The Pauli energy grows exponentially with the electronic localisation

We investigate the Pauli energy in atoms and molecules as a measure of electron localisation. Our results indicate that the Pauli energy has an exponential dependence on the number of localised electrons. This relationship yields to a kinetic energy density expression that depends on the electron density ρ(r) and the pair density ρ₂(r, r′). The proposed equation shows certain advantages over a similar orbital-free kinetic energy functional recently proposed by Delle Site and co-workers. The methodology introduced here is a novel approach for exploring electronic quantities with a partition scheme that might be useful for research in density functional theory.     

Push it to the limit: comparing periodic and local approaches to density functional theory for intermolecular interactions

ABSTRACT

With the aim of systematically comparing two popular approaches to density functional theory – all-electron calculations with local basis sets, and periodic calculations employing plane wave basis sets and norm-conserving pseudopotentials – we have computed complete-basis binding energies across the S22 set of intermolecular interactions, a dataset consisting of noncovalent interactions of small- and medium-sized molecules containing first- and second-row atoms, using the Troullier-Martins norm-conserving pseudopotentials with SPW92, a local spin-density approximation; and PBE, a generalised gradient approximation. We have found that it is challenging to reach the basis set limit with these periodic calculations; for the methods and systems examined, a minimum vacuum distance of 30?Å between a system and its nearest images is necessary – unless some form of dipole correction is employed – as is a kinetic energy cutoff of at least 80 Ry. The trends in convergence with respect to vacuum size and kinetic energy cutoff are largely independent of the level of density functional approximation employed. A sense of the impact of each hyperparameter on basis set error provides a foundation for ensuring quality calculations in future studies and allows us to quantify the basis set errors incurred in existing studies on similar systems.     

Relevance of the slowly varying electron gas to atoms, molecules, and solids

We present a Thomas-Fermi-inspired density scaling under which electron densities of atomic, molecular, or condensed matter become both large and slowly varying, so that semiclassical approximations and second-order density gradient expansions are asymptotically exact for the kinetic and exchange energies. Thus, even for atoms and molecules, density-functional approximations should recover the universal second-order gradient expansions in this limit. We also explain why common generalized gradient approximations for exchange do not.     

Electron density redistribution in Sn-doped Bi2Te3

X-ray photoelectron spectroscopy is used to investigate the redistribution of the density of electronic states in the valence band, and of the binding energies and chemical shifts of core levels in bismuth telluride caused by introduction of impurity tin atoms. A substantial increase in the density of electronic states below the valence-band top at energies μ≈15–30 meV has been revealed. This feature in the energy spectrum accounts for the unusual behavior of the kinetic coefficients in p-Bi₂Te₃:Sn crystals. Fiz. Tverd. Tela (St. Petersburg) 41, 1969–1972 (November 1999)     

B（N）掺杂单壁碳纳米管的Al原子吸附性能的第一性原理研究

采用基于密度泛函理论的平面波赝势方法和广义梯度近似,对未掺杂、掺B、掺N的碳纳米管(CNT)不同位置上Al原子的吸附进行了几何优化,计算了吸附Al、掺杂前后CNT的能带结构、态密度、差分电荷密度、电荷布居数和吸附能.计算结果表明,掺B使CNT形成缺电子状态,利于具有自由电子的Al原子的吸附结合,可显著提高Al在金属性的(5,5)CNT和半导性的(8,0)CNT外壁的吸附能;掺杂N形成多电子状态,在费米能级附近半满的施主能级也利于填充Al的价电子,改善Al在(5,5)CNT和(8,0)CNT外壁的吸附结合性 关键词： 密度泛函理论 单壁碳纳米管 B(N)掺杂 Al原子吸附     

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.     

Kinetic component of the correlation energy density functional: a quantitative description from information theory

In the framework of information theory, a new method to determine T _c , the kinetic energy component of the correlation energy density functional for atoms, is presented. This approach is based on Shannon entropy and information energy that are obtained by fractional occupation probabilities of natural atomic orbitals. It is indicated that the calculated Shannon entropy using discrete probabilities is an increasing function while information energy is a decreasing function of the number of electrons. An expression is proposed with explicit dependence on the Shannon entropy or information energy and atomic number for the purpose. Applications of formulas for estimation of T _c values for neutral atoms up to Xe and their first positive and negative ions are then examined and validity of the proposed approach is numerically verified.     

