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.     

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.     

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.     

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.     

On site coulomb repulsion dominates over the non-local Hartree-Fock exchange in determining the band gap of polymers

The present study deals with the relative performance of the various density functional approaches in evaluating the band gap of polymer materials. Several density functional approximations that includes pure generalized gradient approximated (GGA) functional, meta-GGA, hybrid and range separated hybrid functionals have been used to evaluate the electrical band gap or transport gap of the studied polymers and compared with that obtained using Hubbard U corrected GGA functional (GGA+U). It has been observed that the experimental band gap of the polymers studied is satisfactorily reproducible when GGA+U approach is adopted. The band gap analyses further suggest that range separated hybrid functional, CAM-B3LYP, largely overestimates the band gap of all the polymers studied while the performance of hybrid B3LYP functional and other range separated hybrid functional like HSE is moderate. Better performance of the GGA+U method clearly indicates that short range coulomb correlation plays more significant role over the non-local Hartree-Fock (HF) exchange in determining the electrical band gap of polymer materials. It is also noticeable that the Hubbard U parameter used for the various polymers under consideration is relatively large, indicating the semi-empirical nature of the GGA+U level of calculations. The present finding will help us design new low band gap polymer through estimating band gap by the GGA+U method and this could be very useful for solar cell research.     

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.     

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.     

Nuclear density functional theory

An understanding of atomic nuclei is crucial for a complete nuclear theory, for the nuclear astrophysics, for performing new experimental tasks, and for various other applications. Within a density functional theory, the total binding energy of the nucleus is given by a functional of the nuclear density matrices and their derivatives. The variation of the energy density functional with respect to particle and pairing densities leads to the Hartree-Fock-Bogoliubov equations. The “Universal Nuclear Energy Density Functional” (UNEDF) SciDAC project to develop and optimize the energy density functional for atomic nuclei using state-of-the-art computational infrastructure, is briefly described. The ultimate goal is to replace current phenomenological models of the nucleus with a well-founded microscopic theory with minimal uncertainties, capable of describing nuclear data and extrapolating to unknown regions.     

Nonempirical construction of current-density functionals from conventional density-functional approximations

Density-functional approximations for the exchange-correlation energy Exc[n] of a many-electron ground state are highly developed and widely useful. When a paramagnetic current jp(r) is present, Vignale and Rasolt have extended the Kohn-Sham theorems and presented an additive correction valid to second order in the gauge-invariant vorticity nu=Delta x (jp/n):Exc[n, jp]=Exc[n, jp=0] + DeltaE(VR)(xc)[n, nu]. Apart from spin-polarization effects, their correction is unambiguous for a generalized gradient approximation (GGA). But for a meta-GGA (MGGA), one needs to know how to go back from the orbital kinetic energy density tau([n, jp];r) to tau([n,0];r); we show how to do this here. Numerical tests on the degeneracies for open-shell atoms show that current-density corrections reduce the error of GGA from 2 to 1 kcal/mol, and of MGGA from 5 to 2 kcal/mol.     

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.     

FeP(Im)-AB Bonding Energies Evaluated with A Large Number of Density Functionals (P = porphine, Im = imidazole, AB = CO, NO, and O(2))

Sixty-four (64) density functionals, ranging from GGA, meta-GGA, hybrid GGA to hybrid meta-GGA, were tested to evaluate the FeP(Im)-AB bonding energies (E(bond)) in the heme model complexes FeP(Im)(AB) (P = porphine, Im = imidazole, AB = CO, NO, and O(2)). The results indicate that an accurate prediction of E(bond) for the various ligands to heme is difficult with the DFT methods; usually a functional successful for one system does not perform equally well for the other system(s). Relatively satisfactory results for the various FeP(Im)-AB bonding energies are obtained with the meta-GGA funtionals BLAP3 and Bmτ1; they yield E(bond) values of ca.1.1, 1.2, and 0.4 eV for AB = CO, NO, and O(2), respectively, which are in reasonable agreement with experimental data (0.78 - 0.85 eV for CO, 0.99 eV for NO, and 0.44 - 0.53 eV for O(2)). The other functionals show more or less deficiency for one or two of the systems. The performances of the various functionals in describing the spin-state energetics of the five-coordinate FeP(Im) complex were also examined.     

