Showing papers on "Orbital-free density functional theory published in 1996"

Generalized Gradient Approximation Made Simple

Abstract: Generalized gradient approximations (GGA’s) for the exchange-correlation energy improve upon the local spin density (LSD) description of atoms, molecules, and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental constants. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential. [S0031-9007(96)01479-2] PACS numbers: 71.15.Mb, 71.45.Gm Kohn-Sham density functional theory [1,2] is widely used for self-consistent-field electronic structure calculations of the ground-state properties of atoms, molecules, and solids. In this theory, only the exchange-correlation energy EXC › EX 1 EC as a functional of the electron spin densities n"srd and n#srd must be approximated. The most popular functionals have a form appropriate for slowly varying densities: the local spin density (LSD) approximation Z d 3 rn e unif

Density Functional Theory of Electronic Structure

Abstract: Density functional theory (DFT) is a (in principle exact) theory of electronic structure, based on the electron density distribution n(r), instead of the many-electron wave function Ψ(r1,r2,r3,...). Having been widely used for over 30 years by physicists working on the electronic structure of solids, surfaces, defects, etc., it has more recently also become popular with theoretical and computational chemists. The present article is directed at the chemical community. It aims to convey the basic concepts and breadth of applications: the current status and trends of approximation methods (local density and generalized gradient approximations, hybrid methods) and the new light which DFT has been shedding on important concepts like electronegativity, hardness, and chemical reactivity index.

Stability analysis for solutions of the closed shell kohn-sham equation

Abstract: The stability conditions for restricted closed shell Kohn–Sham density functional treatments are derived. In close analogy to the Hartree–Fock method we obtain the equivalent of singlet and triplet instabilities. The nonreal instability now becomes trivial and just expresses the aufbau principle. Demonstrative applications confirm the expected increased stability of density functional treatments as compared to Hartree–Fock. This is an improvement but the unphysical bifurcations do persist.

Comparison shopping for a gradient-corrected density functional

Abstract: mGradient corrections to the local spin density (LSD) approximation for the exchangecorrelation energy are making density functional theory as useful in quantum chemistry as it is in solid-state physics. But which of the many gradient-corrected density functionals should be preferred a priori? We make a graphical comparison of the gradient dependencies of some popular approximations, discussing the exact formal conditions which each obeys and identifying which conditions seem most important. For the exchange energy, there is little formal or practical reason to choose among the Perdew-Wang 86, Becke 88, or Perdew-Wang 91 functionals. But, for the correlation energy, the best formal properties are displayed by the nonempirical rw91 correlation functional. Furthermore, the real-space foundation of rw91 yields an insight into the character of the gradient expansion which suggests that rw91 should work especially well for solids. Indeed, while improving dissociation energies over LSD, rw91 remains the most "local" of the gradient-corrected exchange-correlation functionals and, thus, the least likely to overcorrect the subtle errors of LSD for solids. To show that our analysis of spin-unpolarized functionals is sufficient, we also compute spin-polarization energies for atoms, finding ~w91 values only slightly more negative than SD values. Wiley & Sons, Inc. 0 1996 John

Comparison of NMR Shieldings Calculated from Hartree−Fock and Density Functional Wave Functions Using Gauge-Including Atomic Orbitals

Abstract: A numerically accurate implementation of the gauge-including atomic orbital method for the calculation of NMR shieldings in density functional theory (DFT) is presented Results calculated by this method are compared with results of SCF and accurate coupled cluster calculations for eight small molecules Three sets of DFT results, obtained using different exchange-correlation functionals, are further compared with each other, with the SCF data, and with experiment for a set of 10 somewhat larger organic molecules The DFT values show a modest improvement compared to SCF theory Potential computational savings using density functional theory are discussed

A critical assessment of the Self-Interaction Corrected Local Density Functional method and its algorithmic implementation

Abstract: We calculate the electronic structure of several atoms and small molecules by direct minimization of the Self-Interaction Corrected Local Density Approximation (SIC-LDA) functional. To do this we first derive an expression for the gradient of this functional under the constraint that the orbitals be orthogonal and show that previously given expressions do not correctly incorporate this constraint. In our atomic calculations the SIC-LDA yields total energies, ionization energies and charge densities that are superior to results obtained with the Local Density Approximation (LDA). However, for molecules SIC-LDA gives bond lengths and reaction energies that are inferior to those obtained from LDA. The nonlocal BLYP functional, which we include as a representative GGA functional, outperforms both LDA and SIC-LDA for all ground state properties we considered.

Improved radial grids for quadrature in molecular density‐functional calculations

Abstract: A new radial coordinate transformation and associated integration grid scheme is presented for the problem of integrating functions of atomic electron density. Remarkable accuracy and stability is attained. Together with standard atomic partitioning and angular quadrature schemes, the new radial grid is applied to molecular density‐functional theory, and it is shown that acceptable accuracy is attained with significantly fewer grid points than in previously presented schemes.

On the adiabatic connection method, and scaling of electron-electron interactions in the thomas-fermi limit

Abstract: In this paper we examine three aspects of electron–electron scaling: (i) the electron–electron repulsions are only scaled in Thomas–Fermi theory; (ii) the electron–electron repulsions are scaled, and the one electron potential is adjusted to give a prescribed density, in Thomas–Fermi–Dirac theory; and (iii) new approaches to the adiabatic connection formulas are presented to help improve the exchange–correlation functional. A new generalized two‐point expression is presented. Models (i) and (ii) are solved exactly.

