Approximate Exchange-correlation Research Articles

Electronic band structure and optical properties of titanium oxyphosphates Li 0.50Co 0.25TiO(PO 4) single crystals: An ab-initio calculations

From the refined atomic positions obtained by Belmal et al. (2004) [1] using X-ray diffraction for Li 0.50Co 0.25TiO(PO 4), we have performed a structural optimization by minimizing the forces acting on the atoms keeping the lattice parameters fixed at the experimental values. With this relaxed (optimized) geometry we have performed a comprehensive theoretical study of electronic properties and dispersion of the linear optical susceptibilities using the full potential linear augmented plane wave (FP-LAPW) method. The generalized gradient approximation (GGA) exchange-correlation potential was applied. In addition, the Engel-Vosko generalized gradient approximation (EVGGA) was used for comparison with GGA because it is known that EVGGA approach yields better band splitting compared to the GGA. We have calculated the band structure, and the total and partial densities of states. The electron charge densities and the bonding properties were analyzed and discussed. The complex dielectric optical susceptibilities were discussed in detail.

The influence of density functional approximations on the description of LiH + NH 3 → LiNH 2 + H 2 reaction

In this Letter, we assess the ability of various density functionals to correctly describe the pathway of the simple reaction LiH + NH 3 → LiNH 2 + H 2, a model for hydrogen storage in recent lithium-based materials. To this aim, the ability of 27 exchange–correlation approximations for providing accurate reaction energies, activation barriers and local Bader’s Atoms in Molecules properties is evaluated. Lastly, conceptual DFT is used to broaden the scope of possible relevant interpretative tools.

Structural stabilities, elastic and thermodynamic properties of Scandium Chalcogenides via first-principles calculations

The high-pressure structural (B1–B2) phase transition and the elastic properties of ScS and ScSe are studied using the full-potential augmented plane wave plus local orbitals method (FP-APW+LO) with the generalized-gradient approximation (GGA) exchange-correlation functional. The elastic constants and their pressure dependence are calculated following the total energy variation with strain technique. The stability and the ductility mechanisms for these compounds are discussed via the electronic density of states (DOS) and the elastic constants Cij. The thermodynamic properties of (B1) structure are predicted through the quasi-harmonic Debye model, in which the lattice vibrations are taken into account. The variation of bulk moduli, the thermal expansion coefficient, the heat capacities and the Debye temperature with pressure and temperature are successfully obtained. To our knowledge this is the first quantitative theoretical prediction of the elastic, high pressure and thermal properties for the investigated compounds and still awaits experimental confirmations.

Van der Waals density functionals applied to solids

The van der Waals density functional (vdW-DF) of Dion et al. [Phys. Rev. Lett. 92, 246401 (2004)] is a promising approach for including dispersion in approximate density functional theory exchange-correlation functionals. Indeed, an improved description of systems held by dispersion forces has been demonstrated in the literature. However, despite many applications, standard general tests on a broad range of materials are lacking. Here we calculate the lattice constants, bulk moduli, and atomization energies for a range of solids using the original vdW-DF and several of its offspring. We find that the original vdW-DF overestimates lattice constants in a similar manner to how it overestimates binding distances for gas phase dimers. However, some of the modified vdW functionals lead to average errors which are similar to those of PBE or better. Likewise, atomization energies that are slightly better than from PBE are obtained from the modified vdW-DFs. Although the tests reported here are for "hard" solids, not normally materials for which dispersion forces are thought to be important, we find a systematic improvement in cohesive properties for the alkali metals and alkali halides when non-local correlations are accounted for.

Electronic structure, chemical bonding features, and electron charge density of the double-cubane single crystal [Sb7S8Br2](AlCl4)3

The present calculations were performed using all-electron full potential linearized augmented plane wave method based on the density functional theory. We have optimized the structure of the double-cubane single crystal [Sb7S8Br2](AlCl4)3, starting with the x-ray diffraction data Zhang et al., [J. Am. Chem. Soc. 131, 9896 (2009)], by minimization of the forces (1 mRy/au) acting on the atoms, keeping the lattice parameters fixed at the experimental values. Our calculations show that [Sb7S8Br2](AlCl4)3 possesses a wide indirect energy band gap of about 1.6 eV (2.03 eV) using local density approximation (Engel–Vosko generalized gradient approximation) exchange correlation potentials. To describe the bonding properties we have evaluated the electronic charge space density contour in four planes-namely (001), (110), (100), and (010) which show that this compound possesses a considerable anisotropy. The contour plot shows partial ionic and strong covalent bonding between S–Sb, Al–Cl, S–Br, S–S, Cl–Cl, and Sb–Br atoms.

