The correlation potential for two-electron atomic ions

The correlation potential is computed for two electron atomic ions with atomic numbers from 1 to 10 using the charge density reconstructed from a natural orbital expansion of a Kinoshita-like atomic wave function. Over the wide range of densities involved, the correlation potentials are not even approximately a local function of the density.     

Description of interelectronic correlation with the Pluvinage method

A correlated wave function method, already used for two-electron molecular systems is extended here to the case of two-electron atomic systems. A careful investigation of some exact properties of the wave function is performed (Kato's conditions, Fock's development, fulfilment of the virial theorem), showing its good behaviour at small interelectronic distances or in strongly correlated states. The application to Helium and H^? doubly-excited states is developed as a preliminary case of a more general study concerned with alkali-negative ions featuring in the second paper of this series. Energies and some autoionizing widths of He and H^? are calculated. Given the simplicity of our model, close agreement is found in all cases with experimental and other theoretical works. This provides a confirmation of the large application field of this method to general correlated two-electron systems.     

Nonlocal Wigner-like correlation energy density functional: parametrization and tests on two-electron systems

Reparametrization of Wigner's correlation energy density functional yields a very close fit to the correlation energies of the helium isoelectronic sequence. However, a quite different reparametrization is required to obtain an equally close fit to the isoelectronic sequence of Hooke's atom. In an attempt to avoid having to reparametrize the functional for different choices of the one-body potential, we propose a parametrization that depends on global characteristics of the ground-state electron density as quantified by scale-invariant combinations of expectation values of local one-body operators. This should be viewed as an alternative to the density-gradient paradigm, allowing one to introduce the nonlocal dependence of the density functional on the density in a possibly more effective way. Encouraging results are obtained for two-electron systems with one-body potentials of the form r(zeta) with zeta=-12,+12,1, which span the range between the Coulomb potential (zeta=-1) and the Hooke potential (zeta=2).     

A study of the adiabatic connection for two-electron systems

Some aspects of the adiabatic connection method are studied for two-particle spherically symmetric systems. Ground-state wave functions that are constrained by means of a set of moments to have the same density as a corresponding fully interacting system are obtained for noninteracting or partially interacting systems. Local one-body potentials that support these constrained wave functions are generated using a simple method. We examine an interacting two-particle system with a parameter-dependent one-body potential, which for a particular value of that parameter exhibits an intersection between the (3)S and the (3)P states, whereas the 2s and 2p eigenvalues of the corresponding Kohn-Sham potentials do not intersect along with the total energies. These results show that there do exist cases where occupying the orbitals from below in energy may not lead to the ground state, and that the inherent assumptions behind the adiabatic connection can sometimes be violated.     

Note on the Hylleraas-Eckart split-shell description of the groundstate of atomic two-electron systems

When the space part of the wavefunction of the groundstate of atomic two-electron systems is taken to be Φ(1, 2)=u(1)v(2)+v(1)u(2), where u=exp(?ar) and v=exp(?br), the parameters a and b as well as the energy associated with Φ(1,2) can be determined in the form of power series involving the nuclear charge Z. For small values of Z the convergence of these series is rather slow. The quantities mentioned, however, may be determined to any degree of accuracy by a method of stepwise approximation.     

Hybridization and correlation in a model calculation of a two-electron bond

The paper presents a quantitative examination of some aspects of the molecular two-electron problem, using a calculation for a two-electron homonuclear bond based on a restricted set of one 2s and one 2p orbital per nucleus. The single-determinant approximations with pure 2s STO's and with hybrid AO's are considered, as well as “partial” configuration mixing (CI) over MO's involving one hybrid per atom and “complete” CI over the whole four-orbital basis. The calculations simulate an exact calculation as regards hybridization and (left-right) correlation effects. These are studied, for the lowest state, at various distances, introducing the axial electron density as a means for interpreting quantitatively the various effects. The importance of orthogonalizing the 2s AO's to the corresponding 1s AO's and the MO's used to the MO formed by 1s AO's is reviewed, pending further numerical analysis.     

