Density Gradient Corrections Research Articles

Theoretical foundations of quantum hydrodynamics for plasmas

Quantum hydrodynamics (QHD) theory for finite temperature plasmas is consistently derived in the framework of the local density approximation of the free energy with first order density gradient correction. Previously known results are revised and improved with a clear description of the underlying approximations. A fully non-local Bohm potential, which goes beyond all previous results and is linked to the electron polarization function in the random phase approximation, for the QHD model is presented. The dynamic QHD exchange correlation potential is introduced in the framework of local field corrections and considered for the case of the relaxation time approximation. Finally, the range of applicability of the QHD is discussed.

Gradient correction and Bohm potential for two‐ and one‐dimensional electron gases at a finite temperature

From the static polarization function of electrons in the random phase approximation, the quantum Bohm potential for the quantum hydrodynamic description of electrons and the density gradient correction to the Thomas–Fermi free energy at a finite temperature for the two‐ and one‐dimensional cases are derived. The behaviour of the Bohm potential and of the density gradient correction as a function of the degeneracy parameter is discussed. Based on recent developments in the fluid description of quantum plasmas, the Bohm potential for the high‐frequency domain is presented.

Why are GGAs so accurate for reaction kinetics on surfaces? Systematic comparison of hybrid vs. nonhybrid DFT for representative reactions.

"Jacob's Ladder" of approximate exchange-correlation (XC) functionals in Kohn-Sham density functional theory are widely accepted to have systematic errors in reaction barriers. The first-rung local spin-density approximation (LDA) typically predicts barriers below generalized gradient approximations, which in turn predict barriers below experiment and below fourth-rung hybrid functionals incorporating a fraction of exact exchange. We show that several reactions from previous literature reports, as well as new simulations of carbon-carbon coupling in the Fischer-Tropsch process, do not follow this conventional picture. We introduce the AB9 test set of nine abnormal reaction barriers, in which density gradient corrections and exact exchange admixture tend to lower rather than to raise predicted barriers. Comparisons of normal and abnormal reactions rationalize this phenomenon in terms of how density gradient and exact-exchange corrections stabilize transition states relative to reaction intermediates. Multireference diagnostics confirm that this behavior is not merely a consequence of multireference character. Benchmarks of the AB9 set, using the best available ab initio reference values, highlight the role of symmetry breaking and show surprisingly good performance from both the LDA and "Rung 3.5" functionals. This motivates benchmarks of the AB9 set in future XC functional development.

A Mathematical Model of the Global Ocean Saltwater Density Distribution

We formulate a functional model which closely approximates the actual seawater density distribution. The meth- odology of finding a theoretical density model is based on the analysis of the global data of pressure/depth, salinity, and tem- perature from the World Ocean Atlas 2009 (provided by NOAA's National Oceanographic Data Center) and the World Ocean Cir- culation Experiment 2004 (provided by the German Federal Maritime and Hydrographic Agency). The seawater density values are calculated according to the thermodynamic equation of sea- water TEOS-10. The global seawater density model is defined as a function of the ocean depth (to account for density variations due to pressure) and geographical latitude (to account for density varia- tions due to salinity and temperature). A more complex functional density model is formulated to account for a large seawater density gradient within the pycnocline caused mainly by a combination of decreasing water temperature and increasing salinity with depth. The results of numerical analysis reveal that the new functional model based on the depth and latitudinal density variations approximates the actual seawater density distribution with a rela- tive accuracy better than 0.45%. When incorporating the pycnocline density gradient correction, the accuracy further improves to about 0.25% (except for the shelf seas with the pres- ence of the continental hydrological signal and other oceanographic factors). The results also show that the average seawater density (estimated from the experimental data used in this study) is 1038.5 ± 2.4 kg/m 3 .

