Closed-shell Atoms Research Articles

On the relationship between first-order exchange and Coulomb interaction energies for closed shell atoms and molecules

First-order Heitler-London interaction energies E (1) HL, and their first-order Coulomb and exchange components E (1) C and E (1) X, have been computed for the Rg-Rg′, H2-Rg and N2-Rg interactions, where the rare gas Rg or Rg′ can be He, Ne, Ar or Kr. High quality self-consistent field wavefunctions are used to represent the isolated species and the results are presented as a function of the interspecies distance and relative orientation (where appropriate). The results are used to investigate the relationship between the first-order exchange and Coulomb energies, and it is found that the often used linear relationship, E X = -γ(1 + aR)E (1) C, requires modification for interactions involving molecules for physically significant (small) values of R. The modification proposed is E (1) X = -γ(1 + aR)(E (1) C - E (1) S), where E (1) S is a correction term for the singularity occurring in E (1) C, and two versions of E (1) S are developed. The importance of the singularity, and the validity of the relationshi...

Self-consistent local-density approximation with model Coulomb pair-correlation functions for electronic systems.

The model Coulomb pair-correlation functions proposed several years ago by Gritsenko, Bagaturyants, Kazansky, and Zhidomirov are incorporated into the self-consistent local-density approximation (LDA) scheme for electronic systems. Different correlation functions satisfying well-established local boundary conditions and integral conditions have been tested by performing LDA calculations for closed-shell atoms. Those correlation functions contain a single parameter which can be optimized by fitting the atomic correlation energies to empirical data. In this way, a single (universal) value of the parameter is found to give a very good fit for all the atoms studied

Correlation forces in electron-scattering processes via density-functional theory: Electron collisions with closed-shell atoms.

A reliable knowledge of the short-range behavior of the generalized response function in low-energy electron scattering from atoms (or molecules) is a very important tool for the quantitative study of low-energy resonances, elastic- and inelastic-scattering cross sections, and the corresponding angular distributions. In the present study, a description of the required function is used by starting from a short-range representation of the correlation forces via local density-functional theory. Results are reported for elastic scattering from rare gases at various collision energies and rather good agreement is found in all cases both with experiments and with more sophisticated calculations. The physical correctness of the present approach and its capability of describing angular distributions and elastic collision processes over a broad range of energies through fairly simple calculations make it an attractive proposition for further extensions to molecular targets and to electronic excitation processes.

Many-body perturbation-theory formulas for energy levels of excited states of closed-shell atoms.

Many-body perturbation-theory formulas are derived for one-particle--one-hole excited states of closed-shell atoms. Both analytic results and Goldstone diagrams complete through third order are presented, and a sample calculation of a transition energy in neonlike xenon is carried out.

Bounds on microscopic physics from P and T violation in atoms and molecules

Atomic and molecular electric dipole moments are calculated within the minimal supersymmetric standard model. Present experiments already provide strong bounds on the combination of phases responsible for the dipole moments of the neutron and closed shell atoms. For a supersymmetry breaking scale of 100 GeV, these phases must be smaller than ∼10 −2.

Application of the relativistic theory to the spin-polarized local-density functional theory

The full relativistic method for atomic and molecular calculations may not be incorporated directly into spin-polarized local-density functional theory because of the spin-orbital coupling. The spin-orbital coupling term in the Schrödinger equation causes eigen-states which cannot be labelled by the quantum number ( nlm l m s ). The application of the generalized exchange local-spin-density functional theory combined with a relativistic correction is discussed and tested for some closed-shell atoms. The calculated results are compared with those in ▪ theory, relativistic ▪ theory, Hartree-Fock theory, and Dirac-Hartree-Fock theory.

Relativistic coupled-cluster calculations for closed-shell atoms

Relativistic coupled-cluster calculations including single and double excitations are reported for the ground states of He, Be, Ne and Ar. The no-pair Dirac—Coulomb Hamiltonian is taken as the starting point. The reference state of the single determinant Dirac—Fock wavefunction is calculated in a basis of balanced Gaussian spinors. Comparison with corresponding nonrelativistic calculations indicates relatively small nonadditivity of relativistic and correlation effects, ranging from 10 −6 hartree for He to 10 −3 hartree for Ar.

