Closed-shell Atoms Research Articles

Generalized oscillator strengths for open-shell and closed-shell atoms

A formula, which is a useful improvement over existing ones, has been obtained to calculate the generalized oscillator strengths (GOS's) for the discrete transitions of both open-shell and closed-shell atoms. We illustrate our formula by calculating the GOS for the oxygen ${2p}^{4}{(}^{3}{P)\ensuremath{-}2p}^{3}{(}^{4}{S)3s(}^{3}S)$ transition and obtain overall good agreement with the experimental data. Our calculated GOS reveals a minimum at around the momentum transfer, $K=1.26\mathrm{a}.\mathrm{u}.$ We recommend a careful experimental search for the position of the minimum around the predicted value for confirmation.

Application of MP2 Results in Comparative Studies of Semiempirical Ground-State Energies of Large Atoms

To study the usefulness of second-order Møller-Plesset (MP2) correlation energies for ground states of closed-shell atoms (referred to as MP2/CA energies) in estimations of the total correlation energies of larger closed-shell atoms, we have considered atoms and ions containing from 10 to 86 electrons. First, it is demonstrated that for N-electron systems, 10 ≤ N ≤ 18, the MP2/CA energies provide very good approximations to the very accurate estimates of atomic correlation energies by Chakravorty and Davidson. Next, for systems with 10 ≤ N ≤ 54, comparisons are made with the semiempirical energies obtained when using the models by Chakravorty and Clementi as well as by Clementi and Corongiu. Finally, for atoms with 10 ≤ N ≤ 86, the MP2/CA energies are employed for comparison with DFT energies recently obtained by Andrae et al. (Int. J. Quantum Chem. 2001, 82, 227). The MP2/CA results proved to provide reasonable estimates to the total correlation energies in all the cases considered.

New layered rubidium rare-earth selenides: syntheses, structures, physical properties, and electronic structures for RbLnSe(2).

The compounds RbLnSe(2) (Ln = La, Ce, Pr, Nd, Sm, Gd, Tb, Ho, Er, Lu) have been synthesized by means of the reactive flux method at 1173 K. These isostructural compounds, which have the alpha-NaFeO(2) structure type, crystallize with three formula units in space group D(3d)(5)-R(-)3m of the trigonal system in cells at T = 153 K of dimensions (a, c in A) La, 4.4313(4), 23.710(3); Ce, 4.3873(3), 23.656(3); Pr, 4.3524(11), 23.655(7); Nd, 4.3231(5), 23.670(4); Sm, 4.2799(4), 23.647(3); Gd, 4.2473(7), 23.689(5); Tb, 4.2197(4), 23.631(3); Ho, 4.1869(6), 23.652(5); Er, 4.1541(8), 23.576(7); Lu, 4.1294(6), 23.614(5). The structure consists of close-packed Se layers in a pseudocubic structure distorted along [111]. The Rb and Ln atoms occupy distorted octahedral sites in alternating layers. The Rb-centered octahedra share edges with the Ln-centered octahedra between layers. Within a given layer, both the Rb-centered and Ln-centered octahedra share edges with themselves. RbTbSe(2) and RbErSe(2) exhibit Curie-Weiss paramagnetism between 5 and 300 K, and RbCeSe(2) exhibits Curie-Weiss paramagnetism between 100 and 300 K. The optical transitions for RbCeSe(2), RbTbSe(2), and RbErSe(2) are in the 2.0-2.2 eV region of the spectrum, both from diffuse reflectance spectra and from first-principles calculations. These calculations also provide insight into the electronic structures and chemical bonding in RbLnSe(2). A quadratic fit for the lanthanide contraction of the Ln-Se distance is superior to the linear one only if the closed-shell atoms La and Lu are included.

Relativistic density functional theory using Gaussian basis sets

A four-component formulation of relativistic density functional theory is presented together with the details of its implemention using a G-spinor basis set. The technical features of this approach are compared to those found in the nonrelativistic density functional theory of quantum chemistry which employ scalar basis sets of Gaussian-type functions. Numerical results of the G-spinor expansion method are presented for a sequence of closed-shell atoms, and for a selection of relativistic density functionals, and are compared with finite difference benchmarks.

