Discrete variable representation method calculation of the electronic structure of noble gas atoms (original) (raw)
Related papers
Journal of Physics B: Atomic, Molecular and Optical Physics, 2002
We explore the usefulness of a quantum fluid dynamics (QFD) approach for quantitative electronic structure calculations of many-electron systems. By combining QFD and density functional theory, a single time-dependent nonlinear QFD equation can be derived. The equation is further transformed into a diffusion-type form by an imaginary-time evolution method, whose asymptotic solution reaches a global minimum and the many-body groundstate wavefunction. The time-dependent generalized pseudospectral method is extended to solve the diffusion equation in spherical coordinates, allowing optimal and nonuniform spatial discretization and accurate and efficient solution of the diffusion function in space and time. The procedure is applied to the study of electronic energies, densities and other ground-state properties of noble gas atoms (He, Ne, Ar, Kr, Xe). The results are in good agreement with other best available values. The method offers a conceptually appealing and computationally practical procedure for the treatment of many-electron systems beyond the Hartree-Fock level.
Imaginary Time Density Functional Calculation of Ground States of Atoms Using CWDVR Approach
Journal of Modern Physics, 2019
The self-consistent Kohn-Sham equations for many-electron atoms are solved using the Coulomb wave function Discrete Variable Method (CWDVR). Wigner type functional is used to incorporate correlation functional. The discrete variable method is used for the uniform and optimal spatial grid discretization and solution of the Kohn-Sham equation. The equation is numerically solved using the CWDVR method. First time we have reported the solution of the Kohn-Sham equation on the ground state problem for the many-electronic atoms by the CWDVR method. Our results suggest CWDVR approach shown to be an efficient and precise solution of ground-state energies of atoms. We illustrate that the calculated electronic energies for He, Li, Be, B, C, N and O atoms are in good agreement with other best available values.
Investigating the Nature of Noble Gas−Copper Bonds by the Quantum Theory of Atoms in Molecules
The Journal of Physical Chemistry A, 2010
We investigated noble gas-copper bonds in linear complexes represented by the NgCuX general formula in which Ng and X stand for a noble gas (neon, argon, krypton, or xenon) and a halogen (fluorine, chlorine or bromine), respectively, by coupled cluster methods and modified cc-pVQZ basis sets. The quantum theory of atoms in molecules (QTAIM) shows a linear relation between the dissociation energy of noble gas-copper bonds and the amount of electronic charge transferred mainly from the noble gas to copper during complexation. Large changes in the QTAIM quadrupole moments of copper and noble gases resulting from this bonding and a comparison between NgCuX and NgNaCl systems indicate that these noble gas-copper bonds should be better interpreted as predominantly covalent. Finally, QTAIM atomic dipoles of noble gases in NgNaCl systems agree satisfactorily with atomic dipoles given by a simple model for these NgNa van der Waals bonds.
Electronic transport through single noble gas atoms
We present a theoretical study of the conductance of atomic junctions comprising single noble gas atoms (He, Ne, Ar, Kr, and Xe) coupled to gold electrodes. The aim is to elucidate how the presence of noble gas atoms affects the electronic transport through metallic atomic-size contacts. Our analysis, based on density functional theory and including van der Waals interactions, shows that for the lightest elements (He and Ne) no significant current flows through the noble gas atoms and their effect is to reduce the conductance of the junctions by screening the interaction between the gold electrodes. This explains the observations reported in metallic atomic-size contacts with adsorbed He atoms. Conversely, the heaviest atoms (Kr and Xe) increase the conductance because of the additional current path provided by their valence p states. Noble gases are commonly employed in scanning probe experiments as exchange gases since they are expected to interact weakly with the studied systems. Furthermore, it is often assumed that the adsorption of noble gas (NG) atoms does not affect the electron tunneling between metallic electrodes. However, it has been shown that this is not entirely true. For instance, two decades ago Eigler and coworkers presented scanning tunneling microscope (STM) images of Xe atoms on a Ni(110) surface 1 and they nicely demonstrated that these atoms can be moved to chosen positions on the surface. It has also been shown that it is possible to manipulate individual Xe atoms to construct atomic wires and to measure their electrical resistance 2 or to functionalize molecules. 3 From the theoretical side, while there are numerous works analyzing the interaction between NG atoms and metal surfaces, studies exploring the transport through metal-NG-metal junctions are rather scarce, and most of them have focused either on understanding atomic manipulation or on STM imaging. 2,4–8 There are still important open problems concerning how adsorbed NG atoms modify the transport through metallic atomic-size junctions. A striking example is the observation made in several break-junction and STM experiments that adsorbed He atoms can strongly modify the current through metallic junctions, lowering in particular the low-bias conductance. 9–12 This conductance suppression is surprising since the height of the tunneling barrier in the presence of NG atoms has been predicted to decrease; 5 indeed, Kelvin probe experiments have shown that the work function of noble metal surfaces decreases upon adsorption of Ar, Kr, and Xe. 13 A possible explanation, based on predictions by Lang, 4 suggests that adsorbed He atoms can polarize metal states away from the Fermi energy, leading to a decrease in the metal local density of states. This explanation was based on calculations in which the metal electrodes were described by a jellium model (with no atomistic details) and without taking into account van der Waals interactions. Thus, it is highly desirable to revisit this problem with ab initio transport methods. To shed new light on the influence of adsorbed NG atoms in the transport through metallic atomic contacts, we present in this Brief Report a systematic ab initio study of the conductance of gold atomic junctions containing single atoms of He, Ne, Ar, Kr, and