Closed-shell Atoms Research Articles

Inconsistent kinetic energy functionals of electron gases in the presence of inhomogeneous magnetic fields

The two formally equivalent kinetic energy functionals of an electron gas in the presence of inhomogeneous magnetic fields give inconsistent results when used in a Gordon-Kim (interacting closed-shell atom) calculation. This inconsistency is a direct measure of the accuracy of the Thomas-Fermi (slowly varying potential) assumption for the system studied.

Interaction universality and scaling laws for interaction potentials between closed-shell atoms and ions

A universal scaling scheme is developed for closed-shell interactions. The exchange energies (total energies minus the Coulombic energies) are found to scale with two parameters to universal interaction curves for noble gas–noble gas, alkali ion–noble gas, and halogen ion–noble gas interactions. The interaction potentials constructed from the universal interaction curves agree well with experimentally determined potentials, and also successfully reproduce measured ion mobilities and diffusion coefficients. The universal interactions can be viewed not just as a correlation scheme, but also as operating to extend the range of the potentials for a number of ion–atom systems to both larger and smaller distances than are presently probed by direct measurements. They also provide the basis for predictions of potentials for systems lacking experimental measurements. In the case of the noble gases, they reduce by two the number of parameters required for the formulation of an accurate extended principle of corresponding states.

Alternative static-exchange formalism: Low-energy electron scattering with heavy alkaline-earth atoms.

A static-exchange formalism is proposed based on the assumption that the scattering electron undergoes the same interaction as the extra electron in the negative ion of the target atom. In this method the wave function of the negative ion of the target atom is calculated, and the wave function of the frozen neutral core of the negative ion is used in the calculation of the interaction of scattering electron with the target atom. The screening effect of the incident electron on the target atom is approximated by that of the absorbed extra electron on the neutral core of the corresponding negative ion. The spin-polarization effect of the incident electron on the closed-shell target atoms is also considered by spin-polarized self-consistent field calculations for the negative-ion structures. A parameter-free spin-polarized correlation-polarization potential is included to represent the correlation and polarization effects in both the structure and scattering calculations. In order to account for the relativistic effects for heavy targets, a quasirelativistic approach is applied to the calculations of the negative-ion structures and the scattering processes. The results of low-energy electron scattering with Ca, Sr, Ba, and Ra atoms are given for energies between 0.01 and 5 eV.

Electron correlations and spin-orbit interaction in two-photon ionization of closed-shell atoms: A relativistic time-dependent Dirac-Fock approach.

Electron-correlation and spin-orbit-interaction effects are known to play an important role in the quantitative description of multiphoton ionization of heavy atoms. In this paper an ab initio approach to two-photon ionization (2PI) of closed-shell atoms in the framework of the relativistic time-dependent Dirac-Fock theory is proposed. This formulation is known to contain important electron-correlation corrections and includes the spin-orbit interaction by use of relativistic wave functions. Computational results for nonresonant 2PI total cross sections of the rare gases are given. The approach is suitable for calculations of angular distributions, branching ratios, and autoionizing resonances.

XC and HFD-B potential energy curves for Xe-Xe and related physical properties

The XC (exchange-Coulomb) and the HFD (Hartree-Fock-dispersion) potential models for the interaction of two closed shell atoms are reviewed briefly. It is shown that while the original XC potential model (XC-1) does not lead to an optimal potential for the Xe-Xe interaction, two variants, XC-2 and XC-3, do lead to optimal interaction energies for this interaction as a function of the interatomic distance R. The three XC potentials, two HFD-B type potentials, and three other literature potentials are compared with respect to their predictive ability for various microscopic and (dilute gas) macroscopic properties of Xe. One of the HFD-B potentials, developed here, is a modification of the original HFD-B potential for Xe-Xe and this HFD-B2 potential, and the XC-3 potential, are apparently the most reliable representations of the two-body Xe-Xe interaction available. The two-bodypotentials are also used to help discuss the problems associated with the representation of many-body interactions in rare gas systems.

Low-order perturbation theory for shake-up cross sections in atomic photoionization in a local-potential model.

Cross sections for the process in which photoionization of an atom is accompanied by excitation of an electron from an occupied orbital to an unoccupied orbital are calculated in lowest order in perturbation theory. The calculation is carried out in a local-effective-potential model for the atom that permits the summation over the intermediate states by using the Green's function for ordinary differential equations. It is assumed that the coupling scheme for the final ionic state is that the two holes couple to a state of definite ${L}_{12}$ and ${S}_{12}$ that then combines with the particle state to give a state of definite L and S. Expressions for the total cross section and asymmetry parameter are given for closed-shell atoms. Calculated results for Ne photoionization are compared with experimental results.

