Local Exchange Approximation Research Articles

Leading Correction to the Local Density Approximation for Exchange in Large-Z Atoms.

The large-Z asymptotic expansion of atomic energies has been useful in determining exact conditions for corrections to the local density approximation in density functional theory. The correction for exchange is fit well with a leading ZlnZ term, and we find its coefficient numerically. The gradient expansion approximation also has such a term, but with a smaller coefficient. Analytic results in the limit of vanishing interaction with hydrogenic orbitals (a Bohr atom) lead to the conjecture that the coefficients are precisely 2.7 times larger than their gradient expansion counterparts, yielding an analytic expression for the exchange-energy correction which is accurate to ∼5% for all Z.

Validity of the static-exchange approximation for inner-shell photoionization of polyatomic molecules

Author(s): Marante, CA; Greenman, L; Trevisan, CS; Rescigno, TN; McCurdy, CW; Lucchese, RR | Abstract: The simple single-channel static-exchange approximation completely ignores correlation between the continuum and molecular ion electrons. In molecular systems with symmetry equivalent atoms, the single-channel approximation can seriously fail in core ionization when using delocalized orbitals to represent the core hole states. We present cross sections and molecular frame photoelectron angular distributions with both localized and delocalized core orbitals in CF4 F (1s) ionization. We show that only a full coupled-channel calculation can recover an accurate description of the physics of inner-shell photoionization when using delocalized orbitals, whereas nearly the same result can be obtained from independent single-channel static-exchange calculations when localized core orbitals are used. A grid-based variational method described here makes such single-channel calculations possible on larger systems without local-exchange approximations. Illustrative calculations on the core ionization of SF6 are presented to illustrate the power of the grid-based method.

Transition Metal Spin-State Energetics by MC-PDFT with High Local Exchange.

The energetics of the spin states of transition metal complexes have been explored with a variety of electronic structure methods, but the calculations require a compromise between accuracy and affordability. In this work, the spin splittings of several iron complexes are studied with multiconfiguration pair-density functional theory (MC-PDFT). The results are compared to previously published results obtained by complete active space second-order perturbation theory (CASPT2) and CASPT2 with coupled-cluster semicore correlation (CASPT2/CC). In contrast to CASPT2's systematic overstabilization of high-spin states with respect to the CASPT2/CC reference, MC-PDFT with the tPBE on-top functional understabilizes high-spin states. This systematic understabilization is largely corrected by revising the exchange and correlation contributions to the on-top functional using the high local-exchange approximation (tPBE-HLE). Moreover, tPBE-HLE correctly predicts the spin of the ground state in most cases, while CASPT2 incorrectly predicts high-spin ground states in all cases. This is encouraging for practical work because tPBE and tPBE-HLE are faster than CASPT2 by a factor of 50 even in a moderately sized example.

Distortion and electric-field control of the band structure of silicene

Density functional theory with local density approximation for exchange and correlation functional is used to tune the electronic band structure of silicene monolayer. The cohesive energy of the free-standing monolayer increases (decreases) with the external electric field (distortion). Electrons in silicene behave like Dirac fermions, when the bond angle between the Si atoms is larger than . Large distortions destroy the electronic structure of silicene so that it is no longer a semi-metallic material, and the distorted silicene acts like an n-doped system. The electric field opens a band gap around the K-point in the Brillouin zone, which increases with electric field. The bond angle between the Si atoms is a key player to determine the presence or absence of Dirac cones in silicene.

Wide-range photoabsorption cross-sections of simple metals: large basis-set OPW calculations for sodium

Photoabsorption cross-sections of simple metals are formulated through a solid-state band theory based on the orthogonalized-plane-wave (OPW) method in Slater’s local-exchange approximation, where interband transitions of core and conduction electrons are evaluated up to the soft x-ray regime by using large basis sets. The photoabsorption cross-sections of a sodium crystal are computed for a wide photon energy range from 3 to 1800 eV. It is found that the numerical results reproduce the existing x-ray databases fairly well for energies above the L2,3-edge (31 eV), verifying a consistency between solid-state and atomic models for inner-shell photoabsorption; additional oscillatory structures in the present spectra manifest solid-state effects. Our computed results in the vacuum ultraviolet regime (6–30 eV) are also in better agreement with experimental data compared to earlier theories, although some discrepancies remain in the range of 20–30 eV. The influence of the core eigenvalues on the absorption spectra is examined.

