LDA Functionals Research Articles

Anhydrous proline crystals: Structural optimization, optoelectronic properties, effective masses and Frenkel exciton energy

The anhydrous orthorhombic l-proline crystal P212121 (Z=4) was studied using density functional theory (DFT) calculations to obtain its structural, electronic and optical properties. Optical absorption measurements were carried out as well, and the resulting absorption spectrum was compared with theoretical results. It is shown that pure LDA and GGA functionals fail to obtain lattice parameters close to experiment, being required the inclusion of a dispersion correction scheme to achieve good results. A complex electronic structure with eight very close indirect band gaps starting at 4.87 eV with a 12 meV energy range is hinted by the simulations. Applying the Δ-sol scheme to correct the DFT band gap, a theoretical gap estimate of 5.50 eV was obtained, which is very close to the experimental value of 5.54 eV extracted from the optical absorption experimental data. Calculated effective masses of electrons and holes in anhydrous proline are very anisotropic and large, as well as the complex dielectric function and the optical absorption. This is likely due to the way proline molecules inside the crystal form permanent electron dipoles interacting through hydrogen bonds and van der Waals forces. Furthermore, the Frenkel exciton binding energy in proline was experimentally and theoretically found to be about 1.3 eV.

Structural and electronic properties of SnS2 stacked nanosheets: An ab-initio study

We present an ab-initio study of the structural and electronic properties of SnS2 stacked nanosheets using the standard LDA and GGA functionals as well as the newly developed variants of the non-local van der Waals (vdW) exchange correlation functionals, namely vdW-DF-revPBE and vdW-DF2-C09. We have examined different stacking configurations of the two, three and four SnS2 layers. The GGA-PBE functional fails to describe the interlayer binding energies and interlayer spacing of SnS2 nanosheets, while a good agreement is observed between the calculated and available experimental values when the van der Waals corrected functionals are used, mostly the vdW-DF2-C09. It is found that the interlayer interactions in the SnS2 films are not only vdW type but, the overlap of wave functions of neighboring layers have to be taken into account. We have observed a systematic reduction in the band gap with the increase in the number of stacked layers. This can be another way of controlling the band gap of SnS2 nanosheets as required for electronic devices.

First-principles study of SnS electronic properties using LDA, PBE and HSE06 functionals

Recently, tin sulphide (SnS) has emerged as a promising alternative to conventional CIGS and CZTC for use in solar cells, possessing such properties as non-toxicity, low cost and production stability. SnS has a high theoretically predicted efficiency above 20%, but the experimentally achieved efficiency so far is as low as 4.36%. The reason for the low achieved efficiency is unclear. One of the powerful tools to get deeper insights about the nature of the problem is first-principles calculation approaches. That is why SnS has become an attractive subject for first-principles calculations recently. Previously calculated data, however, show a widespread of such fundamental value as the bandgap varying from 0.26 to 1.26 eV. In order to understand a reason for that, in this work, we concentrate on a systematic study of calculation parameters effects on the resulting electronic structure, with the particular attention paid to the influence of the exchange-correlation functional chosen for calculations. Several exchange-correlation functionals (LDA, PBE and HSE06) were considered. The systematic analysis has shown that the bandgap variation can result from a tensile/compressive hydrostatic pressure introduced by non-equilibrium lattice parameters used for the calculations. The study of the applicability of three functionals has shown that HSE06 gives the best match to both experimentally obtained bandgap and the XPS valence band spectra. LDA underestimates the bandgap but qualitatively reproduces experimentally measured valence DOS similar to that of HSE06 in contrast to PBE. PBE underestimates the bandgap and does not match to the measured XPS spectra.

