As pointed out in the paper preceding this one, in the case of functionals whose independent variable must obey conditions of integral normalization, conventional functional differentiation, defined in terms of an arb...As pointed out in the paper preceding this one, in the case of functionals whose independent variable must obey conditions of integral normalization, conventional functional differentiation, defined in terms of an arbitrary test function, is generally inapplicable and functional derivatives with respect to the density must be evaluated through the alternative and widely used limiting procedure based on the Dirac delta function. This leads to the determination of the rate of change of the dependent variable with respect to its independent variable at each isolated pair, , that may not be part of a functional (a set of ordered pairs). This extends the concept of functional derivative to expectation values of operators with respect to wave functions leading to a density even if the wave functions (and expectation values) do not form functionals. This new formulation of functional differentiation forms the basis for the study of the mathematical integrity of a number of concepts in density functional theory (DFT) such as the existence of a universal functional of the density, of orbital-free density functional theory, the derivative discontinuity of the exchange and correlation functional and the extension of DFT to open systems characterized by densities with fractional normalization. It is shown that no universal functional exists but, rather, a universal process based only on the density and independent of the possible existence of a potential, leads to unique functionals of the density determined through the minimization procedure of the constrained search. The mathematical integrity of two methodologies proposed for the treatment of the Coulomb interaction, the self-interaction free method and the optimized effective potential method is examined and the methodologies are compared in terms of numerical calculations. As emerges from this analysis, the optimized effective potential method is found to be numerically approximate but formally invalid, contrary to the rigorously exact results of the self-interaction-fr展开更多
The Paulie’s principle is used for development of the orbital-free (OF) version of the density functional theory. On the example of the three-atomic clusters, Al<sub>3</sub>, Si<sub>3</sub>, a...The Paulie’s principle is used for development of the orbital-free (OF) version of the density functional theory. On the example of the three-atomic clusters, Al<sub>3</sub>, Si<sub>3</sub>, and C<sub>3</sub>, it is shown that the OF approach may lead to equilibrium configurations of atomic systems with both the metallic and covalent bonding. The equilibrium interatomic distances, interbonding angles and binding energies are found in good accordance with the known data. Results will be useful for developing of theoretical study of huge molecules and nanoparticles.展开更多
The equation of states,diffusions,and viscosities of strongly coupled Fe at 80 and 240 eV with densities from 1.6 to 40 g/cm^(3) are studied by orbital-free molecular dynamics,classical molecular dynamics with a corre...The equation of states,diffusions,and viscosities of strongly coupled Fe at 80 and 240 eV with densities from 1.6 to 40 g/cm^(3) are studied by orbital-free molecular dynamics,classical molecular dynamics with a corrected Yukawa potential and compared with the results from average atom model.A new local pseudopotential is generated for orbital free calculations.For low densities,the Yukawa model captures the correct ionic interaction behavior around the first peak of the radial distribution function(RDF),thus it gives correct RDFs and transport coefficients.For higher densities,the scaled transformation of the Yukawa potential or adding a short range repulsion part to the Yukawa potential can give correct RDFs and transport coefficients.The corrected potentials are further validated by the force matching method.展开更多
We give here an overview of the orbital-flee density functional theory that is used for modeling atoms and molecules. We review typical approximations to the kinetic energy, exchange-correlation corrections to the k...We give here an overview of the orbital-flee density functional theory that is used for modeling atoms and molecules. We review typical approximations to the kinetic energy, exchange-correlation corrections to the kinetic and Hartree energies, and constructions of the pseudopotentials. We discuss numerical discretizations for the orbital-free methods and include several numerical results for illustrations.展开更多
Development of the orbital-free (OF) approach of the density functional theory (DFT) may result in a power instrument for modeling of complicated nanosystems with a huge number of atoms. A key problem on this way is c...Development of the orbital-free (OF) approach of the density functional theory (DFT) may result in a power instrument for modeling of complicated nanosystems with a huge number of atoms. A key problem on this way is calculation of the kinetic energy. We demonstrate how it is possible to create the OF kinetic energy functionals using results of Kohn-Sham calculations for single atoms. Calculations provided with these functionals for dimers of sp-elements of the C, Si, and Ge periodic table rows show a good accordance with the Kohn-Sham DFT results.展开更多