Evaluating the electronic energy eigenvalues for A2B6 crystals obtained with the GGGA+U functional

AbstractElectronic energy bands of ZnS, ZnSe, and ZnTe crystals evaluated within the mixed basis approach with using the core Bloch states and plane waves. The exchange‐correlation potential has been derived from the new exchange‐correlation‐energy functional including the density gradient corrections and the intra‐atomic Coulomb term U. The calculated energy band structure parameters of the crystals show an improvement compared with the LDA results. The semicore Zn 3d state energies are closer to experimental data than those obtained within the LDA approach. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Kinetic energy functional for a two-dimensional electron system

The noninteracting, nonuniform electron gas exhibits simplifications in two dimensions that are of particular interest in the application of density functional theory. The results of linear response theory for an attractive impurity in a two-dimensional gas have been shown to be surprisingly accurate even though there are bound states and are shown to be exact in the high density limit. We offer the alternative view that these results depend not so much on the properties of linear response but on a special feature of all density response functions in two dimensions. This feature leads to the result that all density gradient corrections to the Thomas-Fermi result for the electron kinetic energy functional vanish in two dimensions at zero temperature. This is not to say that the Thomas-Fermi result is exact, but numerical calculations show that it is a very good approximation for an attractive potential even in a low density gas.

Gradient expansions in density functional calculations of intermolecular potentials

Methods for calculations of intermolecular potentials following the local density approximation (LDA) have earlier been considered, especially for inert gas atom – inert gas atom interactions using the so-called electron gas density functional (EGDF) model. In this Letter some density gradient corrections are discussed and new results are presented. The general conclusion based on the results in the present report seems to be that the EGDF method gives surprisingly good numerical results in the LDA limit for calculations of intermolecular potentials. Corrections due to density gradients contribute only small changes in the sum of the density functional terms considered for the total energy in the EGDF method, but they contribute important corrections to the kinetic energy and to the exchange energy separately.

Traversal times and charge confinement for spatially dependent effective masses within semiconductor heterostructures: the quantum potential approach

The classical traversal time is a well-defined functional of the carrier trajectory and in graded heterostructures acquires significant corrections due to the position-dependent effective mass. The quantum potential corrections for pure states and the corrections to quantum Monte Carlo for mixed states are derived using the Wigner formalism. Application to graded SiGe shows additional transport corrections, including enhanced charge confinement, which are of the same order as the conventional constant mass density gradient corrections.

Quantum Potential Corrections for Spatially Dependent Effective Masses with Application to Charge Confinement at Heterostructure Interfaces

The effect of a spatially varying effective mass as encountered in heterostructure devices is shown to lead to classical and quantum corrections to the description of transport. The quantum potential corrections for pure states and the corrections to Quantum Monte Carlo for mixed states are derived using the Wigner formalism. The application to SiGe graded structures is shown to lead to additional corrections, which are of the same order as the conventional density gradient corrections.

Density-functional study of intramolecular ferromagnetic interaction through m-phenylene coupling unit (II): Examination of functional dependence

As a first step toward examination of ferromagnetic polymers and dendrimers by ab initio crystal orbital methods, we elucidated candidates for monomer units with the high-spin ground states in the previous study of Part I [J. Chem. Phys. 113, 4035 (2000)] by employing density-functional (DFT) methods using Becke’s and Becke’s three parameter exchanges with Lee–Yang–Parr correlation or Hartree–Fock (HF) molecular orbital and post HF approximations. However, it was found that further computations applying other DFT functionals should be carried out to clarify the level of approximations which appropriately describe the electronic structures of magnetic molecules. In this part II, we present details of numerical results concerning magnetic properties and electronic structures for m-phenylene molecules with three neutral and one cation radicals by spin-polarized density functional methods using variety of local and nonlocal functionals and unrestricted molecular orbital methods including Mo/ller–Plesset and coupled-cluster (CC) correlation corrections. The dependence of total, exchange and correlation energies, and spin densities on various approximated functionals is investigated thoroughly. The effective exchange integrals in the Heisenberg model are calculated by local and nonlocal DFT methods, and they are compared with those of complete active space (CAS) CI, CASSCF, and CASPT2. It is concluded that nonlocal DFT with density-gradient corrections can be used as a practical alternative to UCCSD(T) and CASPT2. The broken-symmetry Unrestricted Hartree–Fock (UHF) and DFT calculations of m-phenylene polyradicals with polar substituents are carried out to elucidate roles of superexchange interactions arising from the significant mixing of charge-transfer (CT) configurations. The resonance of covalent structures with CT or zwitterionic structures entails antiferromagnetic exchange interactions even in polyradicals with m-phenylene bridges; for example, substituted nitroxide polyradicals. Stable ferromagnetic polymers and dendrimers are designed on the basis of the theoretical grounds.