Implications of many-body forces for equations of state at high pressure

In this paper we review our recent work concerned with assessing the significance of many-body forces for short-range interactions of closed shell atoms and molecules. Ab initio molecular orbital calculations (of the supermolecule type) have been carried out to determine three-body potentials for the following species: He, Ne, H 2 , N 2 , CO and CO 2 . For He, Ne, H 2 and N 2 we have also carried out calculations of the four-body potential for a limited number of orientations. These studies show that, for all these species, there are significant deviations from pair-wise additivity at short separations. The effect of these many-body interactions on the equation of state for dense fluids (such as detonation products) is being investigated by Monte Carlo simulation, and recent results for high-pressure helium are described.

Variational density of electrons for large closed shell atoms

An exact expression for the atomic form factor for closed shell atoms is derived using an antisymmetric multielectron wave function. It is shown that for large atoms it can be written as an integral over a Bessel function. Using the Hankel transform it gives an expression for the density of electrons which is of Thomas–Fermi form which was found earlier by Pucci and March.

Many-electron correlation effects on anomalous scattering factors.

The effect of many-electron correlations on anomalous scattering factors in Rayleigh scattering is studied, in the case of the Ar atom, using dispersion relations and the relativistic random-phase approximation (RRPA). The correlation effect changes the Ar 3s-subshell photoionization cross sections significantly compared with the corresponding independent-particle approximation calculations; thereby the anomalous scattering factors of Rayleigh scattering from this subshell also experience marked structural changes. But the Ar 3p subshells dominate the coherent total-atom scattering amplitude so that subshell structural changes in the Ar 3s subshell due to many-electron correlation effects are not seen in the total-atom scattering cross section or the total-atom anomalous scattering factors, which are the physical observables in Rayleigh-scattering experiments. One anticipates this outcome generally for closed-shell atoms, while in the case of open shells one can anticipate a greater importance for the many-electron-correlation effects.

Relativistic calculations for atoms: self-consistent treatment of Breit interaction and nuclear volume effect

Estimates of the ground state energies of several closed-shell atoms and ions with atomic numbers 1<or=Z<or=102 are presented. A relativistic formulation has been employed: energies are obtained as expectation values of the appropriate combination of the Dirac, Coulomb and Breit Hamiltonians with respect to the corresponding Slater determinants of four-component spherical spinor orbitals. Atomic nuclei have been modelled as uniform spherical charge distributions. An expansion method using a kinetically-balanced basis constructed from Gaussian type functions ( approximately rne- alpha ir2, where n is an integer and the alpha i form a geometric progression) has been used to formulate the variational problem for the optimal orbital radial functions in each case. The resulting sets of coupled algebraic eigenvalue problems were solved approximately using the self-consistent-field iterative method. The authors' results are compared with those of other workers and with finite-difference calculations carried out specifically for this purpose. They estimate the accuracy of their work to be within a few parts in 108 in most cases.

Comparative Study of the Decay Mechanisms for 4d Resonances of lodine and 3p Resonances of Copper

This paper describes the approximations which allow to calculate the rates of the various decay processes for core resonances below inner-shell thresholds of open-shell atomic system (4d thresholds of iodine and 3p of copper). Moreover, it emphasizes the different mechanisms that predominantly produce either singly-charged ions when a valence state decay is considered, or doubly-charged ions in case of an excitation to a level of a Rydberg series. Despite different decay mechanisms, the main conclusions are similar to those obtained for closed-shell atoms. In particular, the rate of the double Auger with the Rydberg electron spectator or nearly spectator (shake-up process) in the first step is increasing as soon as the first resonances but this decay path is progressively replaced by shake-off (2 electrons ejected simultaneously) whose rate is increasing with the principal quantum number n of the Rydberg electron.

Enhancement of tunnel current through closed shell atoms

The self-energy of the tunneling electron due to a foreign atom located in the gap between the surface and the tip of STM is estimated analytically. It is found that the tunnel potential barrier height is significantly reduced in the region directly above the atom. This effect would partly explain the reason why some adsorbed rare gas enhances the tunnel current strongly. A similar enhanced tunnel current would generally be expected when there are intervening molecules in the tunnel gap. An explanation of the bimodal behaviour of the metal/rate gas adsorption system, and direct experimental confirmation thereof through observations on the tunnel current is suggested.

Enhancement of tunnel current through closed shell atoms

The self-energy of the tunneling electron due to a foreign atom located in the gap between the surface and the tip of STM is estimated analytically. It is found that the tunnel potential barrier height is significantly reduced in the region directly above the atom. This effect would partly explain the reason why some adsorbed rare gas enhances the tunnel current strongly. A similar enhanced tunnel current would generally be expected when there are intervening molecules in the tunnel gap. An explanation of the bimodal behaviour of the metal/rate gas adsorption system, and direct experimental confirmation thereof through observations on the tunnel current is suggested.