Rearrangement correction to higher polarizabilities of two-electron systems

In this paper we include the rearrangement correction (discussed in the preceding paper) in a coupled Hartree–Fock (CHF) calculation of atomic hyperpolarizabilities and other related properties. We have studied the effect of these corrections on properties like electric dipole hyperpolarizabilities, uniform electric field quadrupole polarizabilities and shielding factors in two-electron ions and have noticed significant changes in the computed values over the CHF results.     

Effect of Coulomb interaction between the electrons on two-electron redox-mediated tunneling

Two-electron non-adiabatic redox-mediated tunneling through a symmetric electrochemical contact with a bridge molecule having one electron energy level participating in tunneling is considered under ambient conditions. It is shown that the current/overpotential dependence in this system can disclose two distinct or overlapping clear-cut maxima depending on the value of the effective Coulomb repulsion energy. This new effect is due to the opening of the channel for tunneling of second electron with the variation of the electrode potential. The system manifests also a rectification effect in the current/bias voltage curve which depends on the value of the effective Coulomb repulsion energy.     

Variational calculations for the energy levels of confined two-electron atomic systems

An accurate variational calculation has been performed for the ground-state-energy values of confined two-electron isoelectronic series from He to Ar¹⁶⁺. The confinement is obtained by embedding the ion in an overall charge neutral environment like that of a plasma. The confinement potential is chosen as that of a screened Coulomb potential between charges, obtained from a Debye model. The wave function is expanded in terms of product basis sets involving interparticle coordinates. The energy levels are found to be less bound with an increase of the screening parameter and ultimately become unstable. One- and two-particle moments have been calculated for the first time under such screening. The study is expected to throw new light on the behavior of the energy levels of foreign atoms embedded in an overall neutral environment which can be treated like a plasma. Received: 1 May 2002 / Accepted: 4 September 2002 / Published online: 6 November 2002 Acknowledgements. P.K.M. thanks the Max Planck Institute for Astrophysics, Garching, for financial support of his research visit to the institute where part of the work was performed. He also thanks the Council of Scientific and Industrial Research, Government of India, for research grant no. (03)/(0888)/99/EMR II. Correspondence to: P.K. Mukherjee e-mail: sppkm@mahendra.iacs.res.in     

Semiempirical calculation of two-electron integrals using bipolar expansion of the Ohno potential

Bipolar expansion of the Ohno potential as a method of calculating two-center Coulomb integrals that appear in the NDDO approximation is generalized to one-center two-electron integrals. A unified semiempirical scheme is suggested for estimating two-electron interactions in molecules. This scheme can be readily extended to arbitrary Slater basis sets (including the s,p,d-orbitals) and involves no a priori data on the valent states of atoms. In this work, the scheme is employed to extend the semiempirical PM3 method to the s,p,d-basis set. The efficiency of the method is proven by test calculations of 24 chromium compounds (π-complexes, carbonyls, isocyanides, etc.). Scientific Research Institute of Chemistry at N. I. Lobachevskii Nizhnii Novgorod State University. Translated fromZhurnal Struktumoi Khimii, Vol. 36, No. 4, pp. 593–599, July–August, 1995. Translated by I. Izvekova.     

Study of some interelectronic properties in helium-like atoms

By means of the optimumM-term Hylleraastype wavefunctions with 1≦M≦6 we study various interelectronic properties of the Helium-like atoms with nuclear chargeZ=1, 2, 3, 5 and 10. Leth(u) denote the spherically averaged electron-pair density of a finite many-electron system. Firstly we found that the intracule functionh(u)/u ^α of the above-mentioned atoms is (i) monotonically decreasing from the origin for α≥α₁ and (ii) convex for α≥α₂, where α₁ and α₂ are positive constants which depend onZ andM. Then we show that the electron-electron cusp condition, i.e. thath′(0)=h(0), may be extended in the sense that the inequalityh(u)?h′(u)≧0 is valid for anyu≥0. Thirdly, it is shown that the inequalities involving three interelectronic moments 〈u ⁿ 〉 recently found by the authors are, at times, of great quality. Finally the goodness of some bounds to the characteristics of the maximum ofh(u) and to the total interelectronic repulsion energy is discussed in detail.     