Adhesion energy of Cu atoms on the MgO(001) surface

We have studied theoretically the interaction of an isolated Cu atom adsorbed on the oxygen sites of the regular MgO (001) surface with the aim of providing an accurate estimate of the adhesion energy. We performed cluster model calculations using a variety of first principles quantum-chemical approaches; local (spin) density approximation [L(S)DA], density functionals that include density gradient corrections (GC-DF), hybrid density functional (B3LYP), and explicitly correlated wave functions. Various combinations of exchange-correlation functionals and different methods to introduce electron correlation, including MP2 and CCSD(T), have been considered. The dependence of the results on cluster and basis set size has been carefully checked. We found that the hybrid DF method, B3LYP, and explicitly correlated wave functions, CCSD(T), give similar results with an adhesion energy of about 0.40±0.05 eV; GC-DF methods suggest a higher binding energy of 0.6 eV. Therefore, Cu atoms can be considered to bind to oxygen centers of the ideal MgO (001) surface in a relatively weak chemical fashion, in broad agreement with the low sticking coefficient measured experimentally.

Identification of charge states of indium vacancies in InP using the positron-electron auto-correlation function

The positron-electron auto-correlation function (ACF) is calculated for neutral and negatively charged indium vacancies in InP as well as a perfect InP material. Ab initio calculations are performed for the electron wave functions in the density functional theory (DFT) with the local density approximation (LDA) for the exchange-correlation potential of electrons. The positron wave function is calculated by directly diagonalizing the single-particle Hamiltonian of the positron in the LDA with a density-gradient correction. It is found that the ACF is suitable for identifying the charge states of the indium vacancies. Neutral indium vacancies greatly diminish the nearest peaks and dips (P1 and D1) of the ACF which are located after the nearest-neighbouring lattice points in the case of a perfect material. Negatively charged indium vacancies nearly eliminate these peaks and dips, together with the next-nearest peaks (P2) located at the next-nearest-neighbouring lattice points. Therefore, the diminution of the P1 and D1 can be taken as an indication of the formation of neutral indium vacancies, and that of the P2 can be taken as an indication of the formation of negatively charged indium vacancies. However, the three negative charge states of the indium vacancies ( and ) are still difficult to distinguish from each other by means of the ACF method.

Relevance of relativistic exchange-correlation functionals and of finite nuclei in molecular density-functional calculations

Two types of relativistic corrections in molecular electronic structure calculations that are based on the Kohn-Sham approach to density-functional theory have been studied: (1) relativistic corrections to the exchange-correlation functional, both in the local density and in the generalized gradient approximation; (2) a description of the nuclear charge distribution that avoids the Coulomb singularity. The diatomics AuH, AuCl, ${\mathrm{Au}}_{2}$, ${\mathrm{Ag}}_{2}$, and ${\mathrm{Cu}}_{2}$ were chosen as examples. Although significant effects on the total energy and on core-level energies are found, only the relativistic correction to local-density approximation has a noticeable impact on molecular observables: it induces changes of bond lengths by up to 0.005 \AA{}, of vibrational frequencies by up to 10 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, and of binding energies by up to 0.05 eV. Thus, taken together, the relativistic corrections discussed here are much smaller than those obtained with density-gradient corrections to the exchange-correlation functional. Therefore, the common practice to neglect these relativistic corrections in molecular density-functional calculations is justified, at least for compounds without superheavy elements. \textcopyright{} 1996 The American Physical Society.