Applications of electrostatic interpretation of components of effective Kohn–Sham potential in atoms

The fundamental significance of the components of the electronic Kohn–Sham potential evaluated at the nucleus is highlighted via the numerical studies on atoms He–Lu which suggest their formally similar power-law relationship in expressing the associated components of total electronic energy. Similar studies on the isoelectronic series of closed shell atoms lead to the linear correlations. The proposed static exchange–correlation charge density concept [S. Liu, P. A. Ayers, and R. G. Parr, J. Chem. Phys. 111, 6197 (1999)] is used to interpret these relationships. The maxima in the static integrated radial exchange–correlation charge density function, Qxc(r), in atoms are shown to reflect the shell boundaries. The quantum Monte Carlo density derived exchange–correlation potentials for Be and Ne are used to obtain Qxc(r) that can be used as standards to directly assess the quality of approximate exchange–correlation potentials. For the negative ions, Qxc(r) displays a characterstic outer minimum as a consequence of the Sen–Politzer theorem [K. D. Sen and P. Politzer, J. Chem. Phys. 90, 4370 (1989)]. This minimum is found to be related with the stability of negative ions.

Self-consistent solution of Dyson’s equation up to second order for open-shell atomic systems

Green’s function techniques are powerful tools for studying interacting many-fermion systems in a structural and diagrammatical way. The central equation in this method is the Dyson equation which determines, through an approximation for the self-energy, the Green’s function of the system. In a previous paper [J. Chem. Phys. 115, 15 (2001)] a self-consistent solution scheme of the Dyson equation up to second order in the interaction, the Dyson(2) scheme, has been presented for closed-shell atoms. In this context, self-consistency means that the electron propagators appearing in a conserving approximation for the self-energy are the same as the solutions of the Dyson equation, i.e., they are fully dressed. In the present paper this scheme is extended to open-shell atoms. The extension is not trivial, due to the loss of spherical symmetry as a result of the partially occupied shells, but can be simplified by applying an appropriate angular averaging procedure. The scheme is validated by studying the second-row atomic systems B, C, N, O, and F. Results for the total binding energy, ionization energy and single-particle levels are discussed in detail and compared with other computational tools and with experiment. In open-valence-shell atoms a new quantity—the electron affinity—appears which was not relevant in closed-shell atoms. The electron affinities are very sensitive to the treatment of electron correlations, and their theoretical estimate is a stringent test for the adequacy of the applied scheme. The theoretical predictions are in good agreement with experiment. Also, the Dyson(2) scheme confirms the nonexistence of a stable negative ion of N. The overall effect of the self-consistent Dyson(2) scheme with regard to the Dyson(1) (i.e., Hartree–Fock) concept, is a systematic shift of all quantities, bringing them closer to the experimental values. The second-order effects turn out to be indispensable for a reasonable reproduction of the electron affinity.

Adsorption of Radon on Metal Surfaces: A Model Study for Chemical Investigations of Elements 112 and 114

The adsorption properties of Rn on polycrystalline surfaces of the transition metals Cu, Ag, Au, Ni, and Pd are investigated experimentally by vacuum thermochromatography. This experimental approach provides a fast separation of short-lived nuclides of volatile elements on clean metal surfaces. The adsorption enthalpies of Rn are quantified from the experimental results using a thermodynamic equilibrium model and a Monte Carlo based kinetic model of mobile adsorption, developed in this work. The experimentally observed strength of Rn adsorption is given by the sequence: Ni > Pd ≈ Cu > Au > Ag. The obtained adsorption data are compared with results from empirical calculations of the weak interaction of closed shell atoms with metallic surfaces. An empirical model, which was developed on the basis of experimental adsorption data of Ne, Ar, Kr, and Xe, is extended in order to calculate the adsorption enthalpies of Rn. An excellent agreement is found between model results and the experimental data for the ad...

