Showing papers on "Thomas–Fermi model published in 2009"

Condition on the Kohn–Sham kinetic energy and modern parametrization of the Thomas–Fermi density

Abstract: We study the asymptotic expansion of the neutral-atom energy as the atomic number Z→∞, presenting a new method to extract the coefficients from oscillating numerical data. Recovery of the correct expansion yields a condition on the Kohn–Sham kinetic energy that is important for the accuracy of approximate kinetic energy functionals for atoms, molecules, and solids. For example, this determines the small gradient limit of any generalized gradient approximation and conflicts somewhat with the standard gradient expansion. Tests are performed on atoms, molecules, and jellium clusters using densities constructed from Kohn–Sham orbitals. We also give a modern, highly accurate parametrization of the Thomas–Fermi density of neutral atoms.

Nuclear 'pasta' phase within density dependent hadronic models

Abstract: In the present paper, we investigate the onset of the ``pasta'' phase with different parametrizations of the density dependent hadronic model and compare the results with one of the usual parametrizations of the nonlinear Walecka model. The influence of the scalar-isovector virtual $\ensuremath{\delta}$ meson is shown. At zero temperature, two different methods are used, one based on coexistent phases and the other on the Thomas-Fermi approximation. At finite temperature, only the coexistence phases method is used. $\mathit{npe}$ matter with fixed proton fractions and in $\ensuremath{\beta}$ equilibrium are studied. We compare our results with restrictions imposed on the values of the density and pressure at the inner edge of the crust, obtained from observations of the Vela pulsar and recent isospin diffusion data from heavy-ion reactions, and with predictions from spinodal calculations.

Rabi oscillations and few-level approximations in time-dependent density functional theory.

Abstract: The resonant interaction of laser light with atoms is analyzed from the time-dependent density functional theory perspective using a model helium atom which can be solved exactly. It is found that in the exact exchange approximation the time-dependent dipole shows Rabi-type oscillations of its amplitude. However, the time-dependent density itself is not well described. These seemingly contradictory findings are analyzed. The Rabi-type oscillations are found to be essentially of classical origin. The incompatibility of time-dependent density functional theory with few-level approximations for the description of resonant dynamics is discussed.

Is charge transfer transitions really too difficult for standard density functionals or are they just a problem for time-dependent density functional theory based on a linear response approach

Abstract: It is well known that standard time-dependent density functional theory (TD-DFT) affords both a quantitative and qualitative incorrect picture of charge transfer transitions between two spatially separated regions. It is shown here that the well-known failure can be traced back to the use of linear response theory. Further, it is demonstrated that the inclusion of higher order response terms readily affords a qualitatively correct picture even for simple functionals based on the local density approximation. By using the higher order response terms, we finally derive a correction that can be added as a perturbation to charge transfer excitation energies calculated by standard TD-DFT.

Excitation energies with time-dependent density matrix functional theory: Singlet two-electron systems.

Abstract: Time-dependent density functional theory in its current adiabatic implementations exhibits three striking failures: (a) Totally wrong behavior of the excited state surface along a bond-breaking coordinate, (b) lack of doubly excited configurations, affecting again excited state surfaces, and (c) much too low charge transfer excitation energies. We address these problems with time-dependent density matrix functional theory (TDDMFT). For two-electron systems the exact exchange-correlation functional is known in DMFT, hence exact response equations can be formulated. This affords a study of the performance of TDDMFT in the TDDFT failure cases mentioned (which are all strikingly exhibited by prototype two-electron systems such as dissociating H2 and HeH+). At the same time, adiabatic approximations, which will eventually be necessary, can be tested without being obscured by approximations in the functional. We find the following: (a) In the fully nonadiabatic (ω-dependent, exact) formulation of linear respons...

All-electron density functional theory and time-dependent density functional theory with high-order finite elements.

Abstract: We present for static density functional theory and time-dependent density functional theory calculations an all-electron method which employs high-order hierarchical finite-element bases. Our mesh generation scheme, in which structured atomic meshes are merged to an unstructured molecular mesh, allows a highly nonuniform discretization of the space. Thus it is possible to represent the core and valence states using the same discretization scheme, i.e., no pseudopotentials or similar treatments are required. The nonuniform discretization also allows the use of large simulation cells, and therefore avoids any boundary effects.

