Showing papers on "Orbital-free density functional theory published in 1997"

Density-functional thermochemistry. V. Systematic optimization of exchange-correlation functionals

Abstract: A systematic procedure for refining gradient corrections in Kohn–Sham exchange-correlation functionals is presented. The procedure is based on least-squares fitting to accurate thermochemical data. In this first application of the method, we use the G2 test set of Pople and co-workers to generate what we believe to be an optimum GGA/exact-exchange density-functional theory (i.e., generalized gradient approximation with mixing of exactly computed exchange).

A hybrid Gaussian and plane wave density functional scheme

Abstract: A density functional theory-based algorithm for periodic and non-periodic ab initio calculations is presented. This scheme uses pseudopotentials in order to integrate out the core electrons from the problem. The valence pseudo-wavefunctions are expanded in Gaussian-type orbitals and the density is represented in a plane wave auxiliary basis. The Gaussian basis functions make it possible to use the efficient analytical integration schemes and screening algorithms of quantum chemistry. Novel recursion relations are developed for the calculation of the matrix elements of the density-dependent Kohn-Sham self-consistent potential. At the same time the use of a plane wave basis for the electron density permits efficient calculation of the Hartree energy using fast Fourier transforms, thus circumventing one of the major bottlenecks of standard Gaussian based calculations. Furthermore, this algorithm avoids the fitting procedures that go along with intermediate basis sets for the charge density. The performance a...

Comparative Study of Benzene···X (X = O2, N2, CO) Complexes Using Density Functional Theory: The Importance of an Accurate Exchange−Correlation Energy Density at High Reduced Density Gradients

Abstract: Although density functional theory (DFT) is more and more commonly used as a very efficient tool for the study of molecules and bulk materials, its applications to weakly bonded systems remain rather sparse in the literature, except studies that consider hydrogen bonding. It is, however, of essential interest to be able to correctly describe weaker van der Waals complexes. This prompted us to investigate more precisely the reliability of several widely-used functionals. The equilibrium geometries and the binding energies of C6H6···X (X = O2, N2, or CO) complexes are determined within the standard Kohn−Sham approach of DFT using different exchange−correlation functionals and at the MP2 level of theory for comparison. It is comprehensively concluded that extreme care must be taken in the choice of the functional since only those that behave properly at large and intermediate values of the reduced density gradient s give relevant results. The PW91 exchange functional, the enhancement factor of which does not diverge at increasing s, appears as the most reliable for the studied systems. It is furthermore demonstrated that the quality of the DFT results is determined by the exchange energy component of the total energy functional.

Time-dependent density functional theory beyond the adiabatic local density approximation

Abstract: In the current density functional theory of linear and nonlinear time-dependent phenomena, the treatment of exchange and correlation beyond the level of the adiabatic local density approximation is shown to lead to the appearance of viscoelastic stresses in the electron fluid. Complex and frequency-dependent viscosity/elasticity coefficients are microscopically derived and expressed in terms of properties of the homogeneous electron gas. As a first consequence of this formalism, we provide an explicit formula for the linewidths of collective excitations in electronic systems.

Time-dependent Density Functional Results for the Dynamic Hyperpolarizability of C 60

Abstract: The experimental, as well as theoretical, values for the frequency-dependent hyperpolarizability of ${\mathrm{C}}_{60}$ differ by orders of magnitude. We present the first density functional calculation of a molecular frequency-dependent hyperpolarizability. Our implementation is very economical, enabling the treatment of molecules of this size, in a potentially much more accurate way than can be obtained with alternative methods. Our results strongly support the recent results by Geng and Wright, who report much lower experimental values than previous authors.

A correlation-energy density functional for multideterminantal wavefunctions

Abstract: A density functional for dynamical correlation, to be used in connection with wavefunctions of the complete-active-space self-consistent field type, is described, and first applications to the series of two- and four-electron atomic ions as well as to the H2 potential curve are given.

