Application of A Distributed Nucleus Approximation In Grid Based Minimization of the Kohn-Sham Energy Functional

In the distributed nucleus approximation we represent the singular nucleus as smeared over a smallportion of a Cartesian grid. Delocalizing the nucleus allows us to solve the Poisson equation for theoverall electrostatic potential using a linear scaling multigrid algorithm.This work is done in the context of minimizing the Kohn-Sham energy functionaldirectly in real space with a multiscale approach. The efficacy of the approximation is illustrated bylocating the ground state density of simple one electron atoms and moleculesand more complicated multiorbital systems.Comment: Submitted to JCP (July 1, 1995 Issue), latex, 27pages, 2figure

Properties of short-range and long-range correlation energy density functionals from electron-electron coalescence

The combination of density functional theory with other approaches to the many-electron problem through the separation of the electron-electron interaction into a short-range and a long-range contribution is a promising method, which is raising more and more interest in recent years. In this work some properties of the corresponding correlation energy functionals are derived by studying the electron-electron coalescence condition for a modified (long-range-only) interaction. A general relation for the on-top (zero electron-electron distance) pair density is derived, and its usefulness is discussed with some examples. For the special case of the uniform electron gas, a simple parameterization of the on-top pair density for a long-range only interaction is presented and supported by calculations within the ``extended Overhauser model''. The results of this work can be used to build self-interaction corrected short-range correlation energy functionals.Comment: revised version, to appear in Phys. Rev.

Exchange energy in the local Airy gas approximation

The Airy gas model of the edge electron gas is used to construct an exchange-energy functional which is an alternative to those obtained in the local density and generalized gradient approximations. Test calculations for rare gas atoms, molecules, solids and surfaces show that the Airy gas functional performs better than the local density approximation in all cases and better than the generalized gradient approximation for solids and surfaces. Typeset using REVTEX 1 Since the pioneering papers on density functional theory (DFT) [1,2] there has been a constant search for exchange-correlation functionals of chemical accuracy. This includes the works on the generalized gradient approximation (GGA) [3–7] which are dedicated efforts to construct local functionals for inhomogeneous systems ranging from atoms to solids based on the uniform electron gas, i.e., the local density approximation (LDA), and density gradient corrections, as well as the development of a number gradien

Performance of the modified Becke-Johnson potential

Very recently, in the 2011 version of the Wien2K code, the long standing shortcome of the codes based on Density Functional Theory, namely, its impossibility to account for the experimental band gap value of semiconductors, was overcome. The novelty is the introduction of a new exchange and correlation potential, the modified Becke-Johnson potential (mBJLDA). In this paper, we report our detailed analysis of this recent work. We calculated using this code, the band structure of forty one semiconductors and found an important improvement in the overall agreement with experiment as Tran and Blaha [{\em Phys. Rev. Lett.} 102, 226401 (2009)] did before for a more reduced set of semiconductors. We find, nevertheless, within this enhanced set, that the deviation from the experimental gap value can reach even much more than 20%, in some cases. Furthermore, since there is no exchange and correlation energy term from which the mBJLDA potential can be deduced, a direct optimization procedure to get the lattice parameter in a consistent way is not possible as in the usual theory. These authors suggest that a LDA or a GGA optimization procedure is used previous to a band structure calculation and the resulting lattice parameter introduced into the 2011 code. This choice is important since small percentage differences in the lattice parameter can give rise to quite higher percentage deviations from experiment in the predicted band gap value.Comment: 10 pages, 2 figures, 5 Table

Rearrangement of cluster structure during fission processes

Results of molecular dynamics simulations of fission reactions $Na_{10}^{2+} \to Na_7^+ + Na_3^+$ and $Na_{18}^{2+} \to 2 Na_9^+$ are presented. Dependence of the fission barriers on isomer structure of the parent cluster is analyzed. It is demonstrated that the energy necessary for removing homothetic groups of atoms from the parent cluster is largely independent of the isomer form of the parent cluster. Importance of rearrangement of the cluster structure during the fission process is elucidated. This rearrangement may include transition to another isomer state of the parent cluster before actual separation of the daughter fragments begins and/or forming a "neck" between the separating fragments