Density functional theory and Kohn-Sham scheme for self-bound systems

Abstract: We demonstrate how the separation of the total energy of a self-bound system into a functional of the internal one-body Fermionic density and a function of an arbitrary wave vector describing the center-of-mass kinetic energy can be used to set up an "internal" Kohn-Sham scheme.

Thomas-Fermi approximation for a condensate with higher-order interactions

Abstract: We consider the ground state of a harmonically trapped Bose-Einstein condensate within the Gross-Pitaevskii theory including the effective-range corrections for a two-body zero-range potential. The resulting nonlinear Schroedinger equation is solved analytically in the Thomas-Fermi approximation neglecting the kinetic-energy term. We present results for the chemical potential and the condensate profiles, discuss boundary conditions, and compare to the usual Thomas-Fermi approach. We discuss several ways to increase the influence of effective-range corrections in experiment with magnetically tunable interactions. The level of tuning required could be inside experimental reach in the near future.

Green's function method in quantum chemistry: New numerical algorithm for the Dirac equation with complex energy and Fermi‐model nuclear potential

Abstract: We present a new effective approach to construction of the electron Green function for the Dirac equation with a nonsingular central nuclear Fermi-model potential and complex energy. We represent the radial Green function as a combination of two fundamental solutions of the Dirac equation. The approach proposed includes a procedure of generating the relativistic electron functions Ψ with performance of the gauge invariance principle. To reach the gauge invariance principle performance, we use earlier developed QED perturbation theory approach. In the fourth order of the QED perturbation theory (PT) there are diagrams, whose contribution into imaginary part of radiation width ImdE for the multielectron system accounts for many-body correlation effects. A minimization of the functional ImdE leads to integral-differential Kohn-Sham-like density functional equations. Further check for the gauge principle performance is realized by means of the Ward identities. In the numerical procedure we use the effective algorithm, within which a definition of the Dirac equation fundamental solutions is reduced to solving the single system of the differential equations. This system includes also the differential equations for the Fermi-model nuclear potential and equations for calculating the integrals of the ∫ ∫ dr1dr2 type in the Mohr formula for definition of the self-energy shift to atomic levels energies. Such an approach allows to compensate a main source of the errors, connected with numerical integration ∫dξ and summation on χ in the Mohr expressions during calculating the self-energy radiative correction to the atomic levels energies. Some numerical illustrations of applying the approach within QED PT to calculate the intermediate and high-Z Li-like ions transitions energies are presented. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

Studies of the energy density functional approach. I. Kinetic energy

Abstract: The quantum kinetic energy density is defined and its properties discussed. Its limiting values, at the nucleus of an atom and at large distances from it, are both shown to be proportional to the corresponding values of the charge density. The properties of existing kinetic energy density functionals are analyzed with respect to their local behavior and compared with the quantum results at the Hartree--Fock level. Their local behavior is found to be unsatisfactory. It is shown that the higher-order terms in the general gradient expansion, which may be considered as the basis for these models, diverge in the long-range limit. In view of these findings, a model of the kinetic energy density functional is proposed which possesses the correct limiting values for an exact as well as for a Hartree--Fock charge density. Its local behavior is found to be in good agreement with the quantum results. Thus, the integrated values of this kinetic energy density functional are in excellent general agreement with Hartree--Fock values, the percentage error in the estimate for argon, for example, being 0.04%. The basis for this model is a partitioning of the charge density into core-like and valence components. The charge density itself is notmore » modeled, as the proposed partitioning scheme may be applied to any density, including the exact one. Consequently, the present model should be useful in the energy density functional approach to the study of the physical properties of atoms, molecules, and solids. 38 references.« less

Orbital-free energy functional for electrons in two dimensions

Abstract: We derive a nonempirical, orbital-free density functional for the total energy of interacting electrons in two dimensions. The functional consists of a local formula for the interaction energy, where we follow the lines introduced by Parr for three-dimensional systems [R. G. Parr, J. Phys. Chem. 92, 3060 (1988)], and the Thomas-Fermi approximation for the kinetic energy. The freedom from orbitals and from the Hartree integral makes the proposed approximation numerically highly efficient. The total energies obtained for confined two-dimensional systems are in a good agreement with the standard local-density approximation within density-functional theory and considerably more accurate than the Thomas-Fermi approximation.

