Intershell nl4f electron correlation effects

The pair correlation energies for some nl4f pairs of the ground state of the Yb atom are calculated for the first time. The partial wave (PW ) increments to the second-order pair energies are generated using numerical first-order radial pair functions obtained as the solution of two-dimensional differential equations. The analysis of the PW s contributions shows the dominant role of the df, fg, and gh PW s for the 4d4f pair, of the pf and dg PW s for the 4p4f and 5p4f pairs, and of the sf and pg PW s for the 4s4f, 5s4f, and 6s4f pairs. A discussion of the similarities and differences of the structure of the correlation energy found in this paper with those calculated earlier for smaller atoms is given.     

Ground state correlation energy of the Be-sequence forZ=4–20 in MCDF approximation

The ground state (J=0) electronic correlation energy of the 4-electron Be-sequence is calculated in the Multi-Configuration Dirac-Fock approximation forZ=4–20. The 4 electrons were distributed over the configurations arising from the 1s, 2s, 2p, 3s, 3p and 3d orbitals. Theoretical values obtained here are in good agreement with experimental correlation energies.     

Dynamic Lone Pair Expression as Chemical Bonding Origin of Giant Phonon Anharmonicity in Thermoelectric InTe

Loosely bonded (“rattling”) atoms with s² lone pair electrons are usually associated with strong anharmonicity and unexpectedly low thermal conductivity, yet their detailed correlation remains largely unknown. Here we resolve this correlation in thermoelectric InTe by combining chemical bonding analysis, inelastic X-ray and neutron scattering, and first principles phonon calculations. We successfully probe soft low-lying transverse phonons dominated by large In¹⁺ z-axis motions, and their giant anharmonicity. We show that the highly anharmonic phonons arise from the dynamic lone pair expression with unstable occupied antibonding states induced by the covalency between delocalized In¹⁺ 5s² lone pair electrons and Te 5p states. This work pinpoints the microscopic origin of strong anharmonicity driven by rattling atoms with stereochemical lone pair activity, important for designing efficient materials for thermoelectric energy conversion.     

Theoretical investigation on the GaH molecule and its positive ion

The gallium monohydride (GaH) molecule and its positive ion were theoretically investigated by abinitio molecular orbital calculations with a flexible basis set including g-type functions on the Ga atom. Electron correlations among not only the valence electrons of Ga 4s4p and H 1s but also the semi-core electrons of Ga 3d were incorporated by a size-consistent scheme of the coupled pair approximation. The contribution of the 3d electron correlation was found to be considerable on spectroscopic constants of both GaH and GaH⁺, especially on the bond length. Received: 25 July 1997 / Accepted: 13 November 1997     

Proton-impact excitation of HeI triplet levels

We investigated the excitation of the λ(1s3d ³ D?1s2p ³ P)=588 nm line of atomic helium by proton and deuteron impact for projectile energies 10 keV≦E _p≦25 keV. In apparent contradiction to Wigner's spin conservation rule, the emission cross section does not vanish. By measuring the intensity of the impact radiation as a function of homogeneous magnetic and electric fields applied to the collision volume, it has been shown thatp- andd-impact excitation of the 1s3d ³ D level of HeI proceeds via 1snl states withl≧3, which populate the 3³ D states by cascade decays. The well-known strong singlet-triplet mixing of these 1snl states enables a population of triplet states in accord with Wigner's rule. Accordingly, we determine the excitation cross section of the 1s4f multiplet from the measured emission cross section of the 588 nm line. The field-dependent signals give evidence that predominantly substates with |m _L|≦1 are excited.     

Identification of new lines in the beam-foil spectrum of B II–IV

Ten, six, and twenty-one new lines appearing in the beam-foil spectra of boron (30–200 nm) have been identified in B II, B III, and B IV, respectively. Energies have been determined with higher accuracy than obtained before for the 2p3s ¹ P ⁰, 2s6d ³ D, 2p3p ³ D, 2p3p ³ S, 2p3p ³ P, and 2p3p ¹ D terms in B II. First energy values are also reported for the 2s6d ¹ D and 2s7d ³ D terms in B II.     

