Closed-shell Atoms Research Articles

On the impossibility to perform a complete valence-shellphotoionization experiment with closed-shell atoms

A detailed investigation of the relation between five dynamical parameters(partial photoionization cross section σ, angular asymmetryparameterβ and three spin polarization parameters A,α,ξ) and fivecorresponding theoretical values (three dipole matrix elements and two phaseshiftdifferences) describing photoionization from p3/2,d3/2andd5/2subshells of rare-gas atoms reveals a systematic ambiguitypreventing the extraction of a unique set of five theoretical valuesfrom the experimental data which constitute a `complete experiment'.Xe(5p3/2)-1 photoionization serves as an example toillustratethe problem using a numerical procedure as well as a mathematicalanalysis.A new equation is presented which connects four dynamical parameters.From these facts it follows that a complete experiment onclosed-shell atoms with the extraction of five theoreticalvalues is, in principle, impossible,if the photoelectron properties are measured exclusively.

Predicted modifications in the direct and indirect gaps of Ge

The charge density of Ge was studied at various k-points and for various bands, by the ab initio pseudopotential method, using additionally the interstitial sites. The lowest Xc conduction-band points were found to be unique in having a high charge density in the interstitial site. It has been therefore predicted and verified that the Xc points move up in energy relative to the Γc point when closed-shell atoms (like H) are substituted at the interstitial sites. The calculations also indicate the change of the band-gap for HGeH.

Angular distributions of s-subshell electrons in open-shell atoms: 3s photoionization of atomic chlorine

A determination of the angular distribution parameter beta of the atomic chlorine 3s photoelectrons over the photon-energy range from 29 to 70 eV has been carried out using electron spectrometry in conjunction with synchrotron radiation. Our results confirm the basic theoretical predictions that beta, for s-subshell photoionization in open-shell atoms, is in general term and photon-energy dependent, in contrast to closed-shell atoms where beta is always 2 nonrelativistically. However, our measurements of beta for the Cl+ 3s((1,3)P) channels demonstrate that significant details are not handled well by simple Hartree-Fock theory.

The optimized effective potential and the self-interaction correction in density functional theory: Application to molecules

The Krieger, Li, and Iafrate approximation to the optimized effective potential including the self-interaction correction for density functional theory has been implemented in a molecular code, NWChem, that uses Gaussian functions to represent the Kohn and Sham spin–orbitals. The differences between the implementation of the self-interaction correction in codes where planewaves are used with an optimized effective potential are discussed. The importance of the localization of the spin–orbitals to maximize the exchange-correlation of the self-interaction correction is discussed. We carried out exchange-only calculations to compare the results obtained with these approximations, and those obtained with the local spin density approximation, the generalized gradient approximation and Hartree–Fock theory. Interesting results for the energy difference (GAP) between the highest occupied molecular orbital, HOMO, and the lowest unoccupied molecular orbital, LUMO, (spin–orbital energies of closed shell atoms and molecules) using the optimized effective potential and the self-interaction correction have been obtained. The effect of the diffuse character of the basis set on the HOMO and LUMO eigenvalues at the various levels is discussed. Total energies obtained with the optimized effective potential and the self-interaction correction show that the exchange energy with these approximations is overestimated and this will be an important topic for future work.

Hartree-Fock-Roothaan calculations of dipolar polarizabilities for closed-shell atoms

Methods are suggested for optimization of Slater type atomic orbitals in polarizability calculations of closed-shell atoms using “bound” perturbation theory (algebraic version of the Hartree-Fock method). The size and composition of the basis set of atomic orbitals providing the Hartree-Fock limit for perturbation parameters are considered. Dipolar polarizabilities are calculated for He, Be, Ne, and Mg atoms and their isoelectronic series.

Optimization of basis sets for isoelectronic series of closed-shell atoms in Hartree-Fock-Roothaan calculations

Optimization of the nonlinear parameters (orbital exponents) of basis functions in Hartree-Fock-Roothaan calculations may be canied out with a high degree of accuracy. A scheme using second-order methods is suggested for optimization of the orbital exponents of Slater type basis functions defining the ground state of closed-shell atoms. An exact fomula is derived for calculating the partial second derivatives of energy with respect to nonlinear parameters in temis of the density matrix. In bases of isoelectronic series, the orbital exponents are shown to be the linear functions of the charge of the ion nucleus. Optimization calculations are reported for He, Be, Ne, and Mg atoms and their isoelectronic series.

Generalized Local Density Approximation in an Inhomogeneous Electron Liquid

A differential equation relating an unknown, but local, function of ground-state electron density ρ, say S(ρ), is shown first to have an analytical solution for S(r) in terms of ρ(r) for spherically symmetric systems. For closed shell atoms Kr and Xe, S(r) and S(ρ) over the density range 0<ρ<ρ(r = 0) are plotted and examined. S(r) has a roughly monotonically decreasing behaviour with small additional features reflecting electronic shell structure. the general shape of S(ρ) is also found to be the same for these atoms, use of which is made to present an approach to the non-relativisitic limit of large numbers of electrons via these closed shell atoms. Relaxing spherical symmetry, it is proposed that the resulting partial differential equation should be powerful enough to describe the ground-state electron density in neutral homonuclear molecules and clusters for large number of electrons.