First-principles investigation of the thermo-physical properties of Ca3Si4

The first-principles calculations were applied to investigate the thermo-physical properties of Ca3Si4 compound with increasing pressure. Those properties are based on density functional theory (DFT) method within the generalized gradient approximation (GGA) and local density approximation (LDA) for exchange and correlation. The optimized lattice constant and formation enthalpy are in good agreement with the experimental data and other theoretical data available. The calculated band structures confirm that Ca3Si4 is a semiconductor with an indirect band gap of 0.363eV (GGA) and 0.311eV (LDA) at 0GPa, and the calculated band gap decreased with the increasing pressure. The elastic constants, elastic anisotropy, elastic moduli and Poisson's ratio of Ca3Si4 have also been obtained under high pressures. The Debye temperature, heat capacity, coefficient of thermal expansion and Grüneisen parameter have also been calculated in the quasiharmonic Debye model.

Benchmark results for empirical post-GGA functionals: Difficult exchange problems and independent tests

Many of the most promising new density functionals have improved the treatment of non-local exchange effects with the help of semi-empirical information and more sophisticated recipes for combining Hartree-Fock and local exchange approximations. In order to quantify recent advancements and identify directions for improvement, we have examined a broad spectrum of test problems. We evaluate the performance of several new hybrid density functionals (ωB97, ωB97X, ωB97X-D, LRC-ωPBEh, M06, M06-2X, and M06-HF) on a variety of chemical problems, some sensitive to the treatment of exact exchange (which we have hoped to systematically improve) and some which require a balanced treatment of correlation. Since all of the functionals under consideration are parameterized with ground-state thermochemical data, the benchmark aims to determine the applicability of the new density functionals to cases that have not been considered in the optimization of the semi-empirical parameters. The first class of benchmarks includes the excitation energies of 21 molecules (83 states) primarily from a recent benchmark conducted by Tozer and co-workers, with some additional references from data made available from the groups of Thiel and Truhlar. We briefly examine the conformational preferences of a small peptide and complete our study with two recently published sets of data that have shown large, systematic errors in simple alkane thermochemistry. While our results indicate that the more general hybrids currently under development perform well for problems outside of their parameterization and improve over the standard hybrid density functionals in an essentially systematic way, there is still a significant self-interaction error in the more difficult cases. Functionals based on a range-separation of exchange and functionals depending on the kinetic-energy density both perform comparably, and there is evidence for complementary strengths.

Aluminum SCOPW energy band dependence upon the local exchange approximation

The dependence of the energy bands of aluminum upon the parameter α in the Slater exchange is shown using the self-consistent orthogonalized plane wave (SCOPW) method. Two fully self-consistent calculations at different α's were performed. These calculations indicate that an a less than 1 should be chosen to obtain agreement with previous work.

Local density exchange approximations versus hartree-fock for ground-state calculations

Crystalline x-ray structure factors are presented for C (diamond) which have been calculated using the local density approximation and an LCAO-plane wave mixed basis. They are compared to both experimental and crystalline Hartree-Fock calculated values.

Theoretical study of the structural, elastic and electronic properties of the GeX2O4 (X = Mg, Zn, Cd) compounds under pressure

The effect of high pressures, up to 30 GPa, on the structural, elastic and electronic properties of GeX2O4, with X = Mg, Zn and Cd, were studied by means of the pseudo-potential plane waves method within the local density approximation for exchange and correlation. The results of bulk properties, including lattice constants, internal parameters, bulk modulus and derivatives are obtained. The band structures show a direct (Γ–Γ) band gap for the three compounds. All the calculated band gaps increase with increasing pressure and fit well to a quadratic function. The analysis of the density of states revealed that the lowering of the direct gap Γ–Γ from GeMg2O4 to GeZn2O4 to GeCd2O4 can be attributed to the p–d mixing in the upper valence band of GeZn2O4 and GeCd2O4. The elastic constants and their pressure dependence are calculated using the static finite strain technique. We have observed a linear dependence of the elastic moduli on the pressure. We derived the bulk modulus, shear modulus, Young's modulus and Poisson's ratio for ideal polycrystalline GeX2O3 aggregates. We estimated the Debye temperature of GeX2O4 from the average sound velocity.