The relativistic polarized orbital theory of the elastic electron and positron scattering from closed-shell atoms

The relativistic polarized orbital theory of the elastic electron and positron scattering from closed-shell atoms is formulated in a similar way to that used in the non-relativistic case. The scattering equations involving the relativistic polarization potential for both types of projectile and also the exchange-polarization terms for the electron projectile are derived. The relativistic formula for the positron-atomic-electron annihilation coefficient Zeff is presented.

Property calculations by coupled cluster based linear response theory: dynamic polarizability and van der Waals coefficient

We propose and implement in this paper a highly correlated method for computing dynamic polarizability of closed-shell atoms and molecules and the van der Waals coefficient C 6 of atoms within the framework of coupled cluster based linear response theory (CC-LRT). Excitation energies (EE), oscillator strengths and the dynamic dipole polarizability have been computed for He, Be and CH +. The coefficient C 6 has been calculated for He and Be. Comparison with the existing data and high quality CI results is found to be quite encouraging, indicating the promise of the method.

Spin density and density moments for the lithium ground state.

Accurate analytical charge and spin-electron densities for the lithium atom are obtained by using a systematic and reliable method recently developed and applied to closed-shell atoms. The convergence of the densities is analyzed in terms of well-defined improvements in the corresponding configuration-interaction wave functions, and mathematical criteria are used to test the stability of the densities and their derivatives. Fully converged results for one-electron properties and, in particular, for the Fermi-contact interaction are reported.

Wave functions with terms linear in the interelectronic coordinates to take care of the correlation cusp. II. Second-order Mo/ller–Plesset (MP2-R12) calculations on closed-shell atoms

The MP2-R12 method in approximations A and B as outlined in part I of this series is applied to the ground states of the closed-shell atoms He, Be, Ne, Mg, Ar, Ca, Cu+, Zn2+, and Kr, in terms of both STO and GTO basis sets. For He, Be, and Ne the partial wave increments of the various pairs are documented and compared with their conventional counterparts. The fast convergence of the partial wave increments, that go as (l+ (1)/(2) )−8 in the MP2-R12/B scheme, is demonstrated. From the MP2-R12 calculations more accurate estimates of the exact MP2 energies are possible than from the conventional partial wave expansion. The actually calculated values differ generally by a fraction of a 1% from the estimated basis sets limits if STO basis sets with l≤5 (in some cases l≤6) are used, while errors of typically 1% are obtained with GTO basis sets and l≤3.

Eight coordination—I. Effect of inter-ligand repulsion on the geometry of eight-coordinate complexes

The effect of non-bonded interactions (inter-ligand repulsion, ILR) on the geometry of eight-coordinate complexes was studied in the range of symmetry coordinates of the two highest symmetry structures, cube and hexagonal bipyramid (HBP). Only a few of the symmetry coordinates that convert the cube and the HBP into lower symmetry [dodecahedron (DD), square antiprism (SAP) and trigonal bicapped prism] were found to be important. ILR was demonstrated as the dominant factor in producing the lower symmetry structures for the closed-shell central atoms and it most certainly plays a very important role in helping or opposing the Jahn-Teller distortions for the orbitally degenerate complexes. The theoretical predictions were compared with a variety of structural data for ML 8. The predicted radial distortions were much larger than the experimental values and this was attributed to the electronic factors. Most of the angular distortions for ML 8 were explained in terms of a single e u vibration.

Diagrammatic many-body perturbation expansion for atoms and molecules: VII experiments in vector and parallel processing for fourth-order energy terms involving triply excited intermediate states

The efficient evaluation of the fourth-order energy terms corresponding to linked diagrams involving triply excited intermediate states which arise in the many-body perturbation expansion for the electron correlation energy of closed-shell atoms and molecules on vector processing and parallel processing computers is discussed. The linked-diagram theorem decouples the many-electron problem allowing efficient implementation on parallel processing machines. Furthermore, the computation associated with each of the resulting subproblems is very well suited to vector processing machines. A “dynamic load balancing” technique is employed in both a dedicated and a multi-user environment. Timing tests are reported for the CRAY X-MP/416 computer. Execution rates in excess of 828 Mflops are observed.