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.

Excitation energies from ground-state density-functionals by means of generator coordinates

The generator-coordinate method is a flexible and powerful reformulation of the variational principle. Here we show that by introducing a generator coordinate in the Kohn-Sham equation of density-functional theory, excitation energies can be obtained from ground-state density functionals. As a viability test, the method is applied to ground-state energies and various types of excited-state energies of atoms and ions from the He and the Li isoelectronic series. Results are compared to a variety of alternative DFT-based approaches to excited states, in particular time-dependent density-functional theory with exact and approximate potentials.

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.

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.

Reverse engineering in many-body quantum physics: Correspondence between many-body systems and effective single-particle equations

The mapping, exact or approximate, of a many-body problem onto an effective single-body problem is one of the most widely used conceptual and computational tools of physics. Here, we propose and investigate the inverse map of effective approximate single-particle equations onto the corresponding many-particle system. This approach allows us to understand which interacting system a given single-particle approximation is actually describing, and how far this is from the original physical many-body system. We illustrate the resulting reverse engineering process by means of the Kohn-Sham equations of density-functional theory. In this application, our procedure sheds light on the nonlocality of the density-potential mapping of density-functional theory, and on the self-interaction error inherent in approximate density functionals.

Empirical analysis of the Lieb-Oxford bound in ions and molecules

Universal properties of the Coulomb interaction energy apply to all many-electron systems. Bounds on the exchange-correlation energy, in particular, are important for the construction of improved density functionals. Here we investigate one such universal property-the Lieb-Oxford lower bound-for ionic and molecular systems. In recent work [J Chem Phys 127, 054106 (2007)], we observed that for atoms and electron liquids this bound may be substantially tightened. Calculations for a few ions and molecules suggested the same tendency, but were not conclusive due to the small number of systems considered. Here we extend that analysis to many different families of ions and molecules, and find that for these, too, the bound can be empirically tightened by a similar margin as for atoms and electron liquids. Tightening the Lieb-Oxford bound will have consequences for the performance of various approximate exchange-correlation functionals. (C) 2008 Wiley Periodicals Inc.

Combining Monte Carlo simulation and density-functional theory to describe the spectral changes of Na(2) in liquid helium

Spectral changes of Na(2) in liquid helium were studied using the sequential Monte Carlo-quantum mechanics method. Configurations composed by Na(2) surrounded by explicit helium atoms sampled from the Monte Carlo simulation were submitted to time-dependent density-functional theory calculations of the electronic absorption spectrum using different functionals. Attention is given to both line shift and line broadening. The Perdew, Burke, and Ernzerhof (PBE1PBE, also known as PBE0) functional, with the PBE1PBE/6-311++G(2d,2p) basis set, gives the spectral shift, compared to gas phase, of 500 cm(-1) for the allowed X (1)Sigma(+)(g) -> B (1)Pi(u) transition, in very good agreement with the experimental value (700 cm(-1)). For comparison, cluster calculations were also performed and the first X (1)Sigma(+)(g) -> A (1)Sigma(+)(u) transition was also considered.

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]

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.

Orbital-polarization terms: From a phenomenological to a first-principles description of orbital magnetism in density-functional theory

Phenomenological orbital-polarizition (OP) terms have been repeatedly introduced in the single-particle equations of spin-density-functional theory, in order to improve the description of orbital magnetic moments in systems containing transition metal ions. Here we show that these ad hoc corrections can be interpreted as approximations to the exchange-correlation vector potential A(xc) of current-density functional theory (CDFT). This connection provides additional information on both approaches: phenomenological OP terms are connected to first-principles theory, leading to a rationale for their empirical success and a reassessment of their limitations and the approximations made in their derivation. Conversely, the connection of OP terms with CDFT leads to a set of simple approximations to the CDFT potential A(xc), with a number of desirable features that are absent from electron-gas-based functionals. (C) 2008 Wiley Periodicals, Inc.

Analyzing the n→π* Electronic Transition of Formaldehyde in Water. A Sequential Monte Carlo/Time-Dependent Density Functional Theory

The n→π* absorption transition of formaldehyde in water is analyzed using combined and sequential classical Monte Carlo (MC) simulations and quantum mechanics (QM) calculations. MC simulations generate the liquid solute-solvent structures for subsequent QM calculations. Using time-dependent density functional theory in a localized set of gaussian basis functions (TD-DFT/6-311++G(d,p)) calculations are made on statistically relevant configurations to obtain the average solvatochromic shift. All results presented here use the electrostatic embedding of the solvent. The statistically converged average result obtained of 2300 cm-1 is compared to previous theoretical results available. Analysis is made of the effective dipole moment of the hydrogen-bonded shell and how it could be held responsible for the polarization of the solvent molecules in the outer solvation shells.