The zero-order regular approximation for relativistic effects: The effect of spin–orbit coupling in closed shell molecules

In this paper we will calculate the effect of spin–orbit coupling on properties of closed shell molecules, using the zero-order regular approximation to the Dirac equation. Results are obtained using density functionals including density gradient corrections. Close agreement with experiment is obtained for the calculated molecular properties of a number of heavy element diatomic molecules.

The effect of density-gradient corrections for a molecule-surface potential energy surface. Slab calculations on Cu(100)c(2x2)-CO

We have performed slab calculations on the periodic adsorption, with a coverage θ = 0.5, of CO on the Cu(100) surface. Using nonlocal corrections to the local density approximation (LDA), the calculated chemisorption energy is 0.7 eV, and the top site slightly preferred over the hollow site. These results are in substantially better agreement with the experiment than the LDA results. The structure and vibrational frequencies are not much influenced.

A modified Thomas-Fermi treatment of nuclei

An improved nuclear Thomas-Fermi theory is studied in which, rather than adding density-gradient corrections to the standard expression for the kinetic energy density (proportional to ϱ 5 3 , where ϱ is the density) one simply modifies this ϱ 5 3 function to reflect the fact that the kinetic energy density becomes negative for small values of ϱ when, in a typical nuclear problem, one is dealing with the outer fringes of the surface region. The net result of this study is simply stated: in order to find the density associated with a given nuclear potential, one exponentiates this potential instead of raising its depth with respect to the chemical potential to the three-halves power, as in the standard treatment. An improved description of the nuclear surface profile is obtained, including the quantal halo in the classically forbidden region. But since density derivatives are not involved, there is no need to solve a partial differential equation in order to find the density.

Dissociation of doubly charged alkali metal clusters

We have studied the competition experimentally observed between fission and neutral atom evaporation, as dissociation channels of excited doubly charged sodium clusters, using the Density Functional Theory and the jellium model. The fission barrier has been obtained from an Extended Thomas-Fermi calculation including density gradient corrections to the kinetic energy of the electronic cloud. We discuss the influence of the coefficient of the density gradient term on the barrier height.

Exchange and exchange-correlation functionals based on the gradient correction of the electron gas.

We demonstrate that the functional form of the Pad\'e approximant of the second-order density gradient correction of Rasolt and Geldart [Phys. Rev. Lett. 35, 1234 (1975)] for the inhomogeneous electron gas yields excellent results when applied to atoms. The gradient correction employed by us uses the 10/7 factor as suggested by Kleinman and Lee [Phys. Rev. B 37, 4634 (1988)] with the constants of Rasolt and Geldart replaced by an empirically derived set, based upon numerical fits of the exchange and exchange-correlation energies of the atoms He through Ar. The resulting fitted nonlocal gradient corrections were then used in the minimization of the Kohn-Sham functional to solve for the exchange-only and exchange-correlation total energies. The resulting standard deviations in the calculated total energies were 0.0043 for exchange only and 0.0014 for exchange correlation.

Representation of lowest-order density-gradient correction to kinetic energy in light molecules at equilibrium.

For ${\mathrm{N}}_{2}$, ${\mathrm{O}}_{2}$, and ${\mathrm{F}}_{2}$ homonuclear molecules, for six neutral diatomic molecules of the form XH, where X ranges from Be to F, and for the isoelectronic series HF, ${\mathrm{H}}_{2}$O, ${\mathrm{NH}}_{3}$, and ${\mathrm{CH}}_{4}$, it is shown that a substantial part of the accurate numerical calculations reported by Allan et al. [J. Chem. Phys. 83, 4562 (1985)] and by Lee and Ghosh [Phys. Rev. A 33, 3506 (1986)] can be interpreted in terms of basic scaling laws.

Density Functional Approach to the Surface Tension of Liquid Metals

AbstractThe local density functional formalism of Evans and Hasegawa, previously developed for the study of surface properties, is re‐examined by including nonlocality of pseudopotential in the theory. It is found that (i) when the pseudopotential is nonlocal, the fourth order density gradient correction of Ma and Sahni must be included in order that the density profiles obtained are physically meaningful and (ii) the first order perturbation is inadequate for understanding the surface tension of simple liquid metalsin accordance with conclusions made by other investigators.