Generalized gradient approximations to density functional theory: comparison with exact results

Abstract: In order to assess the accuracy of commonly used approximate exchange-correlation density functionals, we present a comparison of accurate exchange and correlation potentials, exchange energy densities and energy components with the corresponding approximate quantities. Four systems are used as illustrative examples: the model system of two electrons in a harmonic potential and the He, Be and Ne atoms. A new ingredient in the paper is the separation of the exchange-correlation potential into exchange and correlation according to the density functional theory definition.

Quantum-mechanical interpretation of density functional theory

Abstract: This article describes the rigorous quantum-mechanical interpretation of Hohenberg-Kohn-Sham density-functional theory based on the original ideas of Harbola and Sahni, and of their extension by Holas and March. The local electron-interaction potential v ee KS (r) of density-functional theory is defined mathematically as the functional derivative v ee KS (r)=δE ee KS [ρ]/δρ(r), where E ee KS [ρ] is the electron-interaction energy functional of the density ρ(r). This functional and its derivative incorporate the effects of Pauli and Coulomb correlations as well as those of the correlation contribution to the kinetic energy. The potential v ee KS (r) also has the following physical interpretation. It is the work done to move an electron in a field ℱ(r), which is the sum of two fields. The first, ℰee(r), is representative of Pauli and Coulomb correlations, and is determined by Coulomb's law from its source charge which is the pair-correlation density. The second field, \(Z_{t_c } (r)\), represents the correlation contribution to the kinetic energy, and is proportional to the difference of fields derived from the kinetic-energy-density tensor for the interacting and non-interacting systems. The field ℱ(r) is conservative, and thus the work done in this field is path-independent. The quantum-mechanical electron-interaction energy component Eee[ρ] of E ee KS [ρ] is the energy of interaction between the electronic and pair-correlation densities. The correlation-kinetic-energy component Tc[ρ] can also be written in terms of its source through the field \(Z_{t_c } (r)\). Some results for finite atomic (both ground and excited states) and extended metal surface systems derived via the interpretation are presented. Certain consequences of the physical interpretation such as the understanding of Slater theory, and the implications with regard to electron correlations within approximate Kohn-Sham theory are also discussed.

Local-scaling transformation version of density functional theory: Generation of density functionals

Abstract: We review in the present work the local-scaling transformation version of density functional theory both for ground and excited states. The historical development of the concept of space-coordinate density-transformation and of its effect on the formulation of several versions of density functional theory is discussed. We then present the various steps in the elaboration of the local-transformation version and indicate some of its accomplishments with respect to the N-representability problem for the energy functionals. Examples are given showing how the application of these methods to atomic sample systems lead to Hartree-Fock energies that are undistinguishable from the SCF values. In addition, the explicit construction of analytic density functionals for the energy, via local-scaling transformations, is discussed and is exemplified for the particular case of the Hartree-Fock approximation for atoms. Finally, applications of local-scaling transformations to the direct solution of the Kohn-Sham equations are reviewed.

An assessment of density functional theory on evaluating activation barriers for small organic gas-phase rearrangement reactions

Abstract: Several gas-phase isomerization reactions have been studied with density functional theory (DFT) using both the local density approximation (LDA) and non-local (NL) gradient-corrected methods. Besides the validity of each of these pure density functional procedures, the relative accuracy of the hybrid B3LYP model (Becke's 3 parameter-functional with the NL correlation of Lee, Yang and Parr) has also been tested. The predicted geometries and relative energetics for the reactions have been examined and compared with those of Hartree-Fock (HF), MP2 and QCISD (quadratic configuration interaction with single and double excitations) calculations. Our results indicate that the NL level of DFT is reliable at estimating reaction barriers and transition state structures, especially when using the B3LYP functional, which outperforms or at least equals MP2 calculations. This theoretical investigation demonstrates that DFT methods can be used to obtain thermochemical information as accurate as that provided by means of some ab initio post-HF methods.

Density Functional Theory

Abstract: The subject of quantum chemistry may have reached an impasse. Keeping the discussion to ab initio quantum chemistry we now know how to do very large SCF calculations, thanks to the introduction of the Direct methodology by Almlof[1]. We can also manage to work with good basis sets for such calculations, although I consider that 6–31G* are not good enough, and probably something nearer to TZ2P is required for definitive SCF calculations.

Deformations of density functions in molecular quantum chemistry

Abstract: We generalize the use of the local scaling transformation developed by E. S. Kryachko and E. V. Ludena to molecules in order to deform density functions. The connection with the Jacobian problem is clearly made, and we solve that problem using a formalism introduced by J. Moser. As a consequence, we can control the density information contained in a wave function, in some sense, at the same time as we keep particular regularity and behavior assumptions in the wave function (in particular concerning the symmetries of the wave function). The principal aim of the paper is to develop a correct mathematical background for further utilization in connection with density functional theory. Theoretical implications and numerical aspects are also discussed.

Improving energies by using exact electron densities

Abstract: The exact electronic ground-state density and external potential are used to improve the accuracy of approximate density functionals. Our approach combines the advantages that the exact exchange-correlation energy functional is more local for full-coupling strength than for the coupling-constant average, and that knowledge of the exact virial can be used to reduce the exchange energy error by a factor of 2.