Application of a New Non-relativistic Self-consistent-Field lMethocd to Heavy Closed-Shell Atoms

Application of a New Non-relativistic Self-consistent-Field lMethocd to Heavy Closed-Shell Atoms

Correlation and relativistic effects for many-electron systems. II. Second-order energies for closed-shell atoms

The perturbation approach to the Dirac-Coulomb equation recently developed by the present authors is applied to the calculation of the energy correction at the first- and second-order level for a zero-order Hamiltonian taken as a symmetric sum of Fock operators. Results for several He-, Be- and Ne-like systems (up to Z=80) as well as for Zn2+ are presented and discussed.

Electron and kinetic energy densities for an arbitrarily closed shell in a bare Coulomb field from s-state densities.

It is known from previous work that the total electron density matrix for closed-shell atoms in a bare Coulomb field is determined solely by the corresponding s-state contribution. In keeping with this philosophy, an expression is derived for the closed-shell electron density ${\ensuremath{\rho}}_{n}$(r) and kinetic energy density ${t}_{n}$(r) in terms only of s-state components ${\ensuremath{\rho}}_{\mathrm{no}}$(r) and ${t}_{\mathrm{no}}$(r) for arbitrary quantum number n. A proposal for the generalization of the present model for any central field of force is given in the Appendix.

A complete basis set model chemistry. I. The total energies of closed-shell atoms and hydrides of the first-row elements

The major source of errror in most ab initio calculations of molecular energies is the truncation of the one-electron basis set. A complete basis set model chemistry is defined to include corrections for basis set truncation errors. This model uses double zeta plus polarization level atomic pair natural orbital basis sets to calculate molecular self-consistent-field (SCF) energies and correlation energies. The small corrections to give the complete basis set SCF energies are then estimated using the l−6 asymptotic convergence of the multicenter angular momentum expansion. The calculated correlation energies of the atoms He, Be, and Ne, and of the hydrides LiH, BH3, CH4, NH3, H2O, and HF, using the double zeta plus polarization basis sets vary from 83.0% to 91.2% of the experimental correlation energies. However, extrapolation of each of the pair energies and pair-coupling terms to the complete basis set values using the asymptotic convergence of pair natural orbital expansions retrieves from 99.5±0.7% to 101.1±0.6% of the experimental correlation energies for these atoms and molecules. With the exception of ammonia which gave 101.1%, the calculated correlation energies agree with the experimental values to within the error limits of the experiments for all these atoms and molecules with more than four electrons. The total extrapolated energies (ESCF+ECorrelation) are then in agreement with experiment to within ±0.0014 hartree (root mean square deviation) and represent the most accurate total energy calculations yet reported for the molecules. The largest discrepancies with experiment occur for methane, where we obtain ETotal =−40.5112 hartree compared to EExpt =−40.514±0.002 hartree, and ammonia, where we obtain ETotal =−56.5659 hartree compared to EExpt =−56.563±0.002 hartree.

ATOMIC MANY-BODY CALCULATIONS ON THE GROUND STATE EXCHANGE-CORRELATION ENERGY OF BERYLLIUM ATOM

Up to now, almost all many-body theoretical calculations on the ground state of atoms took the Hartree-Fock (HF) model as zeroth order approximation. In this paper, zeroth order Hamiltonian is taken to be Hartree-Fock-Slater (HFS) type, in the double excitation approximation, many-body calculation on the ground state exchangecorrelation energy of beryllium atom is made, the result is in good agreement with experiments and other many-body theoretical calculations, which take HF model as zeroth order approximation. Our calculation shows that, take the HFS model as zeroth order approximation instead, successful many-body calculation on the ground state property of closed shell atoms can also be made.

Asymptotic formula far from nucleus for exchange energy density in Hartree-Fock theory of closed-shell atoms.

In Hartree-Fock theory, the exchange energy density can be expressed solely in terms of the first-order density matrix. Far from the nucleus of a closed-shell atom, idempotency of the density matrix yields the exchange energy density as the magnitude of the Coulomb energy ${e}^{2}$/r times the electron density \ensuremath{\rho}. Thus two lengths enter the asymptotic form in contrast to ${\ensuremath{\rho}}^{\mathrm{\ensuremath{-}}1/3}$ alone of local-density theory.

Complex-basis-function treatment of photoionization in the random-phase approximation.

Complex-basis-function techniques are used to implement the equations of the random-phase approximation (RPA) in matrix form. This approach allows the direct extraction of total photoionization cross sections from a finite series of (complex) transition energies and oscillator strengths. The RPA is an effective means for including electron correlation effects on the photoionization of closed-shell atoms and molecules. The procedure demonstrated here provides a rigorous way of solving the RPA equations for continuum photoabsorption without resorting to numerical integration. The results of calculations on He and N/sub 2/ are presented. Correlation effects are found to significantly influence the threshold behavior of the N/sub 2/ photoionization cross sections.

Chemical bonding between closed shell atoms? Structural and physical properties of alkali metal mercury compounds

Chemical bonding between closed shell atoms? Structural and physical properties of alkali metal mercury compounds

Wigner's phase-space function and atomic structure: II. Ground states for closed-shell atoms.

