Nonempirical hyper-generalized-gradient functionals constructed from the Lieb-Oxford bound

A simple and completely general representation of the exact exchange-correlation functional of density-functional theory is derived from the universal Lieb-Oxford bound, which holds for any Coulomb-interacting system. This representation leads to an alternative point of view on popular hybrid functionals, providing a rationale for why they work and how they can be constructed. A similar representation of the exact correlation functional allows to construct fully nonempirical hyper-generalized-gradient approximations (HGGAs), radically departing from established paradigms of functional construction. Numerical tests of these HGGAs for atomic and molecular correlation energies and molecular atomization energies show that even simple HGGAs match or outperform state-of-the-art correlation functionals currently used in solid-state physics and quantum chemistry.

Systematic investigation of a family of gradient-dependent functionals for solids

Eleven density functionals are compared with regard to their performance for the lattice constants of solids. We consider standard functionals, such as the local-density approximation and the Perdew-Burke-Ernzerhof (PBE) generalized-gradient approximation (GGA), as well as variations of PBE GGA, such as PBEsol and similar functionals, PBE-type functionals employing a tighter Lieb-Oxford bound, and combinations thereof. On a test set of 60 solids, we perform a system-by-system analysis for selected functionals and a full statistical analysis for all of them. The impact of restoring the gradient expansion and of tightening the Lieb-Oxford bound is discussed, and confronted with previous results obtained from other codes, functionals or test sets. No functional is uniformly good for all investigated systems, but surprisingly, and pleasingly, the simplest possible modifications to PBE turn out to have the most beneficial effect on its performance. The atomization energy of molecules was also considered and on a testing set of six molecules, we found that the PBE functional is clearly the best, the others leading to strong overbinding.

Gradient-dependent density functionals of the Perdew-Burke-Ernzerhof type for atoms, molecules, and solids

One of the standard generalized-gradient approximations (GGAs) in use in modern electronic-structure theory [Perdew-Burke-Ernzerhof (PBE) GGA] and a recently proposed modification designed specifically for solids (PBEsol) are identified as particular members of a family of functionals taking their parameters from different properties of homogeneous or inhomogeneous electron liquids. Three further members of this family are constructed and tested, together with the original PBE and PBEsol, for atoms, molecules, and solids. We find that PBE, in spite of its popularity in solid-state physics and quantum chemistry, is not always the best performing member of the family and that PBEsol, in spite of having been constructed specifically for solids, is not the best for solids. The performance of GGAs for finite systems is found to sensitively depend on the choice of constraints stemming from infinite systems. Guidelines both for users and for developers of density functionals emerge from this work.

Amorphous HfO(2) and Hf(1-x)Si(x)O via a melt-and-quench scheme using ab initio molecular dynamics

We have performed ab initio molecular dynamics simulations to generate an atomic structure model of amorphous hafnium oxide (a-HfO(2)) via a melt-and-quench scheme. This structure is analyzed via bond-angle and partial pair distribution functions. These results give a Hf-O average nearest-neighbor distance of 2.2 angstrom, which should be compared to the bulk value, which ranges from 1.96 to 2.54 angstrom. We have also investigated the neutral O vacancy and a substitutional Si impurity for various sites, as well as the amorphous phase of Hf(1-x)Si(x)O(2) for x=0.25, 0375, and 0.5.

Optical absorption and electronic band structure first-principles calculations of alpha-glycine crystals

Light absorption of alpha-glycine crystals grown by slow evaporation at room temperature was measured, indicating a 5.11 +/- 0.02 eV energy band gap. Structural, electronic, and optical absorption properties of alpha-glycine crystals were obtained by first-principles quantum mechanical calculations using density functional theory within the generalized gradient approximation in order to understand this result. To take into account the contribution of core electrons, ultrasoft and norm-conserving pseudopotentials, as well as an all electron approach were considered to compute the electronic density of states and band structure of alpha-glycine crystals. They exhibit three indirect energy band gaps and one direct Gamma-Gamma energy gap around 4.95 eV. The optical absorption related to transitions between the top of the valence band and the bottom of the conduction band involves O 2p valence states and C, O 2p conduction states, with the carboxyl group contributing significantly to the origin of the energy band gap. The calculated optical absorption is highly dependent on the polarization of the incident radiation due to the spatial arrangement of the dipolar glycine molecules; in the case of a polycrystalline sample, the first-principles calculated optical absorption is in good agreement with the measurement when a rigid energy shift is applied.