A study of the electronic structure of polyvinylsiloxane (CH<Superscript>2</Superscript>CHSiO<Subscript>1.5</Subscript>)<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> by X-ray photoelectron spectroscopy and quantum chemical modeling in the DFT approximation

The electronic structure of polyvinylsiloxane polymeric chains (Si₂O₃(CHCH₂)₂)_n is studied by X-ray photoelectron spectroscopy and quantum chemistry in the DFT approximation. The binding energy of C and O ls electrons occupying inequivalent positions in the polymer coincides within the experimental accuracy. The binding energies for C and O (284.9 eV and 532.4 eV) and for Si2p-electrons (102.7 eV) well agree with the values for related compounds. The experimental data for the binding energy are reproduced in HF and DFT calculations only with the extended 6–311**(d) basis set. The highest occupied levels of the polymer are fy orbitals of vinyl groups     

1/Z perturbation theory for calculation of line strengths in the neon isoelectronic sequence

The line strengths of 2–2 and 3–3 transitions (2s²2p⁵3s–2s²2p⁵3p–2s²2p⁵3d, 2s2s2p⁶3s–2s2p⁶3p-2s2p⁶3d, 2s²2p⁵3l-2s2p⁶3l) have been calculated for the Ne isoelectronic sequence (Z = 14 ÷ 100). The calculation has been carried out in intermediate coupling. Relativistic corrections have been included through the Breit operator. Perturbation theory in 1/Z has been used to account for electronic interactions.     

Nature of closed‐ and open‐shell interactions between noble metals and rare gas atoms

Interactions between noble metals and rare gases have become an interesting topic over the last few years. In this work, a computational study of the open‐shell (d¹⁰s¹) and closed‐shell (d¹⁰s and d¹⁰s²) noble metals (M = Cu, Ag, and Au) with three heaviest rare gas atoms (Rg = Kr, Xe, and Rn) has been performed. Potential energy curves based on ab initio [MP2, MP4, QCISD, and CCSD(T)] and DFT functionals (M06‐2X and CAM‐B3LYP) were obtained for ionic and neutral AuXe complexes. Dissociation energies indicate that neutral metals have the lowest and cationic metals have the highest affinities for interaction with rare gas atoms. For the same metals, there is a continuous increase in dissociation energies (D_e) from Kr to Rn. The nature of bonding and the trend of D_e and equilibrium bond lengths (R_e) have been interpreted by means of quantum theory of atoms in molecules, natural bond orbital, and energy decomposition analysis. © 2013 Wiley Periodicals, Inc.     

An ab initio molecular orbital study of the structures and energies of neutral and charged bimolecular complexes of NH3 with the hydrides AHn (A = N,O, F,P, S,and Cl)

Hartree-Fock 6-31G(d) structures for the neutral, positive ion, and negative ion bimolecular complexes of NH₃ with the first- and second-row hydrides AH_n (AH_n = NH₃, OH₂, FH, PH₃, SH₂, and ClH) have been determined. All of the stable neutral complexes except (NH₃)₂, the positive ion complexes with NH₃ as the proton acceptor, and the negative ion complexes containing first-row anions exhibit conventional hydrogen bonded structures with essentially linear hydrogen bonds and directed lone pairs of electrons. The positive ion complex NH₄⁺ …? OH₂ has the dipole moment vector of H₂O instead of a lone pair directed along the intermolecular line, while the complexes of NH₄⁺ with SH₂, FH, and ClH have structures intermediate between the lone-pair directed and dipole directed forms. The negative ion complexes containing second-row anions have nonlinear hydrogen bonds. The addition of diffuse functions on nonhydrogen atoms to the valence double-split plus polarization 6-31G(d,p) basis set usually decreases the computed stabilization energies of these complexes. Splitting d polarization functions usually destabilizes these complexes, whereas splitting p polarization functions either has no effect or leads to stabilization. The overall effect of augmenting the 6-31G(d,p) basis set with diffuse functions on nonhydrogen atoms and two sets of polarization functions is to lower computed stabilization energies. Electron correlation stabilizes all of these complexes. The second-order Møller–Plesset correlation term is the largest term and always has a stabilizing effect, whereas the third and fourth-order terms are smaller and often of opposite sign. The recommended level of theory for computing the stabilization energies of these complexes is MP2/6-31+G(2d,2p), although MP2/6-31+G(d,p) is appropriate for the negative ion complexes.     