Accurate projected augmented wave datasets for BaFe2As2

By carefully choosing parameters and including more semi-core orbitals as valence electrons, we have constructed a high-quality projected augmented wave dataset that yields results comparable to existing full-potential linearized augmented plane-wave calculations. The dataset was then applied to BaFe2As2 to study the effects of different levels of structure optimization, as well as different choices of exchange-correlation functionals. It was found that the local density approximation exchange-correlation functional fails to find the correct spin-density-wave anti-ferromagnetic (SDW-AFM) ground state under full optimization, while the Perdew–Burke–Ernzerhof (PBE) exchange-correlation functional obtains the correct state but significantly overestimates the magnetism. The electronic structure of the SDW-AFM state is not very sensitive to structure optimizations with the PBE exchange-correlation functional because the positions of the As atoms are preserved under optimizations. We further investigated the Ba atom diffusion process on the BaFe2As2 surface using the nudged elastic bands method. The Ba atom was found to be stable above the center of the squares formed by the surface As atoms, and a diffusion barrier of 1.2 eV was found. Our simulated scanning tunneling microscopy image suggests an ordered surface Ba atom structure, in agreement with Massee et al (2009 Phys. Rev. B 80 140507; van Heumen E et al 2010 arXiv:1009.3493v1).

Static equation of state of bcc iron

Body-centered-cubic (bcc) iron is one of the most investigated solid-state systems. Using four different density-functional methods, we show that there is a magnetic transition close to the ground-state volume of bcc Fe, which originates from the particular magnetic band structure. The common equation of state functions, used to determine the basic ground-state physical quantities from the calculated total energies, cannot capture the physics of this magnetic transition leading to serious underestimation of the Fe bulk modulus. Ignorance of the magnetic transition found here is reflected by large scatter of the published theoretical bulk moduli of ferromagnetic bcc Fe. Due to the low performance of the exchange-correlation functionals, most of the erroneous results are accidentally in good agreement with the experimental values. The present finding is of fundamental importance, especially taking into account that bcc Fe is frequently used as a test system in assessing the performance of exchange-correlation approximations or total-energy methods.

Challenges with range-separated exchange-correlation functionals in time-dependent density functional theory calculations

The conventional approximate exchange-correlation functionals and kernels can lead to a large error in time-dependent density functional theory (TDDFT) calculations in certain cases, such as in the descriptions of charge-transfer excited states, Rydberg states, and double excitations, which can be remedied to some degree with the recently developed range-separated exchange-correlation functionals. How do these range-separated functionals perform in the TDDFT calculations? In this work, we explored the S0(A′) → T1(A′) and S0(A′) → S1(A′) transition energies of C2H4 and other molecules by TDDFT methods and ▵SCF calculations in density functional theory (DFT), with several regular and range-separated exchange-correlation functionals. We have found the following: (1) for the S0 → S1 transition, both range- and non-range-separated exchange-correlation functionals work well and consistently in the TDDFT calculations; (2) for the S0 → T1 transition, the used range-separated exchange-correlation functionals work on average worse than the non-separated ones in the TDDFT calculations; in the ▵SCF DFT calculations, however, both kinds of functionals achieve a similar performance. Because of the common approximations used in DFT and TDDFT, our present computational results suggest that the adiabatic approximation error in the range-separated exchange-correlation functionals is much larger than that in the non-range-separated ones for the S0 → T1 transition, and the adiabatic approximation error for the S0 → T1 transition – a spin-flip process – is larger than that for the S0 → S1 transition. These findings will be useful for designing better exchange-correlation functionals and kernels that will work well not only for excited singlet states, but also for excited triplet states. Furthermore, this study will provide insights into the drawbacks of the present approximate exchange-correlation functionals and kernels used in TDDFT calculations.