Timesaving Double-Grid Method for Real-Space Electronic-Structure Calculations

We present a simple and efficient technique in ab initio electronic-structure calculation utilizing real-space double-grid with a high density of grid points in the vicinity of nuclei. This technique promises to greatly reduce the overhead for performing the integrals that involves non-local parts of pseudopotentials, with keeping a high degree of accuracy. Our procedure gives rise to no Pulay forces, unlike other real-space methods using adaptive coordinates. Moreover, we demonstrate the potential power of the method by calculating several properties of atoms and molecules.Comment: 4 pages, 5 figure

Edge Electron Gas

The uniform electron gas, the traditional starting point for density-based many-body theories of inhomogeneous systems, is inappropriate near electronic edges. In its place we put forward the appropriate concept of the edge electron gas.Comment: 4 pages RevTex with 7 ps-figures included. Minor changes in title,text and figure

Oscillations in meta-generalized-gradient approximation potential energy surfaces for dispersion-bound complexes

© 2009 American Institute of Physics. The electronic version of this article is the complete one and can be found at: http://dx.doi.org/10.1063/1.3177061DOI: 10.1063/1.3177061Meta-generalized-gradient approximations (meta-GGAs) in density-functional theory are exchange-correlation functionals whose integrands depend on local density, density gradient, and also the kinetic-energy density. It has been pointed out by Johnson et al. [Chem. Phys. Lett. 394, 334 (2004) ] that meta-GGA potential energy curves in dispersion-bound complexes are susceptible to spurious oscillations unless very large integration grids are used. This grid sensitivity originates from the saddle-point region of the density near the intermonomer midpoint. Various dimensionless ratios involving the kinetic-energy density, found in typical meta-GGAs, may be ill-behaved in this region. Grid sensitivity thus arises if the midpoint region is sampled by too sparse a grid. For most meta-GGAs, standard grids do not suffice. Care must be taken to avoid this problem when using, or constructing, meta-GGAs

Performance of ab initio and density functional methods for conformational equilibria of CnH2n+2 alkane isomers (n=2-8)

Conformational energies of n-butane, n-pentane, and n-hexane have been calculated at the CCSD(T) level and at or near the basis set limit. Post-CCSD(T) contribution were considered and found to be unimportant. The data thus obtained were used to assess the performance of a variety of density functional methods. Double-hybrid functionals like B2GP-PLYP and B2K-PLYP, especially with a small Grimme-type empirical dispersion correction, are capable of rendering conformational energies of CCSD(T) quality. These were then used as a `secondary standard' for a larger sample of alkanes, including isopentane and the branched hexanes as well as key isomers of heptane and octane. Popular DFT functionals like B3LYP, B3PW91, BLYP, PBE, and PBE0 tend to overestimate conformer energies without dispersion correction, while the M06 family severely underestimates GG interaction energies. Grimme-type dispersion corrections for these overcorrect and lead to qualitatively wrong conformer orderings. All of these functionals also exhibit deficiencies in the conformer geometries, particularly the backbone torsion angles. The PW6B95 and, to a lesser extent, BMK functionals are relatively free of these deficiencies. Performance of these methods is further investigated to derive conformer ensemble corrections to the enthalpy function, $H_{298}-H_0$, and the Gibbs energy function, ${\rm gef}(T)\equiv - [G(T)-H_0]/T$, of these alkanes. While $H_{298}-H_0$ is only moderately sensitive to the level of theory, ${\rm gef}(T)$ exhibits more pronounced sensitivity. Once again, double hybrids acquit themselves very well.Comment: J. Phys. Chem. A, revised [Walter Thiel festschrift