On exact and approximate exchange-energy densities

Based on correspondence rules between quantum-mechanical operators and classical functions in phase space we construct exchange-energy densities in position space. Whereas these are not unique but depend on the chosen correspondence rule, the exchange potential is unique. We calculate this exchange-energy density for 15 closed-shell atoms, and compare it with kinetic- and Coulomb-energy densities. It is found that it has a dominating local-density character, but electron-shell effects are recognizable. The approximate exchange-energy functionals that have been proposed so far are found to account only poorly for the observed behaviors. Instead we use our results in proposing an alternative functional that depends on both first- and second-order derivatives of the electron density.

Atomic MP2 correlation energies fast and accurately calculated by FEM extrapolations

A p-version FEM-MP2 (finite element Møller-Plesset second order perturbation) program for accurate MP2 correlation energies of closed shell atoms has been further improved: by radial transformations , inclusion of global radial factors of the form with a sloping function and discretization in x rather than r. Adding logarithmic extrapolations to a sequence , of MP2 energies obtained from low order (linear) finite-element calculations resulted in a very fast high precision approach to MP2 correlation energies. The accuracy gain over the directly calculated values is around five orders for He bare nucleus, He-HF and Be-HF, four orders for Ne-HF almost tripling the number of significant digits. Maximal effective numbers of 16 to 18 radial points were sufficient. A coupling between the maximal l-value (here ) and a suitable maximal number of radial points is observed amounting to about .

Diatomic potential well depths from analyses of high-resolution electron energy spectra for autoionizing collision complexes

High-resolution energy spectra of electrons released in Penning ionization collisions of metastable rare gas atoms Rg*(ns) (Rg = He, Ne, Ar, Kr, Xe) with several open-shell and closed-shell atoms are analyzed to determine the well depth of the potential energy curve which describes the respective autoionizing collision complex. We thereby elucidate trends in the chemical interaction of Rg* with closed-shell target atoms A(ns2) and establish a basis for detailed comparison with the respective interactions involving open-shell, ground state alkali atoms A(ns). From electron energy spectra due to␣associative ionization (RgH+ formation) in Rg* + H(1s) collisions, we determine binding energies for the RgH+(1Σ) ground state potential (Rg = Ne, Ar, Kr, Xe) with uncertainties around 0.03 eV.

Photoionization of some closed shell atoms and ions

Dipole-allowed single photoionization of some closed shell atoms and ions has been investigated in the relativistic random-phase approximation (RRPA). Application of relativisticmultichannel quantum defect theory (RMQDT) is made together with RRPA to analyse autoionizing resonances. Analysis points to the importance of interchannel coupling in high energy photoionization and reveals various degeneracies in relativistic atomic spectra to influence the low energy dynamics. Interesting threshold behavior in photoelectron spin polarization has been seen. Prospective future studies have been indicated.

Semirelativistic DWBA for the ionization of closed shell atoms at intermediate energies

We develop a semirelativistic distorted-wave Born approximation applicable to the study of (e,2e) processes at intermediate energy. Using this method, we investigate the influence of relativistic interactions for the continuum and bound electrons on the parameters describing spin-polarized (e,2e) experiments on xenon at intermediate energy and for asymmetric kinematics.

Density functional theory in relation to x-ray and neutron scattering experiments

X-ray scattering allows, for example, the ground-state electron density of a crystal, say hexagonal close-packed Be, or a molecular solid, to be extracted. Two routes will be discussed by means of which progress should prove possible on fundamental aspects of density functional theory, given such information on the electron density. In the first of these, the proposal is to extract from X-ray scattering data a function of the density which generalizes the concept of a local density approximation. Specifically, in a closed-shell atom, such as Kr or Xe, the monotonic decay of the electron density from the nucleus is exploited to propose a generalization of local density theories such as Thomas–Fermi, plus Dirac–Slater exchange together with Gell-Mann and Brueckner correlation. In the second route considered, an essentially experimental area termed quantum crystallography is brought into contact with the density matrix approach to density functional theory proposed by Holas and March. Here, though functions of the density are not presently extractable from crystal Bragg reflection data, a method is summarized, due to Holas and this writer, whereby the exchange–correlation potential can be extracted for a given crystal such as Be. This is possible by generalizing the approach of quantum crystallography to include a potential-locality constraint. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 551–557, 1998

Density functional theory in relation to x‐ray and neutron scattering experiments