A comparative study of different exchange-correlation functionals in understanding structural, electronic and thermoelectric properties of Fe2VAl and Fe2TiSn compounds

Fe2VAl and Fe2TiSn are full Heusler compounds with non-magnetic ground state. The two compounds are good thermoelectric materials. PBE and LDA (PW92) are the two most commonly used density functionals to study the Heusler compounds. Along with these two well studied exchange-correlation functionals, recently developed PBEsol, mBJ and SCAN functionals are employed to study the two compounds. Using the five functionals equilibrium lattice parameter and bulk modulus are calculated. Obtained values are compared with experimental reports wherever available. Electronic structure properties are studied by calculating dispersion curves, total and partial density of states. For Fe2VAl, band gap of 0.22 eV is obtained from the mBJ potential which is in reasonable agreement with experimental value while, for Fe2TiSn band gap of 0.68 eV is obtained. Fe2VAl is predicted to be semimetallic with different values of negative gaps from LDA, PBEsol, PBE and SCAN functionals. Whereas, Fe2TiSn is found to be semimetallic (semiconducting) from LDA, PBEsol (PBE,SCAN) functionals employed calculations. From the dispersion curve effective mass values are also computed to see the contribution to the Seebeck coefficient. In Fe2TiSn, a flat band is present along the Γ-X direction with calculated value of effective mass ∼36 more than the mass of electron. The improvements or inadequacies among the functionals in explaining the properties of full Heusler alloys for thermoelectric application are thus observed through this study.

Electrochemical phase diagrams of Ni from ab initio simulations: role of exchange interactions on accuracy

The stabilities of Ni metal and its derived compounds, including oxides, hydroxides, and oxyhydroxides under electrochemical conditions, can be readily predicted from the Ni Pourbaix diagram, where the formation free energies of the involved species are utilized to construct the phase stability map with respect to electrode potential and pH. We calculate and analyze the crystal structures, electronic structures, and thermodynamic energies of Ni metal and its compounds using different exchange-correlation functionals to density-functional-theory (DFT), including the semilocal LDA and GGA density functionals, the nonlocal metaGGA, and the hybrid density functionals. Next, we simulate the corresponding Ni Pourbaix diagrams to compare systematically the performance of the functional to each other and to experimental observations. We show that the structures and energies obtained from experimental databases may not be sufficiently accurate to describe direct electrochemical observations, and we explain how the electronic exchange within the density functionals plays a key role in determining the accuracy of the DFT calculated electronic, thermodynamic, and electrochemical properties. We find that only the hybrid density functional produces reliable results owing to the fractional contribution of exact Fock exchange included therein. Last, based on our accurate Ni Pourbaix diagram, we construct band-gap and magnetic electrochemical maps which can facilitate more experimental measurements and property assessments under variable potential and pH in the future.

Phonon dispersion anomalies and superconductivity in metal substituted MgB2

We have calculated the extent of the E2g phonon anomaly for Mg1−xMxB2 where M=Sc, Ti, Cd and Ba for 0<x<1 using ab initio DFT models with the LDA and GGA functionals. Using superlattice models along the c axis to represent metal substitution in MgB2, we show that phonon dispersion (PD) plots vary significantly with x, in particular, the nature and extent of the phonon anomaly around the origin, G, of the reciprocal lattice. Measurement of this phonon anomaly along the G-K and G-M directions provides an estimate of the thermal energy, Tδ, of the anomaly, which approximates experimentally determined Tc within standard error for Sc and Ti substitution. We demonstrate that substitutions of Cd and Ba in MgB2 show a higher calculated Tδ than MgB2 by more than 20K. Syntheses of these Cd and Ba compositions are not extant and may not be possible given the limited solubility of metals in MgB2. Nevertheless, ab initio DFT models of phonon behaviour in AlB2–type structures provide an effective tool for prediction of physical properties and for design of new materials.

Vibrational properties of anhydrous and partially hydrated uranyl fluoride.