Density and survival rate of Culex quinquefasciatus at Parque Ecológico do Tietê, São Paulo, Brazil

Parity rate, gonotrophic cycle length, and density of a Culex quinquefasciatus female population was estimated at the Parque Ecológico do Tietê (PET), São Paulo, Brazil. Adult Cx. quinquefasciatus females were collected from vegetation along the edges of a polluted drainage canal with the use of a battery-powered backpack aspirator from September to November 2005 and from February to April 2006. We examined 255 Cx. quinquefasciatus ovaries to establish the parity rate of 0.22 and determined the gonotrophic cycle length under laboratory conditions to be 3 and 4 days. From these data, we calculated the Cx. quinquefasciatus survival rate to be 0.60 and 0.68 per day. Density of the Cx. quinquefasciatus female (5.71 females per m2) was estimated based on a population size of 28,810 individuals divided by the sampled area of 5,040 m2. Results of all experiments indicate medium survivorship and high density of the Cx. quinquefasciatus female population. This species is epidemiologically relevant in the PET area and should be a target of the vector control program of São Paulo municipality

Density functional theory study of Fe(3)Ga

First-principles scalar relativistic calculations in supercells of 16 atoms are used to represent disordered B2 ordering of Fe(3)Ga in order to observe the effect of Ga-Ga pairs on the electronic structure of this alloy. From a comparison with pure bcc Fe it is observed that the energy position and occupation of e(g) and t(2g) states are largely affected by the Ga-Ga pairs and strengthened intraplane interactions takes place. The results show that a larger hybridization of the conduction band is in the source of the magnetostriction enhancement experimentally observed in Galfenol. (C) 2011 American Institute of Physics. [doi:10.1063/1.3525609]

WOOD DENSITY VARIATION AND TREE RING DEMARCATION IN Gmelina arborea TREES USING X-RAY DENSITOMETRY

Due to its relationship with other properties, wood density is the main wood quality parameter. Modern, accurate methods - such as X-ray densitometry - are applied to determine the spatial distribution of density in wood sections and to evaluate wood quality. The objectives of this study were to determinate the influence of growing conditions on wood density variation and tree ring demarcation of gmelina trees from fast growing plantations in Costa Rica. The wood density was determined by X-ray densitometry method. Wood samples were cut from gmelina trees and were exposed to low X-rays. The radiographic films were developed and scanned using a 256 gray scale with 1000 dpi resolution and the wood density was determined by CRAD and CERD software. The results showed tree-ring boundaries were distinctly delimited in trees growing in site with rainfall lower than 25 10 mm/year. It was demonstrated that tree age, climatic conditions and management of plantation affects wood density and its variability. The specific effect of variables on wood density was quantified by for multiple regression method. It was determined that tree year explained 25.8% of the total variation of density and 19.9% were caused by climatic condition where the tree growing. Wood density was less affected by the intensity of forest management with 5.9% of total variation.

NEAR INFRARED SPECTROSCOPY FOR ESTIMATING SUGARCANE BAGASSE CONTENT IN MEDIUM DENSITY FIBERBOARD

Medium density fiberboard (MDF) is an engineered wood product formed by breaking down selected lignin-cellulosic material residuals into fibers, combining it with wax and a resin binder, and then forming panels by applying high temperature and pressure. Because the raw material in the industrial process is ever-changing, the panel industry requires methods for monitoring the composition of their products. The aim of this study was to estimate the ratio of sugarcane (SC) bagasse to Eucalyptus wood in MDF panels using near infrared (NIR) spectroscopy. Principal component analysis (PCA) and partial least square (PLS) regressions were performed. MDF panels having different bagasse contents were easily distinguished from each other by the PCA of their NIR spectra with clearly different patterns of response. The PLS-R models for SC content of these MDF samples presented a strong coefficient of determination (0.96) between the NIR-predicted and Lab-determined values and a low standard error of prediction (similar to 1.5%) in the cross-validations. A key role of resins (adhesives), cellulose, and lignin for such PLS-R calibrations was shown. PLS-DA model correctly classified ninety-four percent of MDF samples by cross-validations and ninety-eight percent of the panels by independent test set. These NIR-based models can be useful to quickly estimate sugarcane bagasse vs. Eucalyptus wood content ratio in unknown MDF samples and to verify the quality of these engineered wood products in an online process.