Effective potential model for calculating the energy shift in the ground state of two-electron atoms

An effective operator for the electron–electron interaction derived earlier has been shown to be successful for calculating the ground-state energy shift values for 10 members of the helium isoelectronic sequence in terms of a single free parameter. Some possible applications of the modified interaction operator for semiempirical calculations are suggested.     

The principle-quantum-number (and the radial-quantum-number) expansion of the correlation energy of two-electron atoms

The second-order correlation energy of two-electron ions is studied in terms of an expansion in minimal approximations to the first-order natural orbitals (NOs). The non-linear parameters of these NOs are determined by minimization of the second-order energy. An approximation to the total second-order correlation energy is obtained as a sum of increments e(lp), depending on the angular quantum number l and the radial quantum number p. (Either l or p can be eliminated in favor of the principal quantum number n = l + p.) Closed expressions for these energy increments are derived. For fixed p the increments go as (l + 1)(-5). This is consistent with the behavior of the exact partial wave increments (that depend on the parameter l only) as (l + 1/2)(-4). While the partial wave increments correspond to a summation of e(lp) over p, other partial summations of the two-parameter increments lead to either the principal-quantum-number expansion (PQNE) with energy increments approximately n(-4), or the radial-quantum-number expansion, with a less transparent convergence pattern. Unfortunately these partial summations can neither be done in closed form nor from the asymptotic expansion, but some insight is obtained from a numerical summation. The hope to find a rigorous derivation of the PQNE has not been fulfilled.     

Approximate formulas for the characteristics of interelectronic angle densities

The accuracies of approximate formulas are examined for several characteristics of the interelectronic angle density A(₁₂), where ₁₂ (0₁₂) is the angle subtended by the position vectors r₁ and r₂ of two electrons. Numerical results for 102 atoms show that simple approximations have sufficient accuracies for the moments with n=1–4, the central moments _n with n=2, 4, and the kurtosis, when measured by the absolute and relative errors. For heavy atoms, however, the relative errors for the third central moment ₃ and the skewness are large.     

Subshell-pair interelectronic angles of atoms in momentum space

Average angles between linear momenta of an electron in a subshell nl and another electron in a subshell nl are examined for the 102 atoms He through Lr in their ground states, where n and l are the principal and azimuthal quantum numbers, respectively. Congruency in the mathematical structures of the average interelectronic angles in position and momentum spaces leads to the theoretical results that with even |l–l| are exactly equal to 90°, while with odd |l–l| are always larger than 90°. Numerical analyses of 3,275 subshell-pair angles with odd |l–l| in the 102 atoms clarify that deviations of the total average interelectronic angles from 90° are mainly governed by subshell pairs with |n–n|1 and |l–l|=1, in contrast to the position-space results where only subshell pairs with n=n and |l–l|=1 are important.Acknowledgments. We thank Mr. T. Shimazaki for his assistance in the compilation of data. This work was supported in part by a Grant-in-Aid for Scientific Research from the Ministry of Education of Japan.     

A semiempirical investigation of interelectronic exchange coupling in bisected poly(1,4-phenylene) polycation model systems

AM 1 SCF -MO -CI computations find the bisected biphenyl dication to have nearly degenerate triplet and singlet states, with the lowest-energy state being a quininoid singlet planar dication. The bisected perchlorobiphenyl dication favors a triplet ground state by a small amount (0.4-1.9 kcal/mol), in qualitative agreement with recent experimental findings and with theoretical expectations that such an orthogonal open-shell pi-system should exhibit ferromagnetic exchange coupling. The higher oligomeric bisected para-linked phenylenes polycations do not show an appreciable computational preference for a high-spin multiplicity ground state either with or without perchlorine substitution. Chlorine substitution para to the 1,1′-linkage may lend a unique stabilization to the biphenyl system, which is not available in higher oligomeric analogs of poly(1,4-phenylene)s. The small magnitude of ferromagnetic exchange in these systems suggests that small geometric or substituent effects may confound experimental efforts to design polymeric ferromagnetic materials by this strategy. © 1992 John Wiley & Sons, Inc.