析模型. 并在此基础上, 最终建立了单轴应变Si(001)任意晶向电子电导率有效质量与应力强度和应力类型的关系模型. 本文的研究结果表明: 1) 单轴应力致电子迁移率增强的应力类型应选择张应力. 2) 单轴张应力情况下, 仅从电子电导有效质量角度考虑, [110]/(001)晶向与[100]/(001)晶向均可. 但考虑到态密度有效质量的因素, 应选择[110]/(001)晶向. 3) 沿(001)晶面上[110]晶向施加单轴张应力时, 若想进一步提高电子迁移率, 应选取[100]晶向为器件沟道方向. 以上结论可为应变Si nMOS器件性能增强的研究及导电沟道的应力与晶向设计提供重要理论依据. 关键词： 单轴应变 E-k关系')" href="#">E-k关系 电导有效质量