Reformulation of density functional theory for N-representable densities and the resolution of the v-representability problem

Density functional theory for the case of general, N-representable densities is reformulated in terms of density functional derivatives of expectation values of operators evaluated with wave functions leading to a density, making no reference to the concept of potential. The developments provide proof of existence of a mathematical procedure that determines whether a density is v-representable and in the case of an affirmative answer determines the potential (within an additive constant) as a derivative with respect to the density of a constrained search functional. It also establishes the existence of an energy functional of the density that, for v-representable densities, assumes its minimum value at the density describing the ground state of an interacting many-particle system. The theorems of Hohenberg and Kohn emerge as special cases of the formalism. Numerical results for one-dimensional non-interacting systems illustrate the formalism. Some direct formal and practical implications of the present reformulation of DFT are also discussed.     

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).     

Flow probe of symmetry energy in relativistic heavy-ion reactions

Various definitions of the symmetry energy are introduced for nuclei, dilute nuclear matter below saturation density and stellar matter, which is found in compact stars or core-collapse supernovae. The resulting differences are exemplified by calculations in a theoretical approach based on a generalized relativistic density functional for dense matter. It contains nucleonic clusters as explicit degrees of freedom with medium-dependent properties that are derived for light clusters from a quantum statistical approach. With such a model the dissolution of clusters at high densities can be described. The effects of the liquid-gas phase transition in nuclear matter and of cluster formation in stellar matter on the density dependence of the symmetry energy are studied for different temperatures. It is observed that correlations and the formation of inhomogeneous matter at low densities and temperatures causes an increase of the symmetry energy as compared to calculations assuming a uniform uncorrelated spatial distribution of constituent baryons and leptons.     

Identities for the electron forms 2 and their 3D representation

New type of identities for products of the electron forms 2 (Fs2) and the bilinear forms (BFs) are derived. The identities are found for both temporal Fs2 describing the electron energy and quasi energy densities and spatial Fs2 describing the linear momentum and quasi linear momentum densities. The identities allow one to transform the quasi energy densities into the energy densities as well as the quasi linear momentum densities into the linear momentum densities. It is shown that by choosing any one of the 16 electron temporal or spatial Fs2 one can represent the remaining 15 temporal or spatial Fs2 as combinations of a chosen form 2 (F2) and the derivatives of a number of BFs. Any one of such 16 sets of identities can be considered as a specific form of an irreducible representation for the temporal or spatial Fs2. Similar to the bilinear identities for BFs the derived identities can be used for reduction different physical quantities describing the electron to the forms defined by the basic physical observables. As an example we consider transformation of the electron energy density to a new fundamental form that presents the energy density through the linear momentum density.     

FeP(Im)−AB bonding energies evaluated with a large number of density functionals (P = porphine,Im = imidazole,AB = CO,NO, and O2)

Sixty-four density functionals, ranging from GGA, meta-GGA, hybrid GGA to hybrid meta-GGA, were tested to evaluate the FeP(Im)–AB bonding energies (E _bond) in the heme model complexes FeP(Im)(AB) (P?=?porphine, Im?=?imidazole, AB?=?CO, NO, and O₂). The results indicate that an accurate prediction of E _bond for the various ligands to heme is difficult with the DFT methods; usually, a functional successful for one system does not perform equally well for other system(s). Relatively satisfactory results for the various FeP(Im)–AB bonding energies are obtained with the meta-GGA functionals BLAP3 and Bmτ1; they yield E _bond values of ca. 1.1, 1.2, and 0.4?eV for AB?=?CO, NO, and O₂, respectively, which are in reasonable agreement with experimental data (0.78–0.85?eV for CO, 0.99?eV for NO, and 0.44???0.53?eV for O₂). The other functionals show more or less deficiency for one or two of the systems. The performances of the various functionals in describing the spin-state energetics of the five-coordinate FeP(Im) complex were also examined.     

Investigation of electronic properties of crystalline arsenic chalcogenides: Theory and experiment

The electronic structure of crystalline As₂S₃ and As₂Se₃ has been calculated in this paper. We present the energy bands, density of states (DOS) and the Compton profiles using the linear combination of atomic orbitals (LCAO) scheme based on the density functional theory (DFT). From the calculated total and partial density of states it is seen that the lone-pair p-states of sulphur/selenium contribute closest to the Fermi energy level. To interpret the theoretical data on the Compton line shape, we have measured the Compton profiles on a 100 mCi ²⁴¹Am spectrometer. It is seen that the density functional theory within generalised gradient approximation gives a slightly better agreement with the experimental momentum densities. The nature of chemical bonding in arsenic chalcogenides is studied using Mulliken's population analysis and the experimentally measured equal-valence-electron-density profiles; As₂S₃ is found to be more ionic compared to As₂Se₃.