Nonlinear screening effect in an ultrarelativistic degenerate electron-positron gas

Abstract: Nonlinear screening process in an ultrarelativistic degenerate electron-positron gas has been investigated by deriving a generalized nonlinear Poisson equation for the electrostatic potential. In the simple one-dimensional case, the nonlinear Poisson equation leads to Debye-like (Coulomb-like) solutions at distances larger (less) than the characteristic length. When the electrostatic energy is larger than the thermal energy, this nonlinear Poisson equation converts into the relativistic Thomas–Fermi equation whose asymptotic solution in three dimensions shows that the potential field goes to zero at infinity much more slowly than the Debye potential. The possibility of the formation of a bound state in electron-positron plasma is also indicated. Further, it is investigated that the strong spatial fluctuations of the potential field may reduce the screening length and that the root mean square of this spatial fluctuating potential goes to zero for large r rather slowly as compared to the case of the Debye ...

Finite temperature correction to the Thomas–Fermi approximation for a Bose–Einstein condensate: comparison between theory and experiment

Abstract: We observe experimentally a deviation of the radius of a Bose–Einstein condensate from the standard Thomas–Fermi prediction, after free expansion, as a function of temperature. A modified Hartree–Fock model is used to explain the observations, mainly based on the influence of the thermal cloud on the condensate cloud.

An average atom code for warm matter : application to aluminum and uranium

Abstract: In astrophysics and in other sciences there is sometimes a need for information about the properties of matter, particularly equations of state, in extreme conditions of pressure and temperature. Global equation of state models, which represent solid, fluid and plasma states, typically consist of three parts: the cold curve, the ion-thermal contribution and the electron-thermal contribution. For the calculation of the latest part we present here an average atom embedded in a jellium code. We employ Liberman's relativistic and quantum model of matter which is a significant advance in complexity beyond the commonly used Thomas–Fermi model. We have applied specific algorithms to deal with the highly oscillatory nature of the free wavefunctions at high temperatures and to capture resonances which form in the continuum when bound states are destroyed by pressure ionization. Also we use massive parallel computing to treat the huge number of free wavefunctions at high temperatures (up to 109 K). Densities of states of resonant states are shown for uranium. With our code, which we have called Paradisio, we obtain tables of electron-thermal entropies from which free energies and pressures are derived. Our results are compared with those calculated in the Thomas–Fermi approximation and with available experiments. In aluminum, with our quantum code, a shell structure appears on the Hugoniot and a first-order metallic–nonmetallic transition is created at low densities and temperatures.

Alternative ion-ion pair-potential model applied to molecular dynamics simulations of hot and dense plasmas : Al and Fe as examples

Abstract: A model to calculate the ion-ion pair potentials in hot and dense plasmas is developed based on temperature-dependent density functional theory. The electronic structures, including the energy level and space distributions, are calculated using an average-atom model. The calculated electron space number density is divided into two parts: one is a uniformly distributed electronic sea rho(r_{b}) with a density equal to the total electronic density at the ion sphere boundary, which is redistributed when space overlap occurs between the interacting ions; the left part of the electronic density rho_{i};{2nd}(r) represents the dramatic space variations of the electrons due to the nuclear attraction and the shell structure of the bound states, which maintains unchanged during the interactions between the ions. The pair potential is obtained through space integrations for the energy density functions of electron density. We present molecular dynamics simulations for the ion motion on the basis of the calculated pair potentials in a wide regime of density and temperature. As an example, hot and dense Al and Fe plasmas are simulated to give the equation of state and ion-ion pair distribution function. The results are in agreement with those of other theoretical models.

Phase separation of two-component Bose-Einstein condensates

Abstract: Recently, coupled systems of nonlinear Schrodinger equations have been used extensively to describe mixtures Bose–Einstein condensates. In this paper, we study the distribution of two different hyperfine spin states of a binary mixture of three dimensional Bose–Einstein condensates. In a double condensate, an interface may occur due to large intraspecies and interspecies scattering lengths. We prove that there is an asymptotic separation of different phases in the strong coupling (Thomas–Fermi) limit.