Density functional study of the structural and electronic properties of aluminium-lithium clusters

The reactivity between lithium and the Al$_{13}$ cluster is studied using the density functional theory and the local density approximation (LDA) for exchange and correlation. The effects caused by the addition of two Li atoms on the structural and electronic properties of the Al cluster are analyzed by calculating equilibrium geometries, binding energies and ionization potentials. The corresponding positively and negatively charged species are also studied. The influence of the alkali atoms on the geometrical structure of the cluster is small, but the influence on the electronic structure is much larger. The cluster Al$_{13}$Li, with 40 valence electrons, has closed electronic shells and Al$_{13}$Li$_{2}$ has a single electron in the next shell. A striking result is the large drop of the ionization potential of the cluster induced by the addition of the second Li atom. These properties have been related to the changes of the electronic density by the analysis of density difference maps and atomic Hirshfeld charges. The photoabsorption spectrum has been calculated using the time-dependent version of the density functional theory.

Electronic and magnetic properties and chemical bonding ofCeMSn(M=Rh,Ru)from first principles

The electronic structures of CeRhSn and CeRuSn are self-consistently calculated within density functional theory using the local spin density approximation for exchange and correlation. In agreement with experimental findings, the analyses of the electronic structures and of the chemical bonding properties point to the absence of magnetization within the mixed-valent Rh-based system, while a finite magnetic moment is observed for trivalent cerium within the Ru-based stannide, which contains both trivalent and intermediate-valent Ce.

Effect of pressure on the magneto-optical properties of bcc and bct iron

We have studied the effect of pressure on the electronic structure of bcc and bct iron within the local spin density approximation (LSDA) for the electronic exchange and correlation. We report calculations of the magneto-optical properties of ferromagnetic iron in the bcc and bct phases using the full potential linearized augmented plane wave (FPLAPW) method as implemented in the WIEN2K code. In both phases, we find two prominent minima in Kerr rotation. In bcc phase, both the calculated Kerr minima shift towards higher energies with increase in pressure while in bct phase, the low energy minimum in Kerr rotation spectra ∼2 eV becomes less pronounced and the minimum at ∼7 eV moves towards higher energies on increasing pressure.

Semiempirical van der Waals correction to the density functional description of solids and molecular structures

The influence of a simple semiempirical van der Waals (vdW) correction on the description of dispersive, covalent, and ionic bonds within density functional theory is studied. The correction is based on the asymptotic London form of dispersive forces and a damping function for each pair of atoms. It thus depends solely on the properties of the two atoms irrespective of their environment and is numerically very efficient. The correction is tested in comparison with results obtained using the generalized gradient approximation or the local density approximation for exchange and correlation. The results are also compared with reference values from experiment or quantum chemistry methods. In order to probe the universality and transferability of the semiempirical vdW correction, a range of solids and molecular systems with covalent, heteropolar, and vdW bonds are studied.

Noncollinear magnetic order in the six-atom Mn cluster

We report ab initio calculations of the structures, binding energies, and magnetic moments of the lowest-energy isomers of the cluster Mn6 that were performed using SIESTA, a density-functional method that employs linear combinations of pseudoatomic orbitals as basis sets, nonlocal norm-conserving pseudopotentials, and the local spin-density approximation for exchange and correlation. Our results predict that ground-state Mn6 has a noncollinear magnetic configuration.

Ab initio calculations for the photoelectron spectra of vanadium clusters.