We present formulas for reduced Wigner phase-space functions for atoms, with an emphasis on the first-order spinless Wigner function. This function can be written as the sum of separate contributions from single orbitals (the natural orbitals). This allows a detailed study of the function. Here we display and analyze the function for the closed-shell atoms helium, beryllium, neon, argon, and zinc in the Hartree-Fock approximation. The quantum-mechanical exact results are compared with those obtained with the approximate Thomas-Fermi description of electron densities in phase space.

Correlation energy correction as a density functional. A model of the pair distribution function and its application to the first- and second-row atoms and hydrides

A scheme for correlation energy corrections E c based on asymptotic properties of the effective pair distribution function g( r 1; r 2) and correlation energy densities ϵ c{ϱ( r 1)} has been considered. To obtain ϵ c{ϱ( r 1)} model functions g( r 1; r 2) are used in the local spin density approximation (LSDA). This model yields the correct high-density limit for the homogeneous electron gas ϵ c{ϱ} and reproduces empirical E c values with an average error amounting to 2.2% for the first- and second-row closed-shell atoms, 5.6% for the first-row hydrides XH and 3.4% for the second-row hydrides XH.

Theoretical study of Ca(4s5p 1P)→Ca(4s5p 3P) transitions in collisions with He: Integral cross sections and alignment effects

The fully quantum theory is developed for 1P→3P transitions in collisions of electronically excited (nsn′p) alkaline earth atoms with closed shell atoms. Spin-changing transitions occur by means of the small spin–orbit mixing between the 1P and 3PJ=1 states of the isolated atom, and are facilitated by the crossing between the 1Π and 3Σ potential curves which correlate, respectively, with the 1P and 3P asymptotes. Close-coupled calculations are carried out for the Ca(4s5p)+He system, based on four different choices of the necessary interaction potentials. Particular attention is devoted to the simulation of the recent experiment of Hale, Hertel, and Leone [Phys. Rev. Lett. 53, 2296 (1984)], in which the 1P→3P cross section was determined in a crossed-beam experiment as a function of the orientation of the initially excited 5p orbital. This polarization dependence depends critically on the long-range splitting between the 1Π and 1Σ curves. A fully adiabatic description of the collision dynamics is used to interpret the results of the quantum scattering calculations. No clear-cut theoretical justification is found for the ‘‘orbital following’’ models which have been developed to interpret prior experimental studies of collisions involving excited atoms in P electronic states. Rather, a picture emerges in which the initially selected orientation of the Ca p orbital correlates, at short range, with equal probability to Σ-like and Π-like potential curves. Variations in the 1P→3P cross sections are due to long-range Coriolis coupling between the electronic orbital and nuclear orbital momenta and may reflect quantum interference effects between the Π-like and Σ-like adiabatic potentials.

Reliable Gaussian basis sets for closed‐shell atoms

AbstractMedium size Gaussian basis sets for inert‐gas atoms (from neon to xenon) have been constructed using the energy optimization method which maintains reliable description of the long‐range valence atomic region. These basis sets have been tested in SCF calculations on homonuclear inert‐gas dimers. For Ne2, Ar2, and Kr2, the present results have been analyzed carefully and compared with those obtained using extended basis sets (for Kr2 extended benchmark calculations are also reported). Our interation energies agree well with accurate values and are compared with experimental data. For Ne2 and Ar2, detailed studies of basis set superposition error also are presented.

Nonlinear response of closed-shell atoms in the density-functional formalism

The nonlinear response of an arbitrary electronic system to a time-dependent perturbation is treated within the density-functional formalism. Expressions for quadratic and cubic responses for a system of independent electrons are obtained in a form suitable for numerical calculations. The frequency dependence of the linear and cubic electric susceptibilities of rare-gas atoms are computed and compared with experiment.

Convolution representation of the relation between total electron density and that of s states in closed-shell atoms.

Motivated by the Coulomb-field result that the derivative of the density \ensuremath{\rho}(r) for an arbitrary number of closed shells is directly proportional to the s-state density ${\ensuremath{\rho}}_{s}$(r), we have explored for closed-shell atoms a convolution relation between ${\ensuremath{\rho}}_{s}$(r) and \ensuremath{\partial}\ensuremath{\rho}/\ensuremath{\partial}r. This relation is most readily expressed in K space, and we thereby establish certain relations between the scattering factors f(K) and ${f}_{s}$(K) corresponding to total density and s density, respectively. The method is illustrated by using near-Hartree-Fock accuracy data of Clementi for closed-shell atoms Ne and Ar. For the Hartree-Fock theory, it is shown that at large r, ${\ensuremath{\rho}}_{s}$(r)\ensuremath{\propto}${r}^{\mathrm{\ensuremath{-}}4}$\ensuremath{\rho}(r). Use is made in the convolution representation of the electron-nuclear potential energy of the closed-shell atom and the second derivative ${\ensuremath{\partial}}^{2}$\ensuremath{\rho}/\ensuremath{\partial}${r}^{2}$ evaluated at the nucleus.