Calculation of total energies of the electronic ground states of atoms forms the basis for the frozen-core pseudopotentials used in atomistic calculations of much larger scale. Reference values for these energies prov...Calculation of total energies of the electronic ground states of atoms forms the basis for the frozen-core pseudopotentials used in atomistic calculations of much larger scale. Reference values for these energies provide a benchmark for the validation of new software to calculate such potentials. In addition, basic atomic-scale electronic properties such as the (first) ionization energy provide a simple check on the approximation used in the calculation method. We present a comparison of the total energies and ionization energies of atoms Z = 1 - 92 calculated in density functional theory with several levels of exchange-correlation functional and the Hartree-Fock method, comparing ionization energies to experiment. We also investigate the role of relativistic treatment on these energies.展开更多
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
This paper presents calculating results of the two-dimensional electron gas （2DEG） distributions in AlGaN/GaN material system by solving the Schroedinger and Poisson equations self-consistently. Due to high 2DEG den...This paper presents calculating results of the two-dimensional electron gas （2DEG） distributions in AlGaN/GaN material system by solving the Schroedinger and Poisson equations self-consistently. Due to high 2DEG density in the AlGaN/GaN heterojunction interface, the exchange correlation potential should be considered among the potential energy item of Schroedinger equation. Analysis of the exchange correlation potential is given. The dependencies of the conduction band edge, 2DEG density on the Al mole fraction are presented. The polarization fields have strong influence on 2DEG density in the AlGaN/GaN heterojunction, so the dependency of the conduction band edge on the polarization is also given.展开更多
We introduce a formal definition of a non local functional and show that the non local exchange-correlation potential functional, derived within Density-Functional Theory, is non local in the space of electronic densi...We introduce a formal definition of a non local functional and show that the non local exchange-correlation potential functional, derived within Density-Functional Theory, is non local in the space of electronic densities. A previously developed non local exchange-correlation potential term, is introduced to approach the exact density-functional potential. With this approach, the electronic structure of the graphene surface and the tyrosine amino acid are calculated.展开更多
The layered charges were calculated by means of constructing the complete structure of Tl Ba Ca Cu O superconductor. The weak link between Cu O and Ba O, or between Cu O and Tl O or Ba O or Tl O layers i...The layered charges were calculated by means of constructing the complete structure of Tl Ba Ca Cu O superconductor. The weak link between Cu O and Ba O, or between Cu O and Tl O or Ba O or Tl O layers is explained with the aid of the charge of limited layer unit calculated from the values of ions obtained, in addition to the possibility of forming charges fluctuation, which depends on the π coordination covalent bond on Cu O plane and O Tl O structure. The possible chemical tight bonding orbitals are in accordance with those of other superconductors obtained by quantum theoretical method, which occur at Cu 3d (x 2-y 2) and O 2p x,y . The valence band composed of Cu 3d and O 2p orbital energy levels is obviously an energy band of conduction. The ordered charge on layers is the main reason that raises T c of superconductors. The difference of electronic structure of ab plane and c axis leads to the anisotropy properties.展开更多
文摘Calculation of total energies of the electronic ground states of atoms forms the basis for the frozen-core pseudopotentials used in atomistic calculations of much larger scale. Reference values for these energies provide a benchmark for the validation of new software to calculate such potentials. In addition, basic atomic-scale electronic properties such as the (first) ionization energy provide a simple check on the approximation used in the calculation method. We present a comparison of the total energies and ionization energies of atoms Z = 1 - 92 calculated in density functional theory with several levels of exchange-correlation functional and the Hartree-Fock method, comparing ionization energies to experiment. We also investigate the role of relativistic treatment on these energies.
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
基金Project supported by the Foundation of Hebei Education Department, China (Grant No 2003130)
文摘This paper presents calculating results of the two-dimensional electron gas （2DEG） distributions in AlGaN/GaN material system by solving the Schroedinger and Poisson equations self-consistently. Due to high 2DEG density in the AlGaN/GaN heterojunction interface, the exchange correlation potential should be considered among the potential energy item of Schroedinger equation. Analysis of the exchange correlation potential is given. The dependencies of the conduction band edge, 2DEG density on the Al mole fraction are presented. The polarization fields have strong influence on 2DEG density in the AlGaN/GaN heterojunction, so the dependency of the conduction band edge on the polarization is also given.
文摘We introduce a formal definition of a non local functional and show that the non local exchange-correlation potential functional, derived within Density-Functional Theory, is non local in the space of electronic densities. A previously developed non local exchange-correlation potential term, is introduced to approach the exact density-functional potential. With this approach, the electronic structure of the graphene surface and the tyrosine amino acid are calculated.
文摘The layered charges were calculated by means of constructing the complete structure of Tl Ba Ca Cu O superconductor. The weak link between Cu O and Ba O, or between Cu O and Tl O or Ba O or Tl O layers is explained with the aid of the charge of limited layer unit calculated from the values of ions obtained, in addition to the possibility of forming charges fluctuation, which depends on the π coordination covalent bond on Cu O plane and O Tl O structure. The possible chemical tight bonding orbitals are in accordance with those of other superconductors obtained by quantum theoretical method, which occur at Cu 3d (x 2-y 2) and O 2p x,y . The valence band composed of Cu 3d and O 2p orbital energy levels is obviously an energy band of conduction. The ordered charge on layers is the main reason that raises T c of superconductors. The difference of electronic structure of ab plane and c axis leads to the anisotropy properties.