Uranyl fluoride (UO2F2) is a hygroscopic powder with two main structural phases: an anhydrous crystal and a partially hydrated crystal of the same R3¯m symmetry. The formally closed-shell electron structure of anhydrous UO2F2 is amenable to density functional theory calculations. We use density functional perturbation theory (DFPT) to calculate the vibrational frequencies of the anhydrous crystal structure and employ complementary inelastic neutron scattering and temperature-dependent Raman scattering to validate those frequencies. As a model closed-shell actinide, we investigated the effect of LDA, GGA, and non-local vdW functionals as well as the spherically averaged Hubbard +U correction on vibrational frequencies, electronic structure, and geometry of anhydrous UO2F2. A particular choice of Ueff=5.5 eV yields the correct U-Oyl bond distance and vibrational frequencies for the characteristic Eg and A1g modes that are within the resolution of experiment. Inelastic neutron scattering and Raman scattering suggest a degree of water coupling to the lattice vibrations in the more experimentally accessible partially hydrated UO2F2 system, with the symmetric stretching vibration shifted approximately 47 cm-1 lower in energy compared to the anhydrous structure. Evidence of water interaction with the uranyl ion is present from a two-peak decomposition of the uranyl stretching vibration in the Raman spectra and anion-hydrogen stretching vibrations in the inelastic neutron scattering spectra. A first-order dehydration phase transition temperature is definitively identified to be 125 °C using temperature-dependent Raman scattering.

Electronic and Magnetic Structures of Hole Doped Trilayer La4-xSrxNi3O8 from First-Principles Calculations.

The magnetic and electronic properties of trilayer La4Ni3O8, similar to hole-doped cuprates, are investigated by performing full-potential linearized augmented plane wave method-based spin-polarized calculations with LDA and GGA functionals including Hubbard U parameters to account for strong correlation effects. On the basis of these calculations, we found that La4Ni3O8 is a C-type anti-ferromagnetic (C-AFM) Mott insulator in agreement with previous experimental and theoretical observations. Our calculations suggest that the two crystallographically nonequivalent nickel atoms Ni1 and Ni2 are found to be in high-spin state with an average valency of +1.33. Intermediate band-gap states are originated from dz2 electrons of both types of Ni ions after including the strong correlation effects. To understand the role of hole doping on electronic structure, phase stability, and magnetic properties of La4Ni3O8, similar calculations were performed for La4-xSrxNi3O8 as a function of x, using the supercell approach. We found that the hole doping brings insulator-to-metal transition without changing the C-AFM ordering, though the magnetic moment is enhanced at both Ni sites. Moreover, these Ni atoms are always in an average valence state irrespective of hole doping or volume change. So the electronic properties of hole-doped La4Ni3O8 cannot be compared with hole-doped cuprates that are high-TC superconductors.

Density-functional description of polymer crystals: A comparative study of recent van der Waals functionals.

Due to the lack of treatment of long-range dispersion energies, density functional theory with local and semilocal approximations of exchange-correlation energy is known to fail in describing van der Waals complexes, including polymer crystals. This limitation can be overcome by using a different class of functionals, called van der Waals density functional (vdW-DF), originally developed by Dion et al. [Phys. Rev. Lett. 92, 246401 (2004)]. In this work, we performed a systematic study of structural properties of polymeric crystals using the original vdW-DF functional by Dion et al. and its variants and refinements. Our study shows that this class of functional outperforms the conventional LDA or PBE functionals and gives results with similar accuracy to that of empirical dispersion-corrected schemes such as DFT-D. This study suggests the use of vdW-DF2 functional - a revised version of vdW-DF functional - to obtain a high-fidelity prediction of structural and other properties of polymeric materials.

Performance of quantum Monte Carlo for calculating molecular bond lengths.