Xe. Our calculations, based on density functional theory (DFT), show that, while for He and Ne the current flows directly from one metallic electrode to the other, for Ar, Kr, and Xe the transport occurs mainly through the valence p states of the NG atom. In all cases, the presence of NG atoms induces a dipole moment which screens the interaction between the leads. In the case of He, Ne, and Ar the weakening of the metal-metal coupling (rather than a suppression of the metal density of states, as proposed by Lang 4) leads to a reduction of the tunneling current. On the contrary, for Kr and Xe the additional tunneling path provided by the valence p states overcomes the screening, leading to an enhancement of the current. Our main goal is to analyze the electronic transport through metallic atomic-size contacts containing single atoms of noble gases. In particular, we have chosen gold for the electrode material and studied the elements He, Ne, Ar, Kr, and Xe. For this purpose, we have carried out conductance calculations within the framework of DFT following the method described in Ref. 14, which is built upon the TURBOMOLE 6.1 code. 15 In all our calculations we have used the BP86 functional. 16 The first step in our analysis is the construction of the atomic junctions. This is done by optimizing geometries where the gold electrodes are formed by two finite clusters of 20 atoms and a single NG atom is placed in the middle. In the optimization, the NG atom and the four innermost gold atoms on each side were relaxed, while the other gold atoms were kept frozen. For the optimized atoms, a def2-TZVP basis set 17 was chosen, while a def-SVP basis set 18 was used for the frozen gold atoms. The binding energies calculated in this way were found to differ by only around 5 × 10 −4 eV from those calculated with a def2-TZVP basis set for all the atoms. Subsequently, the gold cluster size was extended to 116 atoms on each side in order to correctly describe the metal-NG atom charge transfer
arXiv (Cornell University), 2019
We have developed the Coulomb wave function discrete variable representation (CWDVR) method to solve the imaginary time dependent Kohn-Sham equation on the many-electronic second row atoms. The imaginary time dependent Kohn-Sham equation is numerically solved using the CWDVR method. We have presented that the results of calculation for second row Li, Be, B, C, N , O and F atoms are in good agreement with other best available values using the Mathematica 7.0 programm.
A study of two-electron quantum dot spectrum using discrete variable representation method
The Journal of Chemical Physics, 2005
A variational method called discrete variable representation is applied to study the energy spectra of two interacting electrons in a quantum dot with a three-dimensional anisotropic harmonic confinement potential. This method, applied originally to problems in molecular physics and theoretical chemistry, is here used to solve the eigenvalue equation to relative motion between the electrons. The two-electron quantum dot spectrum is determined then with a precision of at least six digits. Moreover, the electron correlation energies for various potential confinement parameters are investigated for singlet and triplet states. When possible, the present results are compared with the available theoretical values.
Ground state properties of the one dimensional Coulomb gas
We study the ground state properties of a quasi one dimensional electron gas, interacting via an effective potential with a harmonic transversal confinement and long range Coulomb tail. The exact correlation energy has been calculated for a wide range of electron densities by using the lattice regularized diffusion Monte Carlo method, which is a recent development of the standard projection Monte Carlo technique. In this case it is particularly useful as it allows to sample the exact ground state of the system, even in the low density regime when the exchange between electrons is extremely small. For different values of the width parameter b (0.1 a * 0 ≤ b ≤ 4 a * 0 ), we give a simple parametrization of the correlation energy, which provides an accurate local density energy functional for quasi one dimensional systems. Moreover we show that static correlations are in qualitative agreement with those obtained for the Luttinger liquid model with long range interactions.
Journal of Physics: Conference Series, 2010
In this contribution, we discuss the finite-element discrete variable representation (FE-DVR) of the nonequilibrium Green's function and its implications on the description of strongly inhomogeneous quantum systems. In detail, we show that the complementary features of FEs and the DVR allows for a notably more efficient solution of the two-time Schwinger/Keldysh/Kadanoff-Baym equations compared to a general basis approach. Particularly, the use of the FE-DVR leads to an essential speedup in computing the self-energies.
Fast and accurate calculation of dilute quantum gas using Uehling–Uhlenbeck model equation
Journal of Computational Physics, 2017
The numerical method toward the fast and accurate calculation of the dilute quantum gas is studied by proposing the Uehing-Uhlenbeck (U-U) model equation. In particular, the direct simulation Monte Carlo (DSMC) method is used to solve the U-U model equation. The DSMC analysis of the U-U model equation surely enables us to obtain the accurate thermalization using a small number of sample particles and calculate the dilute quantum gas dynamics in practical time. Finally, the availability of the DSMC analysis of the U-U model equation toward the fast and accurate calculation of the dilute quantum gas is confirmed by calculating the viscosity coefficient of the Bose gas on the basis of Green-Kubo expression or shock layer of the dilute Bose gas around a circular cylinder.
2016
The numerical method toward the fast and accurate calculation of the dilute quantum gas is studied by proposing the Uehing-Uhlenbeck (U-U) model equation. In particular, the direct simulation Monte Carlo (DSMC) method is used to solve the U-U model equation. The DSMC analysis of the U-U model equation surely enables us to obtain the accurate thermalization using a small number of sample particles and calculate the dilute quantum gas dynamics in practical time. Finally, the availability of the DSMC analysis of the U-U model equation toward the fast and accurate calculation of the dilute quantum gas is confirmed by calculating the viscosity coefficient of the Bose gas on the basis of Green-Kubo expression or shock layer of the dilute Bose gas around a circular cylinder