Exact orbital-free kinetic energy functional for general many-electron systems

The exact form of the kinetic energy functional has remained elusive in orbital-free models of density functional theory(DFT).This has been the main stumbling block for the development of a general-purpose framework on this basis.Here,we show that on the basis of a two-density model,which represents many-electron systems by mass density and spin density components,we can derive the exact form of such a functional.The exact functional is shown to contain previously suggested functionals to some extent,with the notable exception of the Thomas-Fermi kinetic energy functional.     

Gradient expansion of the kinetic energy including nonlocal exchange contributions

We discuss the gradient expansion of the kinetic energy density, explicitly including nonlocal exchange contributions to ordere ². Restricting the expansion to orderh ²2 one finds that the expression obtained in the standard TFDW model is unchanged.     

Athermal migration of vacancies in iron and copper induced by electron irradiation

Abstract

Irradiation with high-energy particles induces athermal migration of point defects, which affects defect reactions at low temperatures where thermal migration is negligible. We conducted molecular dynamics simulations of vacancy migration in iron and copper driven by recoil energies under electron irradiation in a high-voltage electron microscope. Minimum kinetic energy required for migration was about 0.8 and 1.0 eV in iron and copper at 20 K, which was slightly higher than the activation energy for vacancy migration. Around the minimum energy, the migration succeeded only when a first nearest neighbour (1NN) atom received the kinetic energy towards the vacancy. The migration was induced by higher kinetic energies even with larger deflection angles. Above several electron-volts and a few 10s of electron-volts, vacancies migrated directly to 2NN and 3NN sites, respectively. Vacancy migration had complicated directional dependence at higher kinetic energies through multiple collisions and replacement of atoms. The probability of vacancy migration increased with the kinetic energy and remained around 0.3–0.5 jumps per recoil event for 20–100 eV. At higher temperatures, thermal energies slightly increased the probability for kinetic energies less than 1.5 eV. The cross section of vacancy migration was 3040 and 2940 barns for 1NN atoms in iron and copper under irradiation with 1.25 MV electrons at 20 K: the previous result was overestimated by about five times.     

Statics and dynamics of phase segregation in multicomponent fermion gas

We investigate the statics and dynamics of spatial phase segregation process of a mixture of fermion atoms in a harmonic trap using the density functional theory. The kinetic energy of the fermion gas is written in terms of the density and its gradients. Several cases have been studied by neglecting the gradient terms (the Thomas-Fermi limit) which are then compared with the Monte-Carlo results using the full gradient corrected kinetic energy. A linear instability analysis has been performed using the random-phase approximation. Near the onset of instability, the fastest unstable mode for spinodal decomposition is found to occur at q = 0. However, in the strong coupling limit, many more modes with q ≈ K _F decay with comparable time scales. Received 12 September 2001 Published online 24 September 2002 RID="a" ID="a"e-mail: k1@sharif.edu RID="b" ID="b"Permanent address: Dr. Vijay Kumar Foundation, 45 Bazaar Street, K.K. Nagar (West), Chennai 600 078, India.     

Ab initio modelling of the interaction of H interstitials with grain boundaries in bcc Fe

Hydrogen that is accumulated within the grain boundaries can lead to a decrease of the critical strain required to fracture the material. The paper presents results of ab initio modelling of hydrogen–grain boundary interaction in ferromagnetic bcc iron. Modelling was performed using density functional theory with generalised gradient approximation (GGA’96), as implemented in WIEN2k package. Three fully relaxed tilt grain boundaries, Σ5(310), Σ5(210) and Σ3(111), were studied. The supercells contained 40–48 atoms, i.e. 20–24 atoms in each of the two ‘grains’. Calculated formation energies of grain boundaries is 1.44, 1.83 and 1.46 J/m² and the maximum binding (trapping) energies of hydrogen to the boundaries are 0.43, 0.83 and 0.39 eV, respectively. These values are close to other researchers’ data. The higher value of trapping energy of the Σ5(210) boundary is probably due to the asymmetrical atom configurations resulting from mutual rigid shift of the two grains that was necessary to be introduced to provide optimal distances between Fe atoms, unlike the other two boundary types.     

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.     

