Ab initio Hartree–Fock and configuration-interaction treatment of the interaction between two nickel atoms

The interaction between two nickel atoms in the configurations (3d)⁸(4s)² and (3d)⁹ (4s)¹ has been calculated using ab initio methods (Hartree–Fock and configuration interaction). The results of the calculations compare favorably with the optical spectrum. The discrepancy between the calculated and the experimental dissociation energy is discussed, and a new estimate of the dissociation energy is given. The configuration-interaction calculations show that the interaction between the two nickel atoms is of a very complex nature. In spite of this the binding can be interpreted in a simple way. The bond is minly due to the 4sσ_g molecular orbital while the 3d orbitals of the two nuclei are exchange coupled.     

Charge transfer mechanism in N4+ + He and B3+ + He/H2 ion–atom/molecule collisions

Ab initio potential energy curves and coupling matrix elements of the molecular states involved in the collision of the N⁴⁺(2s)²S and B³⁺(1s²)¹S multicharged ions on the helium atom or molecular hydrogen have been determined by means of configuration interaction methods. The total and partial electron capture cross-sections have been evaluated in the frame of a semiclassic approach in the 1- to 100-keV laboratory energy range and compared to experimental data. A comparative study of both targets is performed in the case of the B³⁺ ion. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Hyperfine structure measurements of the metastable (3d 6 4s 2)3 H 4, 5, 6 states of57Fe: Configuration interaction in the hyperfine structure of the iron atom

We report the hyperfine structure (hfs) measurement of the metastable (3d ⁶ 4s ²)a ³ H _{4, 5, 6} states of⁵⁷Fe. The kHz-precision of these experimental results together with the hyperfine structure values of (3d ⁶ 4s ²)a ⁵ D _{1, 2, 3, 4}, (3d ⁷ 4s)a ⁵ F _{2, 3, 4, 5}, and (3d ⁷ 4s)a ³ F _{2, 3, 4}, which were measured earlier, allowed to determine a very detailed set of effective radial parameters describing the hfs of these states, using a new parametrization method. This method treats one- and two-body contributions to the hfs separately. In this way configuration interaction effects in the hfs of the⁵⁷Fe atom can be studied in detail and compared with configuration interaction effects in the fine structure of the same atom.     

Ab initio calculations on low-lying electronic states of PdH

Potential energy curves for the low-lying electronic states of PdH have been calculated using the MRCI method with scalar relativistic and spin-orbit corrections, and all electronic states correlating to the 4d¹⁰ (¹S), 4d⁹ 5s¹ (³D), 4d⁹ 5s¹ (¹D) and 4d⁸ 5s² (³F) states of Pd were included. Potential energy curves for the individual Ω states have been obtained, and the experimentally observed spectra of both PdH and PdD isotopologues have been assigned appropriately based on the ab initio results. Einstein A coefficients were calculated for other possible transitions from the low-lying electronic states to the X²Σ⁺ ground state. Diagonal and off-diagonal matrix elements of the spin-orbit Hamiltonian were calculated for all vibrational levels of the X²Σ⁺, 1²Δ, 1²Π, 2²Σ⁺ and 3²Σ⁺ states, and it was found from the eigenvectors that the vibrational wavefunctions of the 1²Δ_3/2 and 1²Π_3/2 states are mixed significantly in both PdH and PdD isotopologues.     

Theoretical investigations of the electronic states of porphyrins. III. Low-lying electronic states of porphinatoiron(II)

Ab initio configuration interaction calculations are reported on the lowest quintet, triplet, and singlet states of Fe^II(P). Due to the large number of states found, a catalog of the low-lying states is presented. Novel triplet and quintet charge-transfer states are reported as low as 1.3 eV. These states are d⁵ (S = 5/2) on the iron low-spin-coupled to the radical anion excited porphyrin ring (S = 1/2 or 3/2). Oscillator strengths originating from each of three low-energy triplet states are reported.     