Rung 3.5 density functionals

This work proposes a new term on the "Jacob's ladder" of approximate exchange-correlation functionals in Kohn-Sham density functional theory. In these Rung 3.5 functionals, the exchange-correlation energy density at a point depends linearly (rather than quadratically) on the nonlocal Kohn-Sham one-particle density matrix in a finite neighborhood around the point. These functionals are intermediate in complexity between the semilocal approximations of Rungs 1-3, and fully nonlocal Rung 4 approximations such as global hybrids. Rung 3.5 functionals built on the model for exchange in [B. G. Janesko, J. Chem. Phys. 131, 234111 (2009)] predict molecular thermochemistry and kinetics with accuracy intermediate between their "parent" semilocal functional and the corresponding global hybrid. The best Rung 3.5 functional presented here gives mean absolute errors of 5.7 kcal/mol for G3/99 thermochemistry, 5.2 kcal/mol for HTBH38/04 hydrogen-transfer reaction barriers, and 5.7 kcal/mol for NHTBH38/04 nonhydrogen-transfer reaction barriers, while incorporating only two empirical parameters.

Ab initio calculations for properties of Ti 2AlN and Cr 2AlC

The electronic structure, dielectric function, Debye temperature and elastic properties of Ti 2AlN and Cr 2AlC were studied by means of pseudo-potential plane-waves method using the density function theory. The exchange-correlation approximation energy was determined by generalized gradient approximation method. The experimental lattice constants and the internal parameters were used in the calculation. The dielectric function was calculated by energy band theory, and the elastic constants were obtained using the static finite strain technique. The bulk and shear module, Young’s module and Poisson’s ratio for ideal polycrystalline Ti 2AlN and Cr 2AlC aggregates were derived in this paper. The Debye temperature of Ti 2AlN and Cr 2AlC from the average sound velocity was also estimated. The obtained results are in agreement with the available theoretical data.

Coupling quantum and continuum scales to predict crack tip dislocation nucleation

A quantum-continuum multiscale coupling of Kohn–Sham density functional theory to continuum material is presented that can handle mechanics problems in metals when long-range stress fields are present, such as occurs for dislocations and cracks. The method has quantifiable and controllable coupling errors that can be minimized at computationally tractable system sizes. Using both generalized gradient and local density approximation exchange–correlation functionals, the nucleation of a dislocation from a crack tip in aluminum is then predicted. Both functionals yield similar results, and predictions using Rice’s continuum Peierls model are within 20% of the quantum values. This multiscale method is easily extendable to crack-tip problems involving alloys and chemical embrittlements.

Incorporation of deMon2k as a new parallel quantum mechanical code for the PUPIL system

The PUPIL system is a combination of software and protocols for the systematic linkage and interoperation of molecular dynamics and quantum mechanics codes to perform QM/MD (sometimes called QM/MM) calculations. The Gaussian03 and Amber packages were added to the PUPIL suite recently. However, efficient parallel QM codes are critical because calculation of the QM forces is the overwhelming majority of the computational load. Here we report details of incorporation of the deMon2k density functional suite as a new parallel QM code. An additional motivation is to add a highly optimized, purely DFT code. We illustrate with a demonstration study of the influence of perchlorate as a dopant ion of the poly(3,4-ethylenedioxythiophene) conducting polymer in explicit acetonitrile solvent using Amber and deMon2k. We discuss unanticipated requirements for use of a scheme for semi-empirical correction of Kohn-Sham eigenvalues to give physically meaningful one-electron gap energies. We provide comparison of both geometric parameters and electronic properties for nondoped and doped systems. We also present results comparing deMon2k and Gaussian03 calculation of forces for a short sequence of steps. We discuss briefly some difficult problems of quantum zone SCF convergence for the anionically doped system. The difficulties seem to be caused by well-know deficiencies in simple approximate exchange-correlation functionals.

Using Nonempirical Semilocal Density Functionals and Empirical Dispersion Corrections to Model Dative Bonding in Substituted Boranes.