The characteristic spectral lines of target atoms in the impact of<Superscript>40</Superscript>Ar<Superscript><Emphasis Type="Italic">q</Emphasis>+</Superscript> ions on metal surfaces

We report the measured results of the 200 nm—1000 nm characteristic spectral lines of target atoms when highly charged ions⁴⁰Ar ^q+(6≤q≤14) with the same kinetic energy and⁴⁰Ar⁶⁺ with different kinetic energies are incident upon Al, Ti, Ni, Ta and Au surfaces, respectively. The results for¹²⁹Xe⁶⁺,¹²⁹Xe¹⁰⁺ and¹²⁹Xe¹⁵⁺ with the same kinetic energy (150 keV) incident upon a Ta surface are also reported. These results show that when the projectile and target are properly selected (⁴⁰Ar¹²⁺ impinges on Al,¹²⁹Xe⁶⁺ impinges on Ta), the spectral intensity of characteristic spectral lines of the target atom is effectively enhanced, and is not strongly dependent on the kinetic energy of the incident ions.     

Ground state properties of titaniumdiboride

Abstract

The electronics structure, the charge distribution and the total energy of hexagonal titaniumdiboride are calculated using non-local pseudopotentials in both the local density approximation (LDA) and the generalized gradient expansion approximation (GGA). In the LDA we obtain a = 3.023 Å, c = 3.166 Å and B_o = 271. GPa. For these quantities the GGA values are slightly lower and both compare well with experiment. We also determined selected elastic constants by fitting the total energies to a quadratic surface in the lattice parameters. Using strains that do not break the hexagonal symmetry we obtain C₁₁ + C₁₂ = 777.GPa, C₁₃ = 83. GPa and C₃₃ = 568. GPa. Again slightly lower values are obtained using the GGA. These values agree well with a recent experiment.     

Electron-stimulated desorption of potassium and cesium atoms from an oxidized molybdenum surface

The yield and energy distributions of potassium and cesium atoms emitted in electron-stimulated desorption (ESD) from a molybdenum surface, oxidized to different extent and maintained at 300 K, have been measured by the time-of-flight technique with a surface ionization detector. The ESD threshold for potassium and cesium atoms lies around 25 eV, irrespective of molybdenum oxidation state. In the case of molybdenum coated by an oxygen monolayer, secondary thresholds at ∼40 and ∼70 eV have been observed, as well as atomic energy distribution tailing down to very low energies. The most probable kinetic energies of the atoms are a few tenths of one eV. The results are explained within a model involving Auger neutralization of the adsorbed alkali metal ions after the filling of the 2s O, 4s Mo, and 4p Mo core holes. The possibility of ESD of a neutral species as a result of oxide-cation core-level ionization has been demonstrated for the first time. Fiz. Tverd. Tela (St. Petersburg) 39, 758–761 (April 1997)     

Hybridized kinetic energy functional for orbital-free density functional method

We propose a hybridized kinetic energy functional, aTTF+bTvW, where TTF is the Thomas-Fermi functional and TvW the von Weizsäcker functional while a and b are adjustable parameters. The new functional is implemented in orbital-free plane-wave density functional method, in which a conjugate-gradient line-search scheme of electronic minimization is incorporated. Calculations with the fitted a and b show that this kinetic energy functional can describe the structures of small Si, Al and Si-Al alloy clusters with reasonable accuracy.     

Scaling and Expansion of Moment Equations in Kinetic Theory

The set of generalized 13 moment equations for molecules interacting with power law potentials [Struchtrup, Multiscale Model. Simul. 3:211 (2004)] forms the base for an investigation of expansion methods in the Knudsen number and other scaling parameters. The scaling parameters appear in the equations by introducing dimensionless quantities for all variables and their gradients. Only some of the scaling coefficients can be chosen independently, while others depend on these chosen scales–their size can be deduced from a Chapman–Enskog expansion, or from the principle that a single term in an equation cannot be larger in size by one or several orders of magnitude than all other terms.It is shown that for the least restrictive scaling the new order of magnitude expansion method [Struchtrup, Phys. Fluids 16(11):3921 (2004)] reproduces the original equations after only two expansion steps, while the classical Chapman–Enskog expansion would require an infinite number of steps. Both methods yield the Euler and Navier–Stokes–Fourier equations to zeroth and first order. More restrictive scaling choices, which assume slower time scales, small velocities, or small gradients of temperature, are considered as well.     

Atom-pair formulation of the rotational and vibrational motions of molecules

We have expressed the angular momentum and the internal kinetic energy of a molecule (a system of point masses) in terms of atom-pair contributions, paralleling the use of pairwise additive potential energy functions. The partitioning of the internal kinetic energy into rotational and vibrational contributions is then made following the analysis of Jellinek, J., and Li, D. H., 1989, 98, Phys. Rev. Lett., 62, 241. The resulting expressions contain pair position and velocity variables whose redundancy may be removed by transformation to Jacobi vector coordinates. These expressions should prove especially useful for describing the internal motions of clusters of like atoms.