This work investigates the accuracy of real-space quantum Monte Carlo (QMC) methods for calculating molecular geometries. We present the equilibrium bond lengths of a test set of 30 diatomic molecules calculated using variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC) methods. The effect of different trial wavefunctions is investigated using single determinants constructed from Hartree-Fock (HF) and Density Functional Theory (DFT) orbitals with LDA, PBE, and B3LYP functionals, as well as small multi-configurational self-consistent field (MCSCF) multi-determinant expansions. When compared to experimental geometries, all DMC methods exhibit smaller mean-absolute deviations (MADs) than those given by HF, DFT, and MCSCF. The most accurate MAD of 3 ± 2 × 10(-3) Å is achieved using DMC with a small multi-determinant expansion. However, the more computationally efficient multi-determinant VMC method has a similar MAD of only 4.0 ± 0.9 × 10(-3) Å, suggesting that QMC forces calculated from the relatively simple VMC algorithm may often be sufficient for accurate molecular geometries.

Assessment of different basis sets and DFT functionals for the calculation of structural parameters, vibrational modes and ligand binding energies of Zr4O2(carboxylate)12 clusters

Different basis sets and functionals in the framework of Density Functional Theory (DFT) were assessed for an accurate prediction of structural parameters and vibrational modes of the cluster Zr4O2(methacrylate)12. A basis set of at least triple-ξ quality is necessary to accurately model the geometry and the IR spectra. Bond distances are best reproduced with hybrid functionals, while IR frequencies are best described by the generalized gradient approximation family of functionals. LDA functionals give the highest GGA functionals the lowest ligand binding energies. Increasing the amount of Hartree Fock exchange in the hybrid functionals results in higher binding energies. Binding energies of ligands in different positions of Zr4O2(methacrylate)12 were calculated. The ligand binding energy decreases when the H atoms in an acetate ligand are successively replaced by F atoms with concomitant lengthening of the Zr–O bond. A chelating acetylacetonate ligand shows a higher ligand binding energy than chelating carboxylate ligands.

Depth dependence of vacancy formation energy at (100), (110), and (111) Al surfaces: A first-principles study

Vacancy defects are known to play an important role in the structural and chemical properties of metallic and semiconductor nanoparticles. Here, we investigate the likelihood of vacancy formation at the surface, in the subsurfaces, and in the interior of a model system of Al nanocrystals. The depth dependence of the vacancy formation energy (VFE) in 14-17 layered low-indexed surfaces of aluminium is studied using LDA, PBE, and PBEsol exchange-correlation functionals. Within a depth of two subsurface layers, the functionals make a transition from a similar description of surfaces to the differences in VFEs observed in bulk Al. The VFE converges to the bulk value within 0.01 eV beyond a maximum depth of 3-6 atomic layers, depending on the crystallographic surface plane. We find that the different convergence behaviors are related to the relaxations of atomic planes, normal to the surface, which in turn depend on the packing density of these surfaces. For the (111) subsurfaces, surprisingly, the defect formation energies are found to be higher than that of bulk Al, which is related to the hindered relaxations in its close-packed atomic planes. Although our results predict considerably lower VFE for the topmost layers of all the surfaces, the likelihood of forming a vacancy in the immediate subsurfaces of multifaceted Al nanoparticles is predicted to be lower than in bulk Al, which is in contrast to expectation.

Importance of Unit Cells in Accurate Evaluation of the Characteristics of Graphene

Abstract Effects of the size of the unit cell on energy, atomic charges, and phonon frequencies of graphene at the Γ point of the Brillouin zone are studied in the absence and presence of an electric field using density functional theory (DFT) methods (LDA and DFT-PBE functionals with Goedecker–Teter–Hutter (GTH) and Troullier–Martins (TM) norm-conserving pseudopotentials). Two types of unit cells containing nC=4–28 carbon atoms are considered. Results show that stability of graphene increases with increasing size of the unit cell. Energy, atomic charges, and phonon frequencies all converge above nC=24 for all functional-pseudopotentials used. Except for the LDA-GTH calculations, application of an electric field of 0.4 and 0.9 V/nm strengths does not change the trends with the size of the unit cell but instead slightly decreases the binding energy of graphene. Results of this study show that the choice of unit cell size and type is critical for calculation of reliable characteristics of graphene.