Dative bonds to substituted boranes represent a challenge for the approximate exchange-correlation functionals typically used in density functional theory (DFT). Accurately modeling these bonds with DFT has usually required highly parametrized functionals, large admixtures of exact exchange, or computationally expensive double hybrids. This work shows that the nonempirical semilocal PBEsol functional, and the nonempirical semilocal PBE and TPSS functionals augmented with empirical interatomic dispersion corrections, accurately treat several representative problems in dative bonding. These methods typically surpass the MPW1K "kinetics" global hybrid previously recommended for dative bonds. This work also provides additional insights into the accuracy of the parametrized M06 functionals and indicates some deficiencies of the B97-D functional relative to PBE-D and TPSS-D. Applications to frustrated Lewis pairs illustrate the potential of these methods.

Ab initio study on copper ferrite

The impact of cation distribution on electronic structure and magnetic properties is investigated by the first-principle calculation. The structure optimization is based on generalized gradient approximation (GGA) exchange-correlation and projector augmented wave method. The optimized structures of inverse and normal copper ferrite are tetragonal (c/a=1.06) and cubic, respectively. The optimized structure of partial inverse copper ferrites can be cubic, tetragonal, or triclinic depending on the distribution of copper ions. The calculation of electronic structure is based on full potential linear augmented plane wave method and GGA+U exchange-correlation. The calculated density of states shows that the distribution of Cu ions impacts the electronic structure significantly. The normal and inverse copper ferrite are half-metallic and semiconducting, respectively. The partial inverse copper ferrites are metallic or half-metallic.

Electronic structure and magnetic coupling in CaV2O5: spin dimer versus spin ladder

The electronic structure and magnetic exchange interactions of the ladder vanadate CaV2O5 have been studied by ab initio electronic structure calculations based on density functional theory (DFT). Geometry optimization and electronic structure calculations are performed using spin-polarized generalized gradient approximation (GGA) exchange-correlation functionals for four possible spin-ordered states. The experimentally observed insulating behavior has been reproduced successfully in the framework of the band theory by considering the magnetic ordering. Calculated results reveal that the true magnetic ground state of CaV2O5 is the antiferromagnetic (AFM) state with AFM exchange interactions both inside the rungs and along the ladder legs. Calculated exchange parameters indicate that the ladder structural vanadate CaV2O5 should be described as weakly coupled dimer system rather than as spin ladder compound. The AFM interactions inside the dimer are crucial to the insulating ground state and magnetic characteristics of CaV2O5.

Theoretical Study of the Hydrolysis of Pentameric Aluminum Complexes

Static quantum chemical calculations and Car−Parrinello molecular dynamics (CPMD) simulations were used to investigate the structural characteristics and the stability of pentameric aluminum clusters in both gas phase and aquatic environments. The accuracy of several generalized gradient approximation (GGA) and hybrid exchange-correlation functionals were tested with and without empirical van der Waals corrections to ensure the accuracy of the selected methods. Conformational analysis was performed for experimentally detected (electrospray ionization mass spectrometry, ESI MS) structural isomers of cationic [Al5O6H2Cl4]+, [Al5O7H4Cl4]+, [Al5O8H6Cl4]+, and [Al5O9H8Cl4]+ complexes. Conductor-like screening model (COSMO) was used to investigate the stability of the gas phase optimized structures in aquatic environments. Four of the main pentameric aluminum complexes were then selected for the CPMD investigation. The effect of the long-range empirical vdW corrections (-D) was also tested employing two identic...

Density functional theory study of the relative stability of the iron disulfide polymorphs pyrite and marcasite

The performance of density functional theory has been widely examined with regard to its ability to predict the properties of minerals, though less attention has been given to the correct determination of the relative stability of structurally similar polymorphs. Here a detailed examination is performed of the numerical and theoretical factors that may influence the structure and relative energetics of two such polymorphs of iron disulfide, namely, pyrite and marcasite, within density functional theory. Both the local-density approximation and commonly used generalized gradient approximation exchange-correlation functionals, such as Perdew, Burke and Ernzerhof (PBE), are found to predict that marcasite is more stable than pyrite, at variance with experiment. Allowing for the zero-point energy of vibration fails to remedy this discrepancy. While inclusion of a sufficiently large Hubbard $U$ parameter for iron is found to reverse the stability, this comes at the expense of a very poor description of other properties. Examination of three generalized gradient approximations developed specifically for the solid state, namely, AM05, Wu-Cohen and PBEsol, demonstrates that all of these functionals offer a superior description of the structures and relative energies of pyrite and marcasite through correctly predicting that the former is the ground-state phase at ambient conditions.