New Insights in Chemical Reactivity by Means of Electron Pairing Analysis

According to the Lewis model, valence electrons in closed-shell atoms and molecules can be arranged into pairs of electrons shared between bonded atoms and lone pairs that belong to a single atom. Within this scheme, ionic bonding arises from the transfer of electrons between atoms, while covalent bonding is related to the sharing of electrons between atoms. Over the years, this simple model has proven to be extremely useful for the description of the bonding patterns in many molecules, and to describe the electronic rearrangements taking place during chemical reactions. However, a physically accurate description of the electron pairing in atoms and molecules has to be based on the electron-pair density. Within the theory of atoms in molecules, one can define atomic localization and delocalization indices which describe the intra- and interatomic distribution of the electron pairs in a molecule. Therefore, these indices can be considered as a physically sound and numerically accurate extension of the Lewi...

Pick-off annihilation in positronium scattering from alkali-metal ions

When orthopositronium collides with a closed-shell atom or ion the ``pick-off'' process is the dominant process for positron annihilation. In pick-off annihilation the positron annihilates with electrons in the target but not with the electron that is part of the positronium atom. The rate for pick-off annihilation, expressed in terms of the dimensionless parameter ${}^{1}{Z}_{\mathrm{eff}},$ for orthopositronium scattering from ${\mathrm{Li}}^{+},{\mathrm{Na}}^{+},$ and ${\mathrm{K}}^{+}$ was computed with an ${L}^{2}$ variant of the fixed-core stochastic variational method. The threshold ${}^{1}{Z}_{\mathrm{eff}}$ for ${\mathrm{Li}}^{+}$ and ${\mathrm{Na}}^{+},$ which can form a stable bound state with Ps were found to be 0.067 and 0.73, respectively, while that for ${\mathrm{K}}^{+},$ which does not bind Ps, was 0.064.

Insertion effects on optical and mechanical properties in BP: the case of hydrogen

In this work, we investigate the effects of the insertion of a light element in the vacant sites of BP. Calculations have been performed by means of the ab initio pseudo-potential method with the local density approximation (LDA), using additionally the interstitial sites. A predictive study is presented for the charge density distribution at various k-points and for various conduction bands. We show that the X C point moves up in energy relative to the Γ C point when closed-shell atoms (H in this case) are substituted at the interstitial sites. Results indicate a change of the optical and mechanical properties for the resulting compound.

Hartree–Fock High-Precision Analytical Functions of Open-Shell Atoms

The algorithm of high-precision optimization of basis functions suggested previously for calculating the analytical Hartree–Fock orbitals of closed-shell atoms is generalized to open-shell systems described by the Roothaan method (1960). Expressions for the first (free gradient) and second (Hesse matrix) derivatives of the system's energy with respect to the nonlinear parameters (orbital exponents) of the basis functions are derived in terms of density matrices for the filled and open shells. An algorithm is proposed for high-precision optimization of the nonlinear parameters using these equations based on Murtagh–Sargent and Newton minimization procedures. To illustrate the application of this algorithm, we give optimization of the basis sets of Slater type functions for atoms from the second row, as well as for Al, Si, P, K, Sc, and Fe atoms. The analytical Hartree–Fock orbitals giving nearly Hartree–Fock energies are calculated with a high degree of accuracy.