Electric field effect in ultrathin zigzag graphene nanoribbons**Project supported by the National Natural Science Foundation of China (Grant Nos. 11204201 and 11147142) and the Natural Science Foundation for Young Scientists of Shanxi Province, China (Grant No. 2013021010-1).

The electric field effect in ultrathin zigzag graphene nanoribbons containing only three or four zigzag carbon chains is studied by first-principles calculations, and the change of conducting mechanism is observed with increasing in-plane electric field perpendicular to the ribbon. Wider zigzag graphene nanoribbons have been predicted to be spin-splitted for both valence band maximum (VBM) and conduction band minimum (CBM) with an applied electric field and become half-metal due to the vanishing band gap of one spin with increasing applied field. The change of VBM for the ultrathin zigzag graphene nanoribbons is similar to that for the wider ones when an electric field is applied. However, in the ultrathin zigzag graphene nanoribbons, there are two kinds of CBMs, one is spin-degenerate and the other is spin-splitted, and both are tunable by the electric field. Moreover, the two CBMs are spatially separated in momentum space. The conducting mechanism changes from spin-degenerate CBM to spin-splitted CBM with increasing applied electric field. Our results are confirmed by density functional calculations with both LDA and GGA functionals, in which the LDA always underestimates the band gap while the GGA normally produces a bigger band gap than the LDA.

A first principles study of hydrogen storage on lithium decorated two dimensional carbon allotropes

Graphene has been intensively investigated as a possible hydrogen storage medium due to the spectacular properties granted by its two-dimensional nature. Since graphene's discovery, several new two-dimensional carbon allotropes have been theorized and synthesized. We investigated the hydrogen storage ability of six such allotropes: C65, C64, C63, C62, C31 and C41. The ability to anchor lithium metal atoms over each allotrope and the hydrogen binding energies for each lithium decorated allotrope were studied with density functional theory using LDA, GGA and vdW-DF2 (for describing van der Waals interactions) functionals. All the allotropes were able to achieve double sided lithium decoration and hydrogen adsorption. Every allotrope other than C31 possesed lithium binding energies stronger than bulk lithium's cohesive energy which indicates that adsorbed lithium atoms will not cluster on the allotrope surface. Furthermore, every structure produced hydrogen binding energies stronger than that of lithium decorated graphene, suggesting the potential of use of these structures in practical hydrogen storage media. The C41 structure was able to adsorb far more hydrogen molecules than any other structure with a maximum hydrogen gravimetric density of 7.12 wt.% using the vdW-DF2 functional.

Hydrogen adsorption of nitrogen-doped carbon nanotubes functionalized with 3d-block transition metals

A systematic study of the most stable configurations, calculation of the corresponding binding and free energies of functionalized 3d transition metals (TMs) on (10,0) Single Walled Carbon Nanotube (SWCNT) doped with porphyrin-like nitrogen defects (4ND-CNxNT) using spin-polarized density functional theory (DFT) formalism with flavours of LDA and GGA exchange-correlation (XC) functionals has been made. A thorough analysis showed that the electronic and magnetic properties of SWCNT are dependent on the TMs absorbed wherein, the composite material TM/4ND-CNxNT can act as a medium for storing hydrogen at room temperature manifested through favourable adsorption energy.

Vacancy formation energies in metals: A comparison of MetaGGA with LDA and GGA exchange–correlation functionals