The atomic states of nickel

The Ni 3d ⁹ 4s ¹(³ D)–3d ¹⁰(¹ S) and 3d ⁹ 4s ¹(³ D)-3d ⁸4s ²(³ F) atomic excitation energies have been computed using large multireference CI wave functions in conjunction with a large ANO basis set. Radial correlation effects in the 3d shell are found to be very important and are included using CASSCF wave functions having the 3d and correlating 3d orbitals in the active space. The previous discrepancy (0.5 eV) with experiment for the ³ D–¹ S excitation is reduced to 0.1 eV when the 3d3d references are included in the CI. For the ³ F state, the 4s-4p near degeneracy gives rise to important 4s ²4p ² excitations in addition to the 3d3d excitations which are important for the ³ D and ¹ S states. Inclusion of only 3d-3d correlation in the ³ F and ³ D CI reference spaces yields a ³ F–³ D separation which is in error by 0.12 eV. Addition of the 4s ²4p ² excitations to the ³ F reference space is estimated to increase the discrepancy with experiment by an additional 0.1 eV.     

Exchange interaction during electron capture in Ar2+, K-collisions

During electron capture of Ar²⁺ from alkali atoms prevailingly Ar⁺ 4p states are occupied. While decaying they give rise to a spectrum which consists almost exclusively of 4p ? 4s and 4p ? 3d lines. The intensity of the lines turns out to be dependent on the Ar²⁺ projectile energy. At energies as low as 1 keV lines which belong to the Ar⁺ 3p ⁴(¹ D)n, l-system are by far the strongest. When increasing the projectile energy to 6 keV and above this system fades away and lines of the 3p ⁴(³ P)n, l-system appear. Considering that the primary beam consists constantly of 65% Ar²⁺ 3p ⁴ (³ P) and 35% Ar²⁺ 3p ³(¹ D) the strength surprises at which the 3p ⁴(¹ D)n, l system evolves from the electron capture. It is suggested that exchange interaction of the valence electron and one 3p-electron changes the 3p ⁴-core. Relative matrix elements for direct and exchange interaction of the valence electron and the 3p ⁴-core are calculated and used in a multi channel Landau Zener calculation. With this concept the measured spectra could be fitted by adopting only two parameters, namely one line strength and the ratio of the reduced matrix elements of direct and exchange interaction.     

Precision measurement of the energy of the 4d 9 5s 2 2 D 5/2 metastable level in Ag I

The energy of the 4d ⁹ 5s ^{2 2} D _5/2 metastable level in Ag I, which is the upper level of the very narrow 5s ² S _1/2 – 4d ⁹ 5s ^{2 2} D _5/2 two-photon transition at 661.2 nm, has been determined from precision measurements of the wavelengths of the 206.1 nm (5s ² S _1/2 – 6p ² P ₃ ^2/0 ) and 547.5 nm (4d ⁹ 5s ^{2 2} D _5/2 – 6p ² P ₃ ^2/0 ) lines emitted from a hollow-cathode discharge. The measured energy of the 4d ⁹ 5s ^{2 2} D _5/2 level, 30 242.286(7) cm^–1, is combined with the known hyperfine splittings and the estimated¹⁰⁷Ag-¹⁰⁹Ag isotope shift to obtain accurate absolute frequencies for the hyperfine components of the 661.2 nm transition. These results should help in the detection of the narrow 661.2 nm two-photon transition, which has been proposed as a new optical frequency standard.     

Isotope shifts and hyperfine structures investigation of doubly excited levels in SrI

We measured isotope shifts and hyperfine structure of visible transitions of stable strontium isotopes by means of Doppler-free saturated absorption spectroscopy. In particular, we investigated transitions between excited states where the upper level involves two excited electrons. We report hyperfine coupling constants for the levels 5p4d¹D₂, 5p4d³F₂, 5s4d³D₁, 5s6s³S₁, 5s5p³P₁ and, for some of the studied transitions, we separate the specific mass and volume contribution to the isotope shifts.     

Theoretical studies of organometallic compounds. III. Structures and bond energies of FeCHn and FeCH (n = 1, 2, 3)

The geometries and dissociation energies for the Fe? C and C? H bonds of FeCH_n and FeCH (n = 1, 2, 3) have been calculated by ab initio quantum mechanical methods using different effective core potential models and Møller–Plesset perturbation theory. The HW3 ECP model, which has a configuration [core] (n?1)s², (n?1)p⁶, (n?1)d¹, (n)s^m for the transition metals, is clearly superior to the larger core LANL1DZ ECP model with the configuration [core] (n?1)d¹, (n)s^m. The Fe? C bond energies calculated at correlated levels using the HW3 ECP are in much better agreement with experiment than the LANL1DZ results. This effect is mainly due to the higher number of correlated electrons rather than the inclusion of the outermost core electrons in the Hartree–Fock calculation. At the PMP4/HW3TZ/6-31G(d)//MP2/HW3TZ/6-31G(d) level, the theoretically predicted Fe? C bond energies for FeCH are in the range of 80% of the experimental values and have nearly the same accuracy as all-electron calculations using large valence basis sets and the MCPF method for the correlation energy. © 1992 by John Wiley & Sons, Inc.     

