Gradient Approximation For Exchange Research Articles

Local hybrid functionals: An assessment for thermochemical kinetics

Local hybrid functionals with position-dependent exact-exchange admixture are a new class of exchange-correlation functionals in density functional theory that promise to advance the available accuracy in many areas of application. Local hybrids with different local mixing functions (LMFs) governing the position dependence are validated for the heats of formation of the extended G3/99 set, and for two sets of barriers of hydrogen-transfer and heavy-atom transfer reactions (HTBH38 and NHTBH38 databases). A simple local hybrid Lh-SVWN with only Slater and exact exchange plus local correlation and a one-parameter LMF, g(r)=b(tau(W)(r)tau(r)), performs best and provides overall mean absolute errors for thermochemistry and kinetics that are a significant improvement over standard state-of-the-art global hybrid functionals. In particular, this local hybrid functional does not suffer from the systematic deterioration that standard functionals exhibit for larger molecules. In contrast, local hybrids based on generalized gradient approximation exchange tend to give rise to nonintuitive LMFs, and no improved functionals have been obtained along this route. The LMF is a real-space function and thus can be analyzed in detail. We use, in particular, graphical analyses to rationalize the performance of different local hybrids for thermochemistry and reaction barriers.

Elastic properties of MgCNi 3 —a superconducting perovskite

The cohesive and elastic properties of the non-oxide perovskite type superconductor MgCNi 3 are calculated using the full-potential linear muffin-tin orbital method with the local density approximation as well as the generalized gradient approximation for exchange and correlation. The calculated equation of state and ground state properties (equilibrium lattice constant, bulk modulus and its pressure derivative) agree well with recent experiments. From the elastic constants the Young’s modulus, shear modulus, Poisson’s ratio, sound velocities and Debye temperature are obtained. By analysing the ratio between bulk modulus and shear modulus we conclude that MgCNi3 is intermediate between brittle and ductile in nature.

An experimental and theoretical study into the valence electronic structure of bicyclo[2.2.1]hepta-2,5-dione

The results from an electron momentum spectroscopy (EMS) study of the outer valence electronic region of bicyclo[2.2.1]hepta-2,5-dione (C7H8O2) are reported for the first time. The measured binding energy spectra are presented for the azimuthal angles 0°, 10° and 0° + 10°, respectively, and are compared to new He(I) photoelectron spectroscopy results, which are measured as a part of this work. These experimental data are compared further with results from theoretical computations, using various methods including Hartree–Fock, density functional and an outer valence Green's function theory. Measured orbital momentum distributions are compared on an orbital by orbital basis against those obtained by calculations which employ the plane-wave impulse approximation. These calculations use orbital wavefunctions obtained from Hartree–Fock and density functional theory with a couple of generalized gradient approximation exchange correlation (XC) functionals and the DGauss triple zeta valence polarization basis set. Agreement between the measured and calculated momentum distributions was found to be only fair. Nonetheless, the orbital momentum distributions of the molecule still provide an orbital based assessment of the XC functionals of the density functional theory employed, and an understanding of the chemical bonding mechanisms within the species. Finally, the spectroscopic strengths calculated using outer valence Green's function theory are compared against those derived from our EMS measurements.

A density-functional study of the structures, binding energies and total spins of Ni–Fe clusters using nonlocal norm-conserving pseudopotentials and the generalized gradient approximation

We report ab initio calculations of the structures, binding energies, and total spins of the clusters Ni(13), Ni(19), Ni(23), Ni(26), Ni(12)Fe, Ni(11)Fe(2), Ni(18)Fe, Ni(17)Fe(2), Ni(22)Fe, Ni(20)Fe(3), and Ni(25)Fe using a density-functional method that employs linear combination of atomic orbitals as basis sets, nonlocal norm-conserving pseudopotentials, and the generalized gradient approximation for exchange and correlation. Our results show that the Fe-doped Ni clusters, which have icosahedral or polyicosahedral ground-state structures similar to those of the corresponding pure Ni clusters, are most stable with the Fe atoms occupying internal positions, as has also been inferred from experimental results on the adsorption of molecular nitrogen on the cluster surfaces. We also rule out the possibility that the experimentally observed difference between the (nonpolyicosahedral) configurations of N(2)-saturated Ni(26) and N(2)-saturated Ni(25)Fe be due to the influence of the Fe atom on the energy of the underlying metal cluster.

Long-range and short-range Coulomb correlation effects as simulated by Hartree-Fock, local density approximation, and generalized gradient approximation exchange functionals

Exchange functionals used in density functional theory (DFT) are generally considered to simulate long-range electron correlation effects. It is shown that these effects can be traced back to the self-interaction error (SIE) of approximate exchange functionals. An analysis of the SIE with the help of the exchange hole reveals that both short-range (dynamic) and long-range (nondynamic) electron correlation effects are simulated by DFT exchange where the local density approximation (LDA) accounts for stronger effects than the generalized gradient expansion (GGA). This is a result of the fact that the GGA exchange hole describes the exact exchange hole close to the reference electron more accurately than the LDA hole does. The LDA hole is more diffuse, thus leading to an underestimation of exchange and stronger SIE effects, where the magnitude of the SIE energy is primarily due to the contribution of the core orbitals. The GGA exchange hole is more compact, which leads to an exaggeration of exchange in the bond and the nonbonding region and negative SIE contributions. Partitioning of the SIE into intra-/interelectronic and individual orbital contributions makes it possible to test the performance of a given exchange functional in different regions of the molecule. It is shown that Hartree–Fock exchange always covers some long-range effects via interelectronic exchange while self-interaction-corrected DFT is lacking these effects.