Electronic states and nature of bonding of the molecule PdSi by all electron ab initio HF-CI calculations and mass spectrometric equilibrium experiments

Six low-lying electronic states of the PdSi molecule have been investigated by performing all electron ab initio Hartree-Fock (HF) and configuration interaction (CI) calculations. The molecule is predicted to have a³∏ ground state and two low-lying excited states,³Σ^? and¹Σ⁺. The electronic structure of the PdSi molecule has been rationalized in a simple molecular orbital diagram. As part of the PdSi molecule the Pd atom essentially retains its (4d)¹⁰ ground term configuration. The chemical bond in the PdSi molecule has been interpreted in terms of donation and back-donation of charge. The bond is polar with charge transfer from the Pd to the Si atom. The dissociation energy of the PdSi molecule has been determined from the mass spectrometric equilibrium data in combination with the theoretical results asD ₀ ^o =257±12 kJ mol^?1.     

High-resolution absorption spectra of diphenylnmethylenes

High-resolution absorption spectra of the following diphenylmethylenes (DPM_s) dispersed in benzophenone crystals at liquid-helium temperatures are presented: DPM-h₁₀, DPM-d₁₀, 4-chloro-DPM, and 4-bromo-DPM. The substituent effects concerning the electronic structure, transition energy and intensity are discussed. From polarization measurements, the electronic configurations of the ground and the first excited triplet states of these DPM_s are assigned as (pπ)¹(pσ)¹ and (pσ)¹(π*)¹, respectively. Further studies reveal a second excited triplet state, designated as (pπ)¹(π*)¹, which lies less than 1000 cm^-1 above the first excited triplet state of DPM. Diffuse broad bands appear as common features in all the spectra. Such diffuseness is discussed in terms of electron-phonon coupling of the low-lying excited states.     

Large atomic natural orbital basis sets for the first transition row atoms

Large atomic natural orbital (ANO) basis sets are tabulated for the Sc to Cu atoms. The primitive sets are taken from the large sets optimized by Partridge, namely (21s13p8d) for Sc and Ti and (20s12p9d) for V to Cu. These primitive sets are supplemented with threep, oned, sixf, and fourg functions. The ANO sets are derived from configuration interaction density matrices constructed as the average of the lowest states derived from the 3d ⁿ 4s ² and 3d ⁿ⁺¹4s ¹ occupations. For Ni, the¹ S(3d ¹⁰) state is included in the averaging. The choice of basis sets for molecular calculations is discussed.     

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.     

Calculation of ground- and excited-state potential energy curves for barium-rare gas complexes in a pseudopotential approach

Adiabatic potential curves for the ground state and several low-lying excited states of the barium atom interacting with Ne, Ar, Kr and Xe have been obtained from valence ab initio configuration-interaction calculations. Atomic cores are replaced by scalar-relativistic l-dependent pseudopotentials, while core-polarization potentials are used for describing correlation contributions of the rare-gas atoms and the Ba²⁺ cores. Implications of the resulting potential curves for the interpretation of experimental data are discussed, together with first applications of the curves for calculating absorption profiles of the (6s ²)¹S→(6p)¹P Ba transition. Received: 7 April 1998 / Accepted: 27 July 1998 / Published online: 12 October 1998     

A matrix-induced change in the electronic ground state of nickel atoms isolated in rare gases

Comparison of the absorption spectra for matrix-isolated Ni atoms with gas-phase data reveals that the electronic ground-state configuration of the isolated atom can be changed by the matrix. While Ni in Ne has the same configuration as in the gas phase, namely 3d⁸4s² we find in Ar, Kr, and Xe the 3d⁹4s¹ configuration to be the ground state. The matrix-induced changes is explained by the repulsive matrix-dopant interaction, which is sufficiently lowered in the 3d⁹4s¹ configuration to overcompensate for the energy difference of 205 cm^?1 by which the 3d⁹4s¹ level lies above the 3d⁸4s² in the free atom.     

Why do the second row transition metal atoms prefer 5s14dm+1 to 5s24dm?

