Meta-generalized gradient approximation: non-empirical construction and performance of a density functional

The local ingredients of a meta-generalized gradient approximation (meta-GGA) include the electron density, its gradient, and the Kohn–Sham orbital kinetic energy density. We discuss the strategy of constructing a successful meta-GGA density functional for the exchange-correlation energy that satisfies exact constraints without empirical parameters. The new feature of this functional is that it simultaneously respects the two paradigms of electronic structure theory: one- or two-electron densities and slowly-varying densities, and so is uniformly accurate for atoms, molecules and solids. Results of extensive numerical tests of the new functional are summarized and evaluated.     

CO adsorption on the Cu(1 1 1) surface: A density functional study

The adsorption of CO on the Cu(1 1 1) surface has been studied with ab initio density functional theory. The adsorbate-metal system was analyzed with the local density approximation, the gradient corrected functional of Perdew and Wang and the B3LYP hybrid functional, for comparison. A slab model was used for the pattern at a coverage of 1/3. The local density approximation and the gradient corrected functional give the fcc site as the favorable adsorption site. In contrast, the B3LYP functional results in the preference of the top site, in agreement with the experiment. These results confirm the suggested explanation for the failure of standard functionals, based on the position of the highest occupied and lowest unoccupied molecular orbital. The results of total energy calculations are presented, together with projected densities of states and Mulliken populations. In addition, the basis set superposition error is discussed for CO/Cu(1 1 1) and for CO/Pt(1 1 1).     

Time-dependent density-functional theory beyond the local-density approximation

Approximations for the ground-state exchange-correlation potential of density-functional theory have reached a high level of sophistication. By contrast, time- or frequency-dependent exchange-correlation potentials are still being treated in a local approximation. Here we propose a novel approximation scheme, which effectively brings the power of the generalized gradient approximation (GGA) and meta-GGA to time-dependent density-functional theory. The theory should allow a more accurate treatment of strongly inhomogeneous electronic systems (e.g. molecular junctions) while remaining essentially exact for slowly varying densities and slowly varying external potentials.     

描述甲烷在Pt(110)-(21)表面的化学吸附解离的密度泛函评估

本文探讨了几种梯度近似(GGA)密度泛函及元梯度近似(meta-GGA)密度泛函在描述甲烷在重构的Pt(110)-(2×1)上的解离化学吸附作用的适用性. 金属的体相和表面结构、甲烷的吸附能量和解离能垒等被用来评估泛函的可靠性. 另外,在从头算分子动力学计算中,采用范德瓦尔斯矫正的GGA函数(optPBE-vdW)和范德瓦尔斯矫正的meta-GGA函数(MS-PBEl-rVV10）计算粘附概率. 计算结果表明,使用这两种泛函能更好地与现有的实验结果吻合,从而为发展甲烷在Pt(110)-(2×1)表面解离的可靠机器学习势能面打下重要基础.     

The electronic structure,electronic charge density and optical properties of the diamond-like semiconductor Ag2ZnSiS4

The electronic structure, electronic charge density and optical properties of the diamond-like semiconductor Ag₂ZnSiS₄ compound with the monoclinic structure have been investigated using a full-relativistic version of the full-potential augmented plane-wave method based on the density functional theory, within local density approximation (LDA), generalized gradient approximation (GGA), Engel–Vosko GGA (EVGGA) and modified Becke Johnson (mBJ) potential. Band structures divulge that this compound is a direct energy band gap semiconductor. The obtained energy band gap value using mBJ is larger than those obtained within LDA, GGA and EVGGA. There is a strong hybridization between Si-s and S-s/p, Si-p and Zn-s, Ag-s/p and Zn-s, and Ag-s and Ag-p states. The analysis of the site and momentum-projected densities shows that the bonding possesses covalent nature. The dielectric optical properties were also calculated and discussed in detail.     

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.     

Optics of semiconductors from meta-generalized-gradient-approximation-based time-dependent density-functional theory

We calculate the optical spectra of silicon, germanium, and zinc blende semiconductors in the adiabatic time-dependent density-functional formalism, making use of kinetic energy density-dependent [meta-generalized-gradient-approximation (GGA)] exchange-correlation functionals. We find excellent agreement between theory and experiment. The success of the theory on this notoriously difficult problem is traced to the fact that the exchange-correlation kernel of meta-GGA supports a singularity of the form α/q(2) (where q is the wave vector and α is a constant), whereas previously employed approximations (e.g., local-density and generalized gradient approximations) do not. Thus, the use of the adiabatic meta-GGA opens a new path for handling the extreme nonlocality of the time-dependent exchange-correlation potential in solid-state systems.     

Overcomplete Free Energy Functional for D = 1 Particle Systems with Next Neighbor Interactions

We deduce an overcomplete free energy functional for D=1 particle systems with next neighbor interactions, where the set of redundant variables are the local block densities _i of i interacting particles. The idea is to analyze the decomposition of a given pure system into blocks of i interacting particles by means of a mapping onto a hard rod mixture. This mapping uses the local activity of component i of the mixture to control the local association of i particles of the pure system. Thus it identifies the local particle density of component i of the mixture with the local block density _i of the given system. Consequently, our overcomplete free energy functional takes on the hard rod mixture form with the set of block densities _i representing the sequence of partition functions of the local aggregates of particle numbers i. The system of equations for the local particle density of the original system is closed via a subsidiary condition for the block densities in terms of . Analoguous to the uniform isothermal-isobaric technique, all our results are expressible in terms of effective pressures. We illustrate the theory with two standard examples, the adhesive interaction and the square-well potential. For the uniform case, our proof of such an overcomplete format is based on the exponential boundedness of the number of partitions of a positive integer (Hardy-Ramanujan formula) and on Varadhan's theorem on the asymptotics of a class of integrals.     