Positronium scattering from closed-shell atoms and ions

The scattering of orthopositronium from He, Ne, Ar, ${\mathrm{Li}}^{+},$ ${\mathrm{Na}}^{+},$ and ${\mathrm{K}}^{+}$ is investigated with the fixed-core stochastic variational method. The scattering length for $\mathrm{Ps}\ensuremath{-}\mathrm{He}$ scattering was ${1.57a}_{0},$ a value consistent with the threshold cross sections derived from three positron lifetime experiments. The scattering lengths for the $\mathrm{P}\mathrm{s}\ensuremath{-}\mathrm{N}\mathrm{e}$ and $\mathrm{P}\mathrm{s}\ensuremath{-}\mathrm{A}\mathrm{r}$ systems were ${1.55a}_{0}$ and ${1.79a}_{0},$ respectively. That there was only a 15% variation among the scattering lengths is compatible with the experiment of Coleman et al. [J. Phys. B 27, 981 (1994)], who found the low-energy cross sections for He, Ne, and Ar to be about the same size. The scattering lengths for Ps scattering from ${\mathrm{Li}}^{+},$ ${\mathrm{Na}}^{+},$ and ${\mathrm{K}}^{+}$ were ${12.9a}_{0},$ ${28.5a}_{0},$ and $\ensuremath{-}{1.9a}_{0}.$ The relatively small magnitude of the ${\mathrm{P}\mathrm{s}\ensuremath{-}\mathrm{K}}^{+}$ scattering length strongly supports previous suggestions that the ${\mathrm{P}\mathrm{s}\ensuremath{-}\mathrm{K}}^{+}$ system does not support a bound state. The annihilation parameter ${}^{1}{Z}_{\mathrm{eff}}$ has also been computed as part of the analysis. The present values of ${}^{1}{Z}_{\mathrm{eff}}$ are about 2.5--3 times smaller than the accepted experimental values since short-range electron-positron correlations were not taken into consideration when the annihilation matrix element was evaluated.

Optimized effective potential in finite-basis-settreatment

A new method for solving the central equation of the optimizedeffective potential method is presented and applied to theexchange-only, orbital-dependent energy functional. Theoptimized local potential is written as the sum of a Slaterexchange potential, that gives the exact asymptotic behaviour,plus a short-range correction represented by a linearcombination of L2-functions. The method is easy to implement, can also be efficiently applied to molecules and clusters and gives high-quality results. Energies, eigenvalues and densities obtained for closed-shell atoms are compared withthe corresponding Hartree-Fock quantities.

Some considerations about Dirac–Fock calculations

In this work, Gaussian basis sets are generated for closed-shell atoms from He (Z=2) through No (Z=102) to be used in Dirac–Fock atomic and molecular calculations. Dirac–Fock–Coulomb total energy values obtained with these wave functions are compared with those calculated using a universal Gaussian basis set and relativistic Gaussian basis sets. A discussion between these three approaches is presented. Besides this, we have found that for several atoms from He through Hg (Z=80) the Dirac–Fock–Coulomb energies obtained with our wave functions are lower than the corresponding ones obtained with numerical-finite-difference calculations. A new procedure to generate Gaussian basis sets useful in relativistic calculations is suggested.

New Insights in Chemical Reactivity by Means of Electron Pairing Analysis

According to the Lewis model, valence electrons in closed-shell atoms and molecules can be arranged into pairs of electrons shared between bonded atoms and lone pairs that belong to a single atom. Within this scheme, ionic bonding arises from the transfer of electrons between atoms, while covalent bonding is related to the sharing of electrons between atoms. Over the years, this simple model has proven to be extremely useful for the description of the bonding patterns in many molecules, and to describe the electronic rearrangements taking place during chemical reactions. However, a physically accurate description of the electron pairing in atoms and molecules has to be based on the electron-pair density. Within the theory of atoms in molecules, one can define atomic localization and delocalization indices which describe the intra- and interatomic distribution of the electron pairs in a molecule. Therefore, these indices can be considered as a physically sound and numerically accurate extension of the Lewis model. In this paper, we use localization and delocalization indices to study the electron-pair reorganization taking place in five different reactions: two intramolecular rearrangements, a nucleophilic substitution, an electrophilic addition, and a Diels−Alder cycloaddition. For each reaction, we perform a comparative analysis of the electron-pairing patterns in reactants, transition states, and products. The evolution of electron-pairing along the reaction path is also studied. In all cases, the use of localization and delocalization indices provides useful insights on the electronic rearrangements taking place during the reactions.

Integrating symbolic and numeric techniques in atomic physics

The article describes ISNAP, a program for calculating atomic properties that uses an integrated symbolic and numerical approach for arbitrary excitations from closed-shell atoms. This program generates transition matrix elements and energy formulas up to third-order perturbation via the symbolic programming language Mathematica.