Comparative study of the adsorption and dissociation of vinylacetic acid and acrylic acid on silicon (001)

In this work, we employ the state of the art pseudopotential method, within a generalized gradient approximation to the density functional theory, to investigate the adsorption process of acrylic acid (AAc) and vinylacetic acid (VAA) on the silicon surface. Our total energy calculations support the proposed experimental process, as it indicates that the chemisorption of the molecule is as follows: The gas phase VAA (AAc) adsorbs molecularly to the electrophilic surface Si atom and then dissociates into H(2)C = CH - COO and H, bonded to the electrophilic and nucleophilic surface silicon dimer atoms, respectively. The activation energy for both processes correspond to thermal activations that are smaller than the usual growth temperature. In addition, the electronic structure, calculated vibrational modes, and theoretical scanning tunneling microscopy images are discussed, with a view to contribute to further experimental investigations.

Lower Bounds on the Exchange-Correlation Energy in Reduced Dimensions

Bounds on the exchange-correlation energy of many-electron systems are derived and tested. By using universal scaling properties of the electron-electron interaction, we obtain the exponent of the bounds in three, two, one, and quasione dimensions. From the properties of the electron gas in the dilute regime, the tightest estimate to date is given for the numerical prefactor of the bound, which is crucial in practical applications. Numerical tests on various low-dimensional systems are in line with the bounds obtained and give evidence of an interesting dimensional crossover between two and one dimensions.

Density functional theory investigation of 3d, 4d, and 5d 13-atom metal clusters

The knowledge of the atomic structure of clusters composed by few atoms is a basic prerequisite to obtain insights into the mechanisms that determine their chemical and physical properties as a function of diameter, shape, surface termination, as well as to understand the mechanism of bulk formation. Due to the wide use of metal systems in our modern life, the accurate determination of the properties of 3d, 4d, and 5d metal clusters poses a huge problem for nanoscience. In this work, we report a density functional theory study of the atomic structure, binding energies, effective coordination numbers, average bond lengths, and magnetic properties of the 3d, 4d, and 5d metal (30 elements) clusters containing 13 atoms, M(13). First, a set of lowest-energy local minimum structures (as supported by vibrational analysis) were obtained by combining high-temperature first- principles molecular-dynamics simulation, structure crossover, and the selection of five well-known M(13) structures. Several new lower energy configurations were identified, e. g., Pd(13), W(13), Pt(13), etc., and previous known structures were confirmed by our calculations. Furthermore, the following trends were identified: (i) compact icosahedral-like forms at the beginning of each metal series, more opened structures such as hexagonal bilayerlike and double simple-cubic layers at the middle of each metal series, and structures with an increasing effective coordination number occur for large d states occupation. (ii) For Au(13), we found that spin-orbit coupling favors the three-dimensional (3D) structures, i.e., a 3D structure is about 0.10 eV lower in energy than the lowest energy known two-dimensional configuration. (iii) The magnetic exchange interactions play an important role for particular systems such as Fe, Cr, and Mn. (iv) The analysis of the binding energy and average bond lengths show a paraboliclike shape as a function of the occupation of the d states and hence, most of the properties can be explained by the chemistry picture of occupation of the bonding and antibonding states.

Transition-metal 13-atom clusters assessed with solid and surface-biased functionals

First-principles density-functional theory studies have reported open structures based on the formation of double simple-cubic (DSC) arrangements for Ru(13), Rh(13), Os(13), and Ir(13), which can be considered an unexpected result as those elements crystallize in compact bulk structures such as the face-centered cubic and hexagonal close-packed lattices. In this work, we investigated with the projected augmented wave method the dependence of the lowest-energy structure on the local and semilocal exchange-correlation (xc) energy functionals employed in density-functional theory. We found that the local-density approximation (LDA) and generalized-gradient formulations with different treatment of the electronic inhomogeneities (PBE, PBEsol, and AM05) confirm the DSC configuration as the lowest-energy structure for the studied TM(13) clusters. A good agreement in the relative total energies are obtained even for structures with small energy differences, e. g., 0.10 eV. The employed xc functionals yield the same total magnetic moment for a given structure, i.e., the differences in the bond lengths do not affect the moments, which can be attributed to the atomic character of those clusters. Thus, at least for those systems, the differences among the LDA, PBE, PBEsol, and AM05 functionals are not large enough to yield qualitatively different results. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3577999]

Effective coordination concept applied for phase change (GeTe)(m)(Sb(2)Te(3))(n) compounds

In this work, we employed the effective coordination concept to study the local environments of the Ge, Sb, and Te atoms in the Ge(m)Sb(2n)Te(m+3n) compounds. From our calculations and analysis, we found an average effective coordination number (ECN) reduction of 1.59, 1.42, and 1.37, for the Ge, Sb, Te atoms in the phase transition from crystalline, ECN=5.55 (Ge), 5.73 (Sb), 4.37 (Te), to the amorphous phase, ECN=3.96 (Ge), 4.31 (Sb), 3.09 (Te), for the Ge(2)Sb(2)Te(5) composition. Similar changes are observed for other compositions. Thus, our results indicate that the coordination changes from the crystalline to amorphous phase are not large as previously assumed in the literature, i.e., from sixfold to fourfold for Ge, which can contribute to obtain a better understanding of the crystalline to amorphous phase transition. (C) 2011 American Institute of Physics. [doi:10.1063/1.3533422]