Numerical Hartree-Fock (NHF) calculations have been performed for 332 ground and low-lying excited states of the fifth period atoms Rb through Xe, with our special interest in the states arising from the 5s ²4d ^m , 5s ¹4d ^m +1, and 5s ⁰ 4d ^m +2 configurations of the second row transition metal atoms. Among various properties, orbital energies and mean values ofr of the outermost orbitals of each symmetry are presented as well as total energies. It is discussed in some detail why the second row transition metal atoms have a tendency to prefers ¹ d ^m +1 as the ground configuration in contrast to the preferreds ² d ^m configuration in the first row transition metal atoms. Our systematic NHF computations reported in this and the previous papers conclude that the Hartree-Fock method correctly predicts the experimental ground state of the atoms He through Xe with the sole exception for Zr.     

On the low-lying electronic states of BiF

Relativistic CI calculations on the low-lying states of BiF(0⁺, 1, 2, 0⁺(II)) arising from the σ²π² configuration are carried out. Comparison calculations of the λ-s states without spin-orbit interaction (³Σ⁻, ¹Σ⁺ and ¹Δ) are also presented. These calculations enable the assignment of three experimentally observed low-lying states. In addition, the properties of a new state (2) are calculated (yet to be observed). The calculated dissociation energy of the ground state is 2.63 eV. The potential energy surfaces of the low-lying electronic states of BiF reveal interesting avoided crossings. Our calculations clarify the earlier assignment of the electronic transitions of BiF.     

The structural,electronic, and magnetic properties of the stoichiometric (001) surface of double perovskite Sr2FeMoO6

The structural, electronic, and magnetic properties of the stoichiometric (001) surface of double perovskite Sr₂FeMoO₆ have been studied by using a 10‐layer FeMoO₄ and SrO terminated (001)‐oriented slab model and the first‐principles projector augmented wave potential within the generalized gradient approximation as well as taking into account the on‐site Coulomb repulsive (U = 2.0 eV for Fe and 1.0 eV for Mo). An outwards relaxation is observed for several layers near surface, and the accompanying layer rumpling has a decrease tend from surface layer to inner layer. Along Fe–O–Mo–O–Fe or Mo–O–Fe–O–Mo chains, the oxygen atom is closer to the adjacent Mo atom than to the adjacent Fe atom. In FeO₆ or MoO₆ octahedra, the two axial TM?O bonds are not equal, and especially, the surface dangling bond makes the remaining one axial TM?O bond slightly shorter than four equally equatorial TM?O bonds. The half‐metallic nature and a complete (100%) spin polarization character ensure the FeMoO₄ and SrO terminated (001)‐oriented slab of double perovskite Sr₂FeMoO₆ a potential application in spintronics devices. The Fe⁺³ and Mo⁺⁵ ions are still in the (3d⁵, S = 5/2) and (4d¹, S = 1/2) states with positive and negative magnetic moments respectively and thus antiferromagnetic coupling via oxygen between them. There is no direct interaction between two nearest Fe–Fe or Mo–Mo pairs, whereas the hybridizations between Fe 3d and 4s, O 2s and 2p, as well as Mo 4d, 5s and 5p orbitals are fairly significant. Copyright © 2016 John Wiley & Sons, Ltd.     

Large-scale configuration interaction calculations on the π-electron states of benzene

Ab initio extensive configuration interaction calculations were carried out on the π-electron states of benzene. Among the three π → π^*(e_1g → e_2u) singlet states, ¹B_2u(S₁). ¹B_1u(S₂), and ¹E_1u(S₃), the π^* orbital was found to be velence-like in S₁ and S₂, but diffuse in S₃. All three corresponding triplet states, ³B_1u(T₁) and ³B_2u(T₃), were found to be valence-like. The valence-like ¹E_2g(S₄) and ³E_2g(T₄) states were found to have significant double-excitation character, and were estimated to lie somewhat above S₃ and T₃, respectively. No low-lying S₅ and T₅ states were found. Several low-lying Rydberg states were identified.     