Second-order picture of correlation effects in closed-shell atoms

Results of many calculations of the MP2 correlation energies for ground states of closed-shell atoms (referred to as MP2/CA energies) are presented and studied. Special attention is paid to laying down rules which govern the dependence on the nuclear charge (Z dependence) and on the number of electrons (N dependence) of (a) the partial wave (PW) increments to the second-order pair energies, (b) the second-order pair energies, and (c) the configurational pair energies. It has been found that these energy increments disclose many regularities useful from both the physical and computational points of view. Some of the MP2/CA increments are quasi-transferable between similar systems. The results obtained are used as a starting point for an extensive discussion of the methodological significance of MP2/CA studies, and for indicating various actual and potential areas of application of the MP2/CA approach in many-electron theory.

Highly accurate relativistic gaussian basis sets for closed-shell atoms from He through to No

We have used the generator coordinate Dirac–Fock method for closed shell atoms, to generate accurate adapted Gaussian basis sets for ab initio relativistic self-consistent field calculations of some atoms from He ( Z=2) through to No ( Z=102). For all atoms studied, our Dirac–Fock–Coulomb and Dirac–Fock–Breit total energies are better than the corresponding ones obtained with previous larger Gaussian basis sets. Except for the Hg atom, our Dirac–Fock–Coulomb total energies are always equal to or lower than those calculated with the numerical finite-difference method (GRASP2 package). For No, we compare our Dirac–Fock–Coulomb and Dirac–Fock–Breit orbital energies with the corresponding values obtained with other approaches.

Exchange Contributions to Spin Polarization in Low-Energy Electron Scattering from Xe and Hg

Spin polarization of electrons scattered elastically from heavy atoms has attracted the attention of experimentalists and theoreticians for many years. A detailed account on the subject of spin polarization in the electron scattering from mercury and xenon is given in papers of Szmytkowski and Sienkiewicz [1, 2]. Since then, the relativistic configuration interaction method has been applied also for calculating spin polarization effects in the elastic scattering of electrons from xenon [3]. Recently, moreover, Dummler et al. [4, 5] measured the spin polarization of electrons for the elastic scattering from xenon and for the inelastic scattering from argon, krypton, and xenon. As has been pointed out by these authors, only the spin—orbit interaction is expected to contribute to the left-right asymmetry of the scattered electrons in the field of the target atom (Mott scattering). Apart from the spin—orbit interaction, however, the exchange interaction of the scattered electron with the bound-state electrons and the continuum—continuum interaction among the scattered electrons may also contribute to the spin polarization. In this paper we investigate the effects of exchange on the spin polarization of electrons which are scattered from heavy, closed-shell atoms like xenon or mercury which has a closed 6s 2 subshell. Our aim is to demonstrate that in elastic electron scattering from the closed-shell atoms substantial contribution to

An atomically detailed description of metal–dielectric interfaces: The crossover from surface to bulk conducting properties of Ag–Xe

An atomically detailed simulation method designed to be efficacious for modeling conduction properties of closed shell atoms or molecules resident at interfaces that was developed earlier is applied to a metal–dielectric interface of Ag–Xe. The effective mass of conduction electrons resident at Ag–Xe interfaces as a function of the number of layers of xenon present has been measured experimentally by the Harris group [J. D. McNeill, R. L. Lingle, Jr., R. E. Jordan, D. F. Padowitz, and C. B. Harris, J. Chem. Phys. 105, 3883 (1996)]. Here a simple yet effective theoretical model of the interface is developed and the effective mass that results is in quantitative agreement with the empirical measurements. 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. The metal is treated as a continuum within the effective mass approximation for the purpose of calculating the eigenenergies. To model the explicit potential energy functions, the electron–atom interaction is taken as a local pseudopotential that is fit to simultaneously reproduce the experimentally measured gas phase s-, p-, and d-wave scattering phase shifts. In simulating the interfacial environment the potential energy interaction between the electron and xenon atoms is modified to account for many-body polarization effects. This approach shows promise in modeling the conduction properties of more complex interfacial environments, including those of technological interest.