Spin-Density Functionals from Current-Density Functional Theory and Vice Versa: A Road towards New Approximations

Abstract: It is shown that the exchange-correlation functional of spin-density functional theory is identical, on a certain set of densities, with the exchange-correlation functional of current-density functional theory. This rigorous connection is used to construct new approximations of the exchange-correlation functionals. These include a conceptually new generalized-gradient spin-density functional and a nonlocal current-density functional.

Density-Gradient Analysis for Density Functional Theory: Application to Atoms*

Abstract: We present an analysis of local or semilocal density functionals for the exchange)correlation energy by decomposing them into their gradients r local Seitz s . . . radius , z relative spin polarization , and s reduced density gradient . We explain the numerical method pertaining to this kind of analysis and present results for a few atoms and ions. The atomic shell structure is prominent, and only the ranges 0 - r - 10 and s 0 - s - 3 are important. The low-density and large-gradient domains, where the approximations for the exchange)correlation energy are least trustworthy, have very little weight. Q 1997 John Wiley & Sons, Inc.

Accurate numerical determination of Kohn-Sham potentials from electronic densities: I. Two-electron systems

Abstract: The extraction of the true Kohn-Sham exchange-correlation potential from near-exact electronic densities is demonstrated, with particular reference to the two-electron systems He and H2. It is shown that if the reference density is obtained from a standard configuration interaction calculation, very large orbital basis sets are required to obtain convergence in the resulting exchange-correlation potential. The correlation contribution to molecular bonding is analysed in terms of contributions from the potential in different regions of real space.

Optimized Effective Potential for Atoms and Molecules

Abstract: We describe the optimized effective potential method of density functional theory and the semi-analytical approximation due to Krieger, Li and Iafrate. Results for atomic and molecular systems including correlation contributions are presented and compared with conventional Kohn–Sham methods. The combination of the exact exchange energy functional with the correlation energy functional of Colle and Salvetti works extremely well for atomic systems, while further improvement is required for molecular systems.

Density matrices and density functionals in strong magnetic fields

Abstract: The equation of motion for the first-order density matrix ~1DM! is constructed for interacting electrons moving under the influence of given external scalar and vector potentials. The 1DM is coupled there to the 2DM by means of the electron-electron interaction. This equation is then employed to obtain the differential virial equation for interacting electrons moving in a magnetic field of arbitrary strength. Suitable integration leads back to the virial theorem derived recently by Erhard and Gross. The exchange-correlation scalar potential of the current-density functional theory of Vignale and Rasolt is derived in two forms, in terms of 1DMs and 2DMs and their noninteracting-system counterparts, involving also ~in a linear way! the vector potentials: external and exchange-correlation ~xc! ones in the first form, and the xc one in the second form. An equation is obtained also for determining the corresponding xc vector potential in terms of the same DMs and the external vector potential. Approximate exchange-only scalar and vector potentials are proposed in terms of noninteracting 1DM. Finally the Hartree-Fock 1DM for atoms and molecules in magnetic fields is shown to satisfy the same equation of motion as the fully interacting 1DM. @S1050-2947 ~97!06312-9#

Density functional theory for hard-sphere fluids: a generating function approach

Abstract: A new density functional for the inhomogeneous hard-sphere fluid is proposed which expresses the free-energy density in terms of a set of derivatives, with respect to the particle radius, of a simple generating function. The three-dimensional version of the theory is used to calculate density profiles for hard spheres near walls and to investigate the bulk fluid g(r), via the test particle procedure. While the performance of the theory is generally poorer than that of a related theory, the fundamental-measure approach of Rosenfeld, it is better than that of approaches based on a single, density-independent weight function. Unlike earlier approaches, the theory is remarkably successful at describing situations where the effective dimensionality is reduced below three. More specifically the three-dimensional functional yields rather accurate equations of state in the and limits and is exact for the limit (a cavity that cannot hold more than one particle). The strict one-dimensional version of the theory yields the exact free-energy functional for hard rods whilst the free-energy functional for is equivalent to that obtained from the fundamental-measure approach. The extension of the theory to hard-sphere mixtures is also described.