Determination of Erbium by Two-Color Three-Photon Resonance Ionization Mass Spectrometry

Excited states and autoionization states of the erbium atom were investigated by the use of multicolor resonance ionization mass spectrometry. Among the observed first excited states, a level [4f¹²(³H₆)6s6p(³P₁)] located 17,348 cm⁻¹from the ground state is regarded as the most efficient state for excitation within the wavelength range investigated (560–600 nm), while a level located 17,080 cm⁻¹from this first excited state (E= 34,458 cm⁻¹) is identified as the best second excited state for the optimal photoionization scheme. Many ionization schemes adopting an autoionization state are also investigated, and the most efficient scheme is identified as 4f¹²6s²(³H₆) → 4f¹²(³H₆)6s6p(³P₁⁰), 17,348 cm⁻¹→ 34,458 cm⁻¹→ continuum state, which corresponds to the two-color (ω₁+ ω₂+ ω_1,2) scheme. Various concentrations of standard solutions for erbium are determined and the minimum amount detectable by two-color three-photon ionization was determined to be 20 pg.     

Semiempirical hyperfine structure and ab initio isotope shift predictions in Zr II

The fine structure of the even‐parity low configurations has been reanalyzed by simultaneous parameterization of the one‐ and two‐body interactions for the model space (4d + 5s)³. Using the calculated eigenfunctions, the magnetic‐dipole A hyperfine constants for the whole 37 existing levels of the model space were predicted and compared partially to those obtained using relativistic configuration‐interaction approach. Moreover, volume shifts (VS) and specific mass shifts (SMS) of numerous configurations of singly ionised zirconium are deduced by means of ab initio estimates combined with a few experimental isotope shift data available in literature: VS(4d¹5s²) = 840 MHz, VS(4d³) = ?649 MHz, VS(4d¹5p²) = ?387 MHz, VS(5s²5p¹) = 1250 MHz, and SMS(4d¹5s²) = ?634 MHz, SMS(4d³) = 484 MHz, SMS(5s²5p¹) = ?1459 MHz, referred to 4d²5s for the pair Zr⁹⁰–Zr⁹². © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Electronic states and nature of bonding of the molecule NiSi by all electron ab initio HF-CI and CASSCF calculations

All electron ab initio Hartree-Fock (HF), configuration interaction (CI) and multiconfiguration self-consistent field (CASSCF) calculations have been applied to investigate the low-lying electronic states of the NiSi molecule. The ground state of the NiSi molecule is predicted to be¹Σ⁺. The chemical bond in the¹Σ⁺ ground state is a double bond composed of one σ and one π bond. The σ bond is due to a delocalized molecular orbital formed by combining the Ni 4s and the Si 3pσ orbitals. The π bond is a partly delocalized valence bond, originating from the coupling of the 3dπ hole on Ni with the 3pπ electron on Si. Withing the energy range 1 eV 18 electronic states have been identified. The lowest lying electronic states have been characterized as having a hole in either the 3dπ or the 3dδ orbital of Ni, and the respective final states are formed when either of these holes are coupled to the 3pπ valence electron of Si.     

Theoretical study of low‐lying electronic states of the LiRb+ molecular ion: Structure,spectroscopy and transition dipole moments

The electronic structure and the spectroscopic properties for low‐lying electronic states of the LiRb⁺ molecular ion, dissociating into Li (2s, 2p, 3s, 3p, 3d, 4s, and 4p) + Rb⁺ and Li⁺ + Rb (5s, 5p, 4d, 6s, 6p, 5d, and 7s), have been investigated using an ab initio approach based on non‐empirical pseudo potentials for the Li and Rb cores and parametrized l‐dependent polarization potential. We have determined the adiabatic potential energy curves and their spectroscopic constants for many electronic states of ²Σ⁺, ²Π, and ²Δ symmetries. A satisfying agreement, for the spectroscopic constants, has been obtained for the ground and the first excited states with the available theoretical works. Potential energy curves were presented, for the first time, for the higher excited states. In addition, we have localised and analysed the avoided crossings between electronic states of ²Σ⁺ and ²Π symmetries. Their existences can be related to the interaction between the potential energy curves and to the charge transfer process between the two ionic systems Li⁺Rb and LiRb⁺. Moreover, we have determined the transition dipole moments from X²Σ⁺ and 2²Σ⁺ states to higher excited states of ²Σ⁺ and ²Π symmetries. For our best knowledge, no experimental data on the LiRb⁺ molecular ion is available. These theoretical data can help experimentalists to optimize photoassociative formation of ultracold LiRb⁺ molecular ion and their longevity in a trap or in an optical lattice. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Berechnung der Röntgen- und Auger-Linien des Methans mit Hilfe des Pseudo-Neon-Modells