Electrostatic solitary ion waves in dense electron-positron-ion magnetoplasma

Abstract: The nonlinear coupled ion-acoustic and ion-cyclotron waves propagating obliquely to the external magnetic field in dense collisionless electron-positron-ion magnetoplasma are investigated using Sagdeev potential method. A semiclassical approach is used. Electrons and positrons are treated as degenerate Fermi gases described by Thomas–Fermi density distribution and ions behave as classical gas. It is found that the presence of degenerate positrons in a dense Thomas–Fermi plasma significantly modifies the structure of solitary waves by restricting the electrostatic potential to a certain maximum value which depends upon the concentration of positrons in the system. It is also noted that only subsonic humplike solitary waves can exist and for a given angle of propagation, the presence of degenerate positrons diminishes the amplitude as well as width of the solitary wave.

Electronic exchange in quantum rings : Beyond the local-density approximation

Abstract: Quantum rings can be characterized by a specific radius and ring width. For this rich class of physical systems, an accurate approximation for the exchange-hole potential and thus for the exchange energy is derived from first principles. Excellent agreement with the exact-exchange results is obtained regardless of the ring parameters, total spin, current, or the external magnetic field. The description can be applied as a density functional outperforming the commonly used local spin-density approximation, which is here explicitly shown to break down in the quasi-one-dimensional limit. The dimensional crossover, which is of extraordinary importance in low-dimensional systems, is fully captured by our functional.

A thomas—fermi‐like analytic independent particle model for atoms and ions

Abstract: The applicability of an independent particle model which was initiated with a particular two-parameter analytic fit to the Thomas--Fermi screening function is further extended. Using the ab initio procedure of Bass, Green, and Wood, the two parameters d and K of the model are determined for all atoms and ions with Z less than or equal to 36, thus extending the determination of Szydlik and Green. The calculated total energies are in excellent agreement with Hartree- -Fock results. To a good accuracy K and 1/d may be represented as linear functions of Z - N where N is the total number of electrons and Z the nuclear charge. The slopes and intercepts of the K lines vary fairly smoothly with N, while those of the 1/d lines vary with N in a manner which reflects atomic shell structure. (auth)

Phase-space explorations in time-dependent density functional theory

Abstract: We discuss two problems which are particularly challenging for approximations in time-dependent density functional theory (TDDFT) to capture: momentum-distributions in ionization processes, and memory-dependence in real-time dynamics. We propose an extension of TDDFT to phase-space densities, discuss some formal aspects of such a “phase-space density functional theory” and explain why it could ameliorate the problems in both cases. For each problem, a two-electron model system is exactly numerically solved and analysed in phase-space via the Wigner function distribution.

Dissipative time dependent density functional theory

Abstract: The simplest density functional theory due to Thomas, Fermi, Dirac and Weizsacker is employed to describe the non-equilibrium thermodynamic evolution of an electron gas. The temperature effect is introduced via the Fermi-Dirac entropy, while the irreversible dynamics is described by a nonlinear diffusion equation. A dissipative Kohn-Sham equation is also proposed, which improves the Thomas-Fermi-Weizsacker kinetic functional.

Solitary waves and double layers in dense magnetoplasma

Abstract: Using Sagdeev’s pseudopotential technique, ion acoustic solitary waves and double layers are studied subject to an external magnetic field in a two-component dense magnetoplasma consisting of ions and degenerate electrons. The ions are described by the hydrodynamic equations, and the electrons are assumed to follow the Thomas–Fermi density distribution. The pseudopotential is derived directly from Poisson’s equation without assuming the quasineutrality condition. The ranges of parameters for which solitary waves and double layers exist are studied in detail using Sagdeev’s technique.

Statistical multifragmentation model with Skyrme effective interactions

Abstract: The statistical multifragmentation model is modified to incorporate the Helmholtz free energies calculated in the finite temperature Thomas-Fermi approximation using Skyrme effective interactions. In this formulation, the density of the fragments at the freeze-out configuration corresponds to the equilibrium value obtained in the Thomas-Fermi approximation at the given temperature. The behavior of the nuclear caloric curve at constant volume is investigated in the micro-canonical ensemble, and a plateau is observed for excitation energies between 8 and 10 MeV per nucleon. A kink in the caloric curve is found at the onset of this gas transition, indicating the existence of a small excitation energy region with negative heat capacity. In contrast to previous statistical calculations, this phase transition takes place even when the system is constrained to fixed volume. The observed phase transition takes place at approximately constant entropy. The charge distribution and other observables also turn out to be sensitive to the treatment employed in the calculation of the free energies and the fragment volumes at finite temperature, specially at high excitation energies. The isotopic distribution is also affected by this treatment, which suggests that this prescription may help obtain information on the nuclear equation of state.