Simple tests for density functional methods

Abstract: The performance of the currently used generalized gradient approximation density functionals is analyzed using several simple, yet critical requirements. We analyze the effects of the self-interaction error, the inclusion of the exact exchange, and the parameter settings used in the popular three-parameter hybrid density functionals. The results show that the elimination of the self-interaction error from the current density functionals lead to very poor results for H2. The inclusion of the exact exchange does not significantly influence the self-interaction corrected results. The variation of the A, B, and C parameters of a hybrid DFT method influences the H(SINGLE BOND)H equilibrium bond length through a very simple linear equation, and it is possible to reproduce the experimental H(SINGLE BOND)H distance with appropriate selection of these parameters, although an infinite number of solutions exists. Similar results were obtained for the total energy and the electron density along the internuclear axis. The analysis of the exact KS potential at the bond critical point of the dissociating H2 molecule shows that, for this property, the second order Moller–Plesset perturbation theory yields a better potential than the density functionals studied in this article. © 1997 John Wiley & Sons, Inc. J Comput Chem18: 1534–1545, 1997

Local and nonlocal density functional calculations of the molecular structure of isomeric thiadiazoles

Abstract: Conjugated organic heterocycles are systems of growing interest in materials science in view of the potential applications in fields such as electronics, photonics, sensors, or corrosion protection. The study of their molecular properties serves as a model for the prediction of the behavior of potentially conductive oligomers and polymers. A detailed analysis of isomeric thiadiazole monoxide molecules has been done using Hartree-Fock and local (SVWN) and nonlocal (BLYP, B3LYP) density functionals and optimizing the molecular geometries by means of the gradient technique. A charge sensitivity analysis of the studied molecules has been performed by resorting to density functional theory, obtaining several sensitivity coefficients such as the molecular energy, net atomic charges, global and local hardness, global and local softness, and Fukui functions. With these results and the analysis of the dipole moments, the molecular electrostatic potentials and the total electron density maps, several conclusions have been inferred about the preferred sites of chemical reaction of the studied compounds.

Hartree-Fock energy-density functionals generated by local-scaling transformations: Applications to first-row atoms

Abstract: We report energy calculations of selected first-row atoms using explicit approximate Hartree-Fock functionals generated in the context of the local-scaling version of density functional theory. We show that these approximate functionals yield highly accurate upper bounds to the Hartree-Fock energies of the atoms considered. The generation of molecular functionals in terms of local-scaling transformations centered at each nucleus is discussed.

Numerical Determination of the Topological Properties of the Electronic Charge Density in Molecules and Solids Using Density Functional Theory

Abstract: A numerical method to analyze the topology of the electronic density regardless of how it was obtained (analytically or numerically) was implemented for the Extreme 94 program. The method allows th...

Notes on the static dielectric response function in the density functional theory

Abstract: We discuss several aspects of the dielectric response theory application to the density functional theory. This field has been an unceasing source of confusion during several decades. The most frequent reasons for this confusion are (a) uncritical transfer of the results, especially regarding so-called local field corrections, obtained in many-body perturbation theory onto density functional theory, and (b) mixing up the statements true for the exact density functional theory with those applicable to the local density approximation only. In these notes we try to draw an appropriate lines between those theories. We also discuss a newly introduced (X. Gonze, Ph. Ghosez and R. W. Godby, Phys. Rev. Lett., 74, 4035, 1995) “polarization + density functional” and show that within a given (e.g., local density) approximation to the exchange-correlation energy the Gonze et al. approach is exactly equivalent to the conventional one.

Coordinate scaling and adiabatic-connection formulation in density-functional theory

Abstract: Modern density-functional theory ~DFT! @1# has benefited much from the coordinate-scaling method @2# and the adiabatic-connection formulation @3#, which have been used extensively in checking and developing density functionals @1–4#. In the following, a unified formalism of these two theoretical techniques is introduced within the framework of DFT. Via the constrained-search formulation @5#, the Hohenberg-Kohn ~HK! universal functional @6# Fl@rabz x y z # , defined within an extended domain