Zusammenfassung Mit Hilfe des Pseudoneonmodells wurden die Energien der aus den folgenden Konfigurationen hervorgehenden Terme bzw. Mittelwerte dieser Energien für das Methanmolekül bestimmt: [(1s)² (2s)² (2p)⁶], [(1s)¹ (2s)² (2p)⁶], [(1s)¹ (2s)² (2p)⁶ (3p)¹], [(1s)¹ (2s)² (2p)⁶ (4p)¹], [(1s)¹ (2s)² (2p)⁶ (3d)¹], [(1s)² (2s)¹ (2p)⁵], [(1s)² (2s)² (2p)⁴] und [(1s)² (2s)⁰ (2p)⁶].Die Energien wurden mit Hilfe der Slater-Condonschen Regeln analytisch berechnet und dann mit einer elektronischen Rechenmaschine (Zuse 23) minimisiert.Aus den erhaltenen Energiewerten wurde die Lage der Röntgen- und Auger-Linien des Methans berechnet. Die von Mehlhorn [8] gemessenen Auger-Elektronenenergien konnten zugeordnet werden.Die Rechenergebnisse stimmen mit den von Chun aus Röntgenabsorptionsmessungen ermittelten experimentellen Werten befriedigend überein.

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The pseudo neon model is used to calculate the energies of the levels deriving from the following configurations (or their mean values) of the methane molecule: [(1s)² (2s)² (2p)⁶], [(1s)¹(2s)²(2p)⁶], [(1s)¹(2s)²(2p)⁶(3p)¹], [(1s)¹ (2s)² (2p)⁶ (4p)¹], [(1s)¹ (2s)² (2p)⁶ (3d)¹], [(1s)² (2s)¹ (2p)⁵], [(1s)² (2s)² (2p)⁴] and [(1s)² (2s)² (2p)⁶].The energy expressions are given by the Slater-Condon rules; the minimization is done with a digital computer (Zuse 23). Prom the energy values obtained the X-ray and Auger lines of methane are calculated. An interpretation of the experimental Auger electron energies of Mehlhorn [8] is made.Calculated and measured (by Chun) values are in satisfactory agreement with each other.

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Résumé A l'aide du modèle du pseudo-atome de néon, les énergies des niveaux dérivant des configurations suivantes (ou leurs moyens) ont été calculées: [(1s)² (2s)² (2p)⁶], [(1s)¹ (2s)² (2p)⁶], [(1s)¹(2s)²(2p)⁶(3p)¹], [(1s)¹(2s)²(2p)⁶(4p)¹], [(1s)¹ (2s)² (2p)⁶ (3d)¹], [(1s)² (2s)¹ (2p)⁵], [(1s)² (2s)² (2p)⁴] et [(1s)² (2s)⁰ (2p)⁶].Les énergies sont données par les règles de Slater et Condon et minimisées à l'aide d'une machine à calculer électronique (Zuse 23).On en dérive les spectres X et d'Auger du méthane. Nous pouvions interpréter les énergies des électrons Auger mesurées par Mehlhorn [8]. Les calculs s'accordent assez bien aux valeurs expérimentales de Chun.

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Auszug aus der Dissertation von T. K. Ha, Frankfurt am Main, 1963.