Equation of state of metallic hydrogen from coupled electron-ion Monte Carlo simulations

We present a study of hydrogen at pressures higher than molecular dissociation using the coupled electron-ion Monte Carlo method. These calculations use the accurate reptation quantum Monte Carlo method to estimate the electronic energy and pressure while doing a Monte Carlo simulation of the protons. In addition to presenting simulation results for the equation of state over a large region of the phase diagram, we report the free energy obtained by thermodynamic integration. We find very good agreement with density-functional theory based molecular-dynamics calculations for pressures beyond 600 GPa and densities above rho=1.4 g/cm(3) , both for thermodynamic and structural properties. This agreement provides a strong support to the different approximations employed in the density-functional treatment of the system, specifically the approximate exchange-correlation potential and the use of pseudopotentials for the range of densities considered. We find disagreement with chemical models, which suggests that a reinvestigation of planetary models--previously constructed using the Saumon-Chabrier-Van Horn equations of state--might be needed.

Effects of magnetism and electric field on the energy gap of bilayer graphene nanoflakes

We study the effect of magnetism and perpendicular external electric field strengths on the energy gap of length confined bilayer graphene nanoribbons (or nanoflakes) as a function of ribbon width and length using a first-principles density-functional electronic structure method and a semilocal exchange-correlation approximation. We assume $AB$ (Bernal) bilayer stacking and consider both armchair and zigzag edges, and for each edge type, we consider the two edge alignments, namely, $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ edge alignment. For the armchair nanoflakes we identify three distinct classes of bilayer energy gaps, determined by the number of carbon chains in the width direction ($N=3p$, $3p+1$ and $3p+2$, $p$ is an integer), and the gaps decrease with increasing width except for class $3p+2$ armchair nanoribbons. Metallic-like behavior seen in armchair bilayer nanoribbons are found to be absent in armchair nanoflakes. Class $3p+2$ armchair nanoflakes show significant length dependence. We find that the gaps decrease with the applied electric fields due to large intrinsic gap of the nanoflake. The existence of a critical gap with respect to the applied field, therefore, is not predicted by our calculations. Magnetism between the layers plays a major role in enhancing the gap values resulting from the geometrical confinement, hinting at an interplay of magnetism and geometrical confinement in finite size bilayer graphene.

Assessment of noncollinear spin-flip Tamm–Dancoff approximation time-dependent density-functional theory for the photochemical ring-opening of oxirane

Under the usual assumption of noninteracting v-representability, density-functional theory (DFT) together with time-dependent DFT (TDDFT) provide a formally exact single-reference method suitable for the theoretical description of the electronic excited-states of large molecules, and hence for the description of excited-state potential energy surfaces important for photochemistry. The quality of this single-reference description is limited in practice by the need to use approximate exchange-correlation functionals. In particular it is far from clear how well approximations used in contemporary practical TDDFT calculations can describe funnel regions such as avoided crossings and conical intersections. These regions typically involve biradical-like structures associated with bond breaking and conventional wisdom would seem to suggest the need to introduce explicit double excitation character to describe these structures. Although this is lacking in ordinary spin-preserving (SP) TDDFT, it is present to some extent in spin-flip (SF) TDDFT. We report our tests of Wang-Ziegler noncollinear SF-TDDFT within the Tamm-Dancoff approximation for describing the avoided crossing in the C(2v) CC ring-opening reaction of oxirane and for describing the conical intersection relevant for the more physical asymmetric CO ring-opening reaction of oxirane. Comparisons are made with complete active space self-consistent field and quantum Monte Carlo benchmark results from two previous papers on the subject [J. Chem. Phys., 2007, 127, 164111; ibid 129, 2008, 124108]. While the avoided crossing in the C(2v) pathway is found to be reasonably well described, the method was found to be only partially successful for the conical intersection (CX) associated with the physically more important asymmetric pathway. The origin of the difficulties preventing the noncollinear SF-TDDFT method from giving a completely satisfactory description of the CX was traced back to the inability of SF-TDDFT based upon a single triplet reference state to correlate all potentially relevant configurations involving not just two but three nearly degenerate orbitals (n, σ(CO), and σ(CO)(*)). This article is also the first report of our implementation of SF-TDDFT within the deMon2k program.