X-ray scattering allows, for example, the ground-state electron density of a crystal, say hexagonal close-packed Be, or a molecular solid, to be extracted. Two routes will be discussed by means of which progress should prove possible on fundamental aspects of density functional theory, given such information on the electron density. In the first of these, the proposal is to extract from X-ray scattering data a function of the density which generalizes the concept of a local density approximation. Specifically, in a closed-shell atom, such as Kr or Xe, the monotonic decay of the electron density from the nucleus is exploited to propose a generalization of local density theories such as Thomas–Fermi, plus Dirac–Slater exchange together with Gell-Mann and Brueckner correlation. In the second route considered, an essentially experimental area termed quantum crystallography is brought into contact with the density matrix approach to density functional theory proposed by Holas and March. Here, though functions of the density are not presently extractable from crystal Bragg reflection data, a method is summarized, due to Holas and this writer, whereby the exchange–correlation potential can be extracted for a given crystal such as Be. This is possible by generalizing the approach of quantum crystallography to include a potential-locality constraint. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 551–557, 1998

Kinetic energy density in terms of electron density for closed-shell atoms in a bare Coulomb field

A long-term aim in density functional theory is to obtain the kinetic energy density t(r) in terms of the ground-state electron density ρ(r). Here, t(r) is written explicitly in terms of ρ(r) for an arbitrary number 𝒩 of closed shells in a bare Coulomb field. In the limit as 𝒩→∞, closed results for t(r) follow from the earlier analysis of ρ(r) by Heilmann and Lieb. [Phys. Rev. A 52, 3628 (1995)]. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 66: 281–283, 1998

The effective mass of excess electrons in condensed xenon: Toward methods for modeling metal-dielectric interfaces

A molecularly detailed simulation method, designed to be efficacious for modeling conduction properties of closed shell atoms or molecules in solids, liquids, and at interfaces, has been developed. This approach successfully predicts the effective mass of a conduction electron in both solid xenon, and liquid xenon over a wide density range, as compared to experimental results. To model the electron-atom interaction, angular momentum and density-dependent semi-local pseudopotentials are employed. The pseudopotentials are first fit to reproduce the gas phase electron-xenon scattering phase shifts, and are then corrected to include many-body polarization effects in a reliable mean field fashion. The effective mass of a conduction electron is calculated by solving the Schrödinger-Bloch equation using Lanczos grid methods to obtain the Bloch wave vector (k) dependent energies in both the solid and the liquid. In the liquid phase, a representative sample of the fluid is replicated to form the “periodic” infinite system. This approximation is shown to be reliable as the effective mass does not depend on the system size or the particular configuration which is chosen. It is shown that the l=0 scattering in the condensed phase determines the k=0 ground state energies; these are coincident with the conduction band energy in this system. In contrast, the l=1 scattering is shown to determine the effective mass of the conduction electrons.

Combining long-range configuration interaction with short-range density functionals

A density functional for short-range electron-electron interaction recently developed by one of us, has been implemented into a multi-reference configuration-interaction code with explicit treatment of long-range interaction only. Possible advantages of such an approach are discussed, using as examples some closed-shell atoms (Be, Ne) and diatomics (H 2, Li 2, C 2, N 2, F 2).

Adapted Gaussian basis sets for closed-shell atoms from samarium to nobelium generated with the generator coordinate Dirac-Fock method

The Generator Dirac-Fock method for closed-shell atoms is applied to generate adapted Gaussian basis sets for the heavy atoms from Sm ( Z = 62) to No ( Z = 102) to be used in the calculations of electronic properties of atomic and molecular systems. Our Dirac-Fock-Coulomb and Dirac-Fock-Breit energies, for all atoms studied here are better than the corresponding Dirac-Fock-Coulomb and Dirac-Fock-Breit energies attained with previous Gaussian basis sets. Besides, our Dirac-Fock-Coulomb energies (except for Yb that is equal) are lower than the corresponding ones obtained by numerical-finite-difference calculations. A discussion between the generation of universal Gaussian basis sets and adapted Gaussian basis sets is presented.

Symmetry-adapted perturbation theory of three-body nonadditivity of intermolecular interaction energy

The many-body symmetry-adapted perturbation theory of intermolecular interactions has been extended to the interactions of three closed-shell atoms or molecules. Orbital formulas for the nonadditivity of the second- and third-order induction energies, third-order induction-dispersion energy, and third- and fourth-order dispersion energies with neglect of intramonomer correlation effects have been derived from the polarization expansion. The first-order intramonomer correlation correction to the third-order dispersion energy has also been obtained. The symmetrized Rayleigh–Schrödinger energy expansion has been used to derive orbital formulas for the first- and second-order exchange energies with neglect of intramonomer correlation effects. The first-order exchange energy was approximated by the terms proportional up to the fourth power in the intermolecular overlap integrals. The second-order exchange energy was developed through the third power of the intermolecular overlap integrals.

A method for the determination of the Hartree-Fock limit: application to closed-shell atoms

A procedure based on the discretized version of the generator coordinate Hartree-Fock method is introduced to reach the Hartree-Fock SCF limit. The method represents a simple and efficient operation to reach a high level of accuracy of electronic energy. Problems of linear dependence and local minima of energy are controlled. Results for some closed-shell atoms are presented.