We report on the results of density-functional-theory based calculations of the vacancy formation energies in metals using the revised Tao–Perdew–Staroverov–Scuseria (revTPSS) functional (Pedrew et al., 2009), which is a self-consistent semilocal meta-generalized gradient approximation functional. The motivation for this work is to determine if the improved accuracy of surface energies for revTPSS compared to local and generalized gradient approximation functionals also leads to improved vacancy formation energies since vacancies can be viewed as internal surfaces. In addition, we report on the lattice constants, cohesive energies and bulk moduli predicted by revTPSS. By comparing the vacancy formation energies and bulk properties, the performance of revTPSS is assessed against four functionals: the local spin density approximation (LSDA), Perdew, Burke and Ernzerhof (PBE), Perdew–Wang-91 (PW91), and PBE for solids (PBEsol). Using an automated computational approach, we calculate the vacancy formation energies and the macroscopic properties of 34 metal systems for the five functionals. For macroscopic properties (lattice constants, cohesive energies and bulk modulus), we find the results for revTPSS typically lie between LDA and PBE with a mean absolute percentage deviation of 1.1% and 12.1% from the experimental data for lattice constants and cohesive energies respectively. Further, it is found that revTPSS predicts higher vacancy formation energies when compared to the four other functionals surveyed. We have observed the following order for the functionals with respect to the computed vacancy formation energies, Efxc:EfrevTPSS>EfPBEsol∼EfLDA>EfPBE>EfPW91. We also consider the effects of a surface-energy error correction that has been proposed for standard LDA and GGA functionals. This correction increases the vacancy formation energies of LDA, PBE and PW91 functionals. The revTPSS computed VFEs are greater than the surface-energy-corrected PBE VFEs by a mean relative difference of 14.8%.

Effects of exchange correlation functional on optical permittivity of gold and electromagnetic responses.

Understanding the optical properties of nanometer-scale noble metals is important for the nanoplasmonic devices. The bulk gold and thin film are calculated by density functional theory (DFT) with LDA, PBE, and GLLBSC functionals, respectively. The GLLBSC results for bulk gold are closer to the experimental data because the GLLBSC functional has better descriptions of transition energy. The Im(ε) of thin film calculated by LDA and PBE are overestimated. The effects of DFT-based optical properties are performed by conducting electromagnetic simulations. The transmission for the gold thin film by GLLBSC is blue-shifted. The gold grating structure with the GLLBSC-based optical permittivity has strong localized streamlines of Poynting vector in the corner edges at the resonance condition.

The Key Role of van der Waals Interactions in MPc/Au(111) (M = Co, Fe, H2) Systems Based on First-Principles Calculations

First-principles calculations for metal–phthalocyanines (MPc, M = Co, Fe, H2) adsorbed on Au(111) surfaces with LDA, PW91, and optB86b-vdW functionals are performed. The adsorption energies, adsorption distances, potential energy surfaces, electron transfer properties, and the migration barriers are calculated and compared with the reported experimental data. Our results show that, while PW91 functional is obviously not suitable for MPc/Au(111) systems due to its intrinsic short comings, LDA and optB86b-vdW functionals give more reliable results. The optB86b-vdW functional has overall the best performance among the three functionals, which indicates that the van der Waals interactions play key roles in such adsorption systems.

Potential energy curves for the ground and low-lying excited states of CuAg.

The ground and low-lying excited states of heteronuclear diatomic CuAg are examined by multi-reference configuration interaction (MRCI) method. Relativistic effects were treated and probed in two steps. Scalar terms were considered using the spin-free DKH Hamiltonian as a priori and spin-orbit coupling was calculated perturbatively via the spin-orbit terms of the Breit-Pauli Hamiltonian based on MRCI wavefunctions. Potential energy curves of the spin-free states and their corresponding Ω components correlating with the separated atom limits (2)S(Cu) + (2)S(Ag) and (2)D(Cu) + (2)S(Ag) are obtained. The results are in fine agreement with the experimental measurements and tentative conclusions for the ion-pair B0(+) state are confirmed by our theoretical calculations. Illustrative results are presented to reveal the relative importance and magnitude of the scalar and spin-orbit effects on the spectroscopic properties of this molecule. Time dependent density functional theory calculations, using the LDA, BLYP, B3LYP, and SAOP functionals have been carried out for CuAg and the accuracy of TD-DFT has been compared with ab initio results.