The role of electron localization in the atomic structure of transition-metal 13-atom clusters: the example of Co(13), Rh(13), and Hf(13)

The crystalline structure of transition-metals (TM) has been widely known for several decades, however, our knowledge on the atomic structure of TM clusters is still far from satisfactory, which compromises an atomistic understanding of the reactivity of TM clusters. For example, almost all density functional theory (DFT) calculations for TM clusters have been based on local (local density approximation-LDA) and semilocal (generalized gradient approximation-GGA) exchange-correlation functionals, however, it is well known that plain DFT fails to correct the self-interaction error, which affects the properties of several systems. To improve our basic understanding of the atomic and electronic properties of TM clusters, we report a DFT study within two nonlocal functionals, namely, the hybrid HSE (Heyd, Scuseria, and Ernzerhof) and GGA + U functionals, of the structural and electronic properties of the Co(13), Rh(13), and Hf(13) clusters. For Co(13) and Rh(13), we found that improved exchange-correlation functionals decrease the stability of open structures such as the hexagonal bilayer (HBL) and double simple-cubic (DSC) compared with the compact icosahedron (ICO) structure, however, DFT-GGA, DFT-GGA + U, and DFT-HSE yield very similar results for Hf(13). Thus, our results suggest that the DSC structure obtained by several plain DFT calculations for Rh(13) can be improved by the use of improved functionals. Using the sd hybridization analysis, we found that a strong hybridization favors compact structures, and hence, a correct description of the sd hybridization is crucial for the relative energy stability. For example, the sd hybridization decreases for HBL and DSC and increases for ICO in the case of Co(13) and Rh(13), while for Hf(13), the sd hybridization decreases for all configurations, and hence, it does not affect the relative stability among open and compact configurations.

The role of carbon impurities on the Si(001)-c(4 x 4) surface reconstruction: Theoretical calculations

In this work we employ the state-of-the-art pseudopotential method, within a generalized gradient approximation to the density functional theory, combined with a recently developed method for the calculation of HREELS spectra to study a series of different proposed models for carbon incorporation on the silicon (001) surface. A fully discussion on the geometry, energetics and specially the comparison between experimental and theoretical STM images and electron energy loss spectra indicate that the Si(100)-c(4 x 4) is probably induced by Si-C surface dinners, in agreement with recent experimental findings. (C) 2009 Elsevier B.V. All rights reserved.

Furan interaction with the Si(001)-(2 x 2) surface: structural, energetics, and vibrational spectra from first-principles

In this work we employ the state of the art pseudopotential method, within a generalized gradient approximation to the density functional theory, to investigate the adsorption process of furan on the silicon (001) surface. A direct comparison of different adsorption structures with x-ray photoelectron spectroscopy (XPS), ultra-violet photoelectron spectroscopy (UPS), high resolution electron energy loss spectroscopy (HREELS), near edge x-ray absorption fine structure (NEXAFS), and high resolution spectroscopy experimental data allows us to identify the [4 + 2] cycloaddition reaction as the most probable adsorbate. In addition, theoretical scanning tunnelling microscopy (STM) images are presented, with a view to contributing to further experimental investigations.

Electronic and optical properties of grossular garnet (Ca(3)Al(2)Si(3)O(12)): An ab initio study

The electronic and optical properties of grossular garnet are investigated using density functional theory (DFT) within generalized gradient approximation (GGA). The calculated lattice parameters are in good agreement with the experiment data. The electronic structure shows that grossular has a direct band gap of 5.22 eV. The dielectric functions, reflective index, extinction coefficient, reflectivity and energy-loss spectrum are calculated. The optical properties of grossular are discussed based on the band structure calculations. The O 2p states and Si 3s play a major role in these optical transitions as initial and final states, respectively. The absorption spectrum is localized in the ultraviolet range between 30 and 250 nm. Finally, we concluded that pure grossular crystal does not absorb radiation in the visible range. (c) 2009 Elsevier B.V. All rights reserved.

Dependence of Response Functions and Orbital Functionals on Occupation Numbers

Explicitly orbital-dependent approximations to the exchange-correlation energy functional of density functional theory typically not only depend on the single-particle Kohn-Sham orbitals but also on their occupation numbers in the ground-state Slater determinant. The variational calculation of the corresponding exchange-correlation potentials with the optimized effective potential (OEP) method therefore also requires a variation of the occupation numbers with respect to a variation in the effective single-particle potential, which is usually not taken into account. Here it is shown under which circumstances this procedure is justified.