Study on Pair Correlation Energies of Isoelectronic Systems F^－, HF and H2F^＋

The intrapair and interpair correlation energies of F-, HF and H2F^ systems are calculated and analyzed using MP2-OPT2 method of MELD program with cc-PVSZ^* basis set. From the analysis of pair correlation energies of these isoelectronlc sysoterns, it is found that the 1sF^2 pair correlation energy is trans-ferable in these three isociectronic systems. According to the definition of pair correlation contribution of one electron pair to a system, the pair correlation contribution values of these three systems are calculated. The correlation contribution values of inner electron pairs and H—F bonding electron pair in HF molecule with those in H2F^ system are compared. The results indicate that the bonding effect of a molecule is one of the im-portant factors to influence electron correlation energy of the system. The comparison of correlation energy contributions in-cluding triple and quadruple excitations with those only includ-ing singles and doubles calculated with 6-311 G(d) basis set shows that the higher.excitation correlation energy contribution gives more than 2 % of the total correlation energy for these sys-tems.     

Calculations of D‐wave bound states and resonance states of the screened helium atom using correlated exponential wave functions

We have investigated the effects of screened Coulomb (Yukawa) potentials on the bound ^1,3D states and the doubly excited ^1,3 D^e resonance states of helium atom using highly correlated exponential basis functions. The Density of resonance states are calculated using stabilization method. Highly correlated exponential basis functions are used to consider the correlation effect between the charged particles. A total of 18 resonances (nine each for ¹ D^e and ³ D^e states) below the n = 2 He ⁺ threshold has been calculated. For each spin states, this includes four members in the 2pnp series, three members in the 2snd series, and two members in 2pnf series. The resonance energies and widths for various screening parameters ranging from infinity to a small value for these ^1,3 D^e resonance states are reported along with the bound‐excited 1s3d ^1,3 D state energies. Overall behavior of the spectral profile of 1s3d ¹D state of helium atom due to electron‐electron and electron‐nucleus screening are also presented. Accurate resonance energies and widths are also reported for He in vacuum. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Application of the extended method of calculation for atoms and ions having the electronic configurations 1s22s22pN

The atoms and ions in the electronic configurations 1s²2s²2p^N (N = 2, 3, 4, 5, 6) are examined. N hydrogen-like radial orbitals for 2p electrons were used. The calculated energies of the 2p shell are compared with those of the ordinary method and with experimental results. The intermultiplet separation ratios are considered as well.     

Lifetimes of the 4s4p 3 P 1 and 4s3d 1 D 2 states of Ca I

The lifetimes of the 4s4p ³ P ₁ and 4s3d ¹ D ₂ metastable states of Ca have been studied using the time-of-flight technique. Two kinds of observations were performed. First, the exponential decay of the fluorescence, using a (continuous) dc discharge for excitation and then the velocity distribution of the radiating atoms, using a pulsed discharge, were measured. From the combined results of these measurements the lifetimes were derived. The lifetimes of the 4s4p ³ P ₁ and 4s3d ¹ D ₂ states of Ca are determined to be 0.57±0.03 ms and 1.5±0.4 ms, respectively.     

Basis set quality versus size II. Approximate GTO wave functions for second row transition metal atoms

Basis sets ranging in size from (16, 10, 7) to (20, 14, 11) have been derived for the atoms Y–Cd. Separate sets represent the energy optimized wave functions for each of the s²dⁿ, s¹dⁿ⁺¹, and s⁰dⁿ⁺² configurations. The energies from the largest sets are within 3 mhartrees of the values obtained in numerical Hartree–Fock calculations. Reasonable Hartree–Fock s²dⁿ– s¹dⁿ⁺¹ and s²dⁿ– s⁰dⁿ⁺² excitation energies may be obtained either using the largest basis sets, or using d-orbitals optimized for the s⁰dⁿ⁺² configurations. The basis sets are slightly unbalanced in favor of the s-functions and in disfavor of the d-functions, but various alternative basis sets may be derived by combining parts of the five parent sets. The convergence of radial expectation values is discussed.