We report ab initio calculations for the electronic and structural properties of V(n), V(n) (-), and V(n) (+) clusters up to n=8. We performed the calculations using a real-space pseudopotential method based on the local spin density approximation for exchange and correlation. This method assumes no explicit basis. Wave functions are evaluated on a uniform grid; only one parameter, the grid spacing, is used to control convergence of the electronic properties. Charged states are easily handled in real space, in contrast to methods based on supercells where Coulombic divergences require special handling. For each size and charge state, we find the lowest energy structure. Our results for the photoelectron spectra, using the optimized structure, agree well with those obtained by experiment. We also obtain satisfactory agreement with the measured ionization potential and electron affinity, and compare our results to calculations using an explicit basis.

Electron correlation effects on SiC(111) and SiC(0001) surfaces

The possibility is discussed that, independent of the polytype, large electronic correlationeffects give rise to semiconducting SiC surfaces with [111] or [0001] orientations. The mostimportant surface translational symmetries and 3 × 3 are considered. The discussion is based on the detailed knowledge of the surfaceatomic geometries and the electronic structures derived for these geometries usinga local density approximation for exchange and correlation. It is argued thatthe resulting half-filled, weakly dispersive dangling-bond bands within thefundamental gaps are split according to a Hubbard interaction parameterU, and that the surface systems undergo a Mott–Hubbard transition. Such a physical pictureprovides a qualitatively correct account of the single-particle excitation spectra eitherinferred from angle-resolved photoemission and inverse photoemission experiments orobtained from scanning tunnelling spectroscopy. The gap opening and hence the HubbardU parameter are discussed in terms of their dependence on the surface reconstruction as wellas the SiC polytype.

Meta-generalized gradient approximation: explanation of a realistic nonempirical density functional.

Tao, Perdew, Staroverov, and Scuseria (TPSS) have constructed a nonempirical meta-generalized gradient approximation (meta-GGA) [Phys. Rev. Lett. 91, 146401 (2003)] for the exchange-correlation energy, imposing exact constraints relevant to the paradigm densities of condensed matter physics and quantum chemistry. Results of their extensive tests on molecules, solids, and solid surfaces are encouraging, suggesting that this density functional achieves uniform accuracy for diverse properties and systems. In the present work, this functional is explained and details of its construction are presented. In particular, the functional is constructed to yield accurate energies under uniform coordinate scaling to the low-density or strong-interaction limit. Its nonlocality is displayed by plotting the factor F(xc) that gives the enhancement relative to the local density approximation for exchange. We also discuss an apparently harmless order-of-limits problem in the meta-GGA. The performance of this functional is investigated for exchange and correlation energies and shell-removal energies of atoms and ions. Non-self-consistent molecular atomization energies and bond lengths of the TPSS meta-GGA, calculated with GGA orbitals and densities, agree well with those calculated self-consistently. We suggest that satisfaction of additional exact constraints on higher rungs of a ladder of density functional approximations can lead to further progress.

Accuracy of local exchange in the calculation of continuum wavefunctions

It is well known that electron exchange can play an important role inelectron-impact elastic, inelastic and ionization scattering from atoms andmolecules. The proper theoretical treatment of exchange yields an inhomogeneousdifferential equation with a non-local exchange operator. To simplify thecalculation, a local approximation is often made for this non-local operator. Inthis paper, we examine the accuracy of this approximation for the calculation ofelastic scattering continuum waves in the presence of an argon ion with asingle vacancy in the p-shell. It is found that one can reliably use the localexchange approximation for ionization leading to s-state vacancies but notp-state vacancies.

Localized non-orthogonal orbitals in silicon

A comparison of orthogonal and non-orthogonal localized wavefunctions for Si in the diamond structure is carried out. We have used a real-space grid formulation of density functional theory in combination with the local density approximation for exchange and correlation to describe the energetics. Maximally localized wavefunctions, obtained from the extended Kohn-Sham states with and without an orthogonality constraint, are calculated and it is found that the wavefunctions calculated without any orthogonality constraint are the most localized. When solving directly for localized states, by applying a localization constraint to each electronic state, we find that there is a large difference between orthogonal and non-orthogonal states: when the localization region is a sphere with a radius of 3.0 Å, we get an error in the total energy due to the localization constraint of 0.2 and 2.7 eV/atom for non-orthogonal and orthogonal wavefunctions respectively.