Band structure and chemical bonding in Cu2O and Ag2O oxides

The band structure, total and projected densities of states, and distributions of the valence and difference electron densities for copper and silver oxides are calculated in the framework of the density functional theory in the local approximation with ab initio norm-conserving pseudopotentials in the basis set of pseudoatomic orbitals. The results obtained are compared with the experimental data and calculations performed by other authors. The energy spectrum and spatial distribution of electrons in crystals are similar to each other. Metal ions are bonded to each other through charge density channels with a weakly pronounced maximum at the center of the empty tetrahedron.     

高压下氧化镉弹性性质、电子结构和光学性质的第一性原理研究

 运用基于密度泛函理论的平面波赝势方法（PWP）,计算研究了氧化镉NaCl结构（B1结构）和CsCl结构（B2结构）在不同压力条件下的几何结构、弹性性质、电子结构和光学性质。交换关联能分别采用广义梯度近似（GGA）和局域密度近似（LDA）。通过比较计算和实验得到的晶格常数和体模量不难发现,LDA的计算结果更符合实验值。在高压的作用下,两种结构的导带能级有向高能级移动的趋势,而价带能级有向低能级移动的趋势,因此直接带隙变大。同时,对照态密度分布图及高压下能级的移动情况,分析了CdO两种结构在高压作用下的光学性质。     

On the calculation of forces and total energy changes via the quantum mechanical stress field

Many-electron systems are within density functional theory described in terms of an appropriately defined local stress tensor. The differential equation for its exchange and correlation part is solved also for the case of density gradient dependent exchange and correlation energy. Formulae are given (i) for the direct calculation of the global stress tensor of a homogeneously strained crystal via surface integrals of the local stress tensor along intercell boundaries, and (ii) similarly for the energy change of inhomogeneously strained crystals.     

Degenerate ground states and a fractional number of electrons in density and reduced density matrix functional theory

For a linear combination of electron densities of degenerate ground states, it is shown that the value of any energy functional is the ground state energy, if the energy functional is exact for ground state densities, size consistent, and translational invariant. The corresponding functional of kinetic and interaction energy is the linear combination of the functionals of the degenerate densities. Without invoking ensembles, it is shown that the energy functional of fractional number electrons is a series of straight lines interpolating its values at integers. These results underscore the importance of grand canonical ensemble formulation in density functional theory.     

Cellular theory of ordered AB alloys

The heat and volume of formation of ordered simple metal AB alloys are calculated using the density functional formalism. A new method is proposed in which the alloy is partitioned into cells defined by surfaces on which the gradient of the electron density vanishes. The total alloy energy is formulated in terms of cellular and Madelung contributions and is minimized subject to the constraint of equal A and B cell boundary densities. Quantitative results for LiMg are presented.     

Spin-polarized structural, electronic and magnetic properties of intermetallic Dy2Ni2Pb from computational study

We report a first-principles study of structural, electronic and magnetic properties of ternary plumbides (rare earth-transition metal-Plumb) Dy₂Ni₂Pb crystallizes with the orthorhombic structure of the Mn₂AlB₂ type (space group Cmmm), were studied by means of the full-relativistic version of the full-potential augmented plane wave plus local orbital method within the frame work of spin-polarized density functional theory (SP-DFT). The electronic exchange-correlation energy is described by generalized gradient approximation (GGA). We have calculated the lattice parameters, bulk modulii and the first pressure derivatives of the bulk modulii, total densities of states and magnetic properties. The calculated total magnetic moment is found to be equal to 9.52 μB.     

Application of density-functional perturbation theory to calculate nonlinear polarizabilities of helium-like systems

Density-based perturbation theory within the Hohenberg-Kohn (HK) formalism of density functional theory (DFT), developed recently by us, is employed to calculate hyperpolarizabilities of helium-like ions from their ground-state densities obtained from their respective Hylleraas wavefunctions. The only approximation made is that of the local density (LDA) for exchange and correlation. Use of densities — instead of wavefunctions — in density-based perturbation theory together with simple approximate energy functionals makes our calculations much simpler than those based on wavefunctions. They lead, however, to accurate results.     

Surface properties of electron-hole droplets in semiconductors

The leading gradient terms in the kinetic energy densities of the electrons and holes in Ge and Si type semiconductors are calculated including band structure effects. Band structure effects are found to increase these gradient terms substantially over those for isotropic bands. The surface properties of electron—hole drops in Ge are studied using these gradient terms with several local energy densities, and band structure effects in the gradient terms are shown to increase the surface thickness, surface energy and dipole barrier over isotropic band results. The difference in the chemical potentials of the electrons and holes obtained from these approximate energy functionals indicates that the drop becomes positively charged, which is opposite in sign to that proposed recently by Rice.