文摘As pointed out in the paper preceding this one, in the case of functionals whose independent variable must obey conditions of integral normalization, conventional functional differentiation, defined in terms of an arbitrary test function, is generally inapplicable and functional derivatives with respect to the density must be evaluated through the alternative and widely used limiting procedure based on the Dirac delta function. This leads to the determination of the rate of change of the dependent variable with respect to its independent variable at each isolated pair, , that may not be part of a functional (a set of ordered pairs). This extends the concept of functional derivative to expectation values of operators with respect to wave functions leading to a density even if the wave functions (and expectation values) do not form functionals. This new formulation of functional differentiation forms the basis for the study of the mathematical integrity of a number of concepts in density functional theory (DFT) such as the existence of a universal functional of the density, of orbital-free density functional theory, the derivative discontinuity of the exchange and correlation functional and the extension of DFT to open systems characterized by densities with fractional normalization. It is shown that no universal functional exists but, rather, a universal process based only on the density and independent of the possible existence of a potential, leads to unique functionals of the density determined through the minimization procedure of the constrained search. The mathematical integrity of two methodologies proposed for the treatment of the Coulomb interaction, the self-interaction free method and the optimized effective potential method is examined and the methodologies are compared in terms of numerical calculations. As emerges from this analysis, the optimized effective potential method is found to be numerically approximate but formally invalid, contrary to the rigorously exact results of the self-interaction-fr
文摘The Paulie’s principle is used for development of the orbital-free (OF) version of the density functional theory. On the example of the three-atomic clusters, Al<sub>3</sub>, Si<sub>3</sub>, and C<sub>3</sub>, it is shown that the OF approach may lead to equilibrium configurations of atomic systems with both the metallic and covalent bonding. The equilibrium interatomic distances, interbonding angles and binding energies are found in good accordance with the known data. Results will be useful for developing of theoretical study of huge molecules and nanoparticles.
基金This work is supported by the National Basic Research Program of China(973 Program)under grant no.2013CB922203the National NSFC under grant Nos.11422432 and 11774429+1 种基金Science Challenge Project under grant no.JCKY2016212A501the Advanced Research Foundation of National University of Defense Technology under grant no.JQ14-02-01.
文摘The equation of states,diffusions,and viscosities of strongly coupled Fe at 80 and 240 eV with densities from 1.6 to 40 g/cm^(3) are studied by orbital-free molecular dynamics,classical molecular dynamics with a corrected Yukawa potential and compared with the results from average atom model.A new local pseudopotential is generated for orbital free calculations.For low densities,the Yukawa model captures the correct ionic interaction behavior around the first peak of the radial distribution function(RDF),thus it gives correct RDFs and transport coefficients.For higher densities,the scaled transformation of the Yukawa potential or adding a short range repulsion part to the Yukawa potential can give correct RDFs and transport coefficients.The corrected potentials are further validated by the force matching method.
基金supported by the National Science Foundation of China under the grant 10425105the National Basic Research Program under the grant 2005CB321704.
文摘We give here an overview of the orbital-flee density functional theory that is used for modeling atoms and molecules. We review typical approximations to the kinetic energy, exchange-correlation corrections to the kinetic and Hartree energies, and constructions of the pseudopotentials. We discuss numerical discretizations for the orbital-free methods and include several numerical results for illustrations.
文摘Development of the orbital-free (OF) approach of the density functional theory (DFT) may result in a power instrument for modeling of complicated nanosystems with a huge number of atoms. A key problem on this way is calculation of the kinetic energy. We demonstrate how it is possible to create the OF kinetic energy functionals using results of Kohn-Sham calculations for single atoms. Calculations provided with these functionals for dimers of sp-elements of the C, Si, and Ge periodic table rows show a good accordance with the Kohn-Sham DFT results.
