Electron correlation effects in the 4<i>f</i><sup>14</sup> shell

Jankowski, K.; Malinowski, P.; Sokołowski, A.; Lindgren, Ingvar; Pendrill, Ann-Marie

doi:10.1002/qua.560270604

Cited by 12 publications

(18 citation statements)

References 37 publications

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“…Although the systems considered are neighbors in the isoelectronic series, they represent various physical situations. On the one hand, the degree of quasi-degeneracy of the ground state increases when proceeding from Be to C2+, which is reflected, e.g., by the deterioration of the second-order correlation energy from 80.8% for Be to 76.7% for C2+ [29]. On the other hand, C2+ is easier to handle by means of VU-cc theories than is Be, which is often related to the impact of intruder states [22] in the latter case.…”

Section: Computational Results and Discussionmentioning

confidence: 99%

Multiple solutions of the valence‐universal coupled‐cluster equations for Be, B⁺, and C²⁺

Jankowski

Malinowski

1993

Int J of Quantum Chemistry

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Sets of nonlinear equations for the cluster amplitudes of the valence-universal coupled-cluster (VU-CC) method have been solved to obtain physically meaningful multiple solutions for Be, B', and Cz+. The wave operator is taken in Lindgren's normal ordered exponential form and the completeness of the model space is postulated. The cluster operator is restricted to its one-and two-electron components that are represented in terms of radial amplitudes defined by the configurational excitations (VU-CCSD/R method). Five solutions giving rise to 10 approximate energies of four ' S states are obtained and discussed. These are the first multiple solutions documented for a nonmodel system. Some attention is paid to the problem of the efficiency of various methods in obtaining alternative solutions and to some consequences of the availability of alternative solutions. 0 1993 John Wiley & Sons, Inc.

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Section: Computational Results and Discussionmentioning

confidence: 99%

Multiple solutions of the valence‐universal coupled‐cluster equations for Be, B⁺, and C²⁺

Jankowski

Malinowski

1993

Int J of Quantum Chemistry

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“…These are quite rare, but the Pr III levels are complete [4]. Retaining the 4f 2 's from Yb I [10], but calculating the "nearby" [4] 4f 2 → 5d 2 pair correlation using RCI, our average error relative to the ground state was 910 cm −1 . If transferability of within 4f 7 levels of Gd IV is valid, which seems likely, then the above results suggest there is negligible contribution to excitation energies within 4f…”

Section: Calculation Of Excitation Energies For Lanthanides and Actinmentioning

confidence: 90%

“…14 treated by Jankowski et al [10], and the 's extracted using the β's for Yb I. These could then be inserted back in the Gd IV problem, using its β's.…”

Section: Calculation Of Excitation Energies For Lanthanides and Actinmentioning

confidence: 99%

Improved RCI techniques for atomic 4fⁿexcitation energies and polarizabilities

Beck¹,

Pan²

2010

J. Phys. B: At. Mol. Opt. Phys.

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Abstract. We propose an efficient method by which previously computationally expensive, but moderately important, pair correlation effects can be incorporated into f n excitation energies. Application is to Gd IV. Secondly, we extend two methods of obtaining static and tensor dipole polarizabilities and apply them to the Ni II ground state. The first uses the sum over f -values approach, and the second is variational. Calculation of Excitation Energies for Lanthanides and ActinidesOur long term computational interest has been to develop (when necessary) and apply the relativistic configuration interaction (RCI) method to predict properties of complicated atoms and ions -specifically, for transition metals, lanthanides and actinides.Triply ionized lanthanide and actinide ions appear as impurities in condensed matter systems where they can serve as centers of lasing activity [1], play a role in MRI medicine as endohedral metallofullerenes (e.g. Gd 3 N-C 80 ) [2], appear as important constituents of high temperature super-conductors, etc. There also has been interest in the free Gd IV ion as a possible means of detecting an electron electric dipole moment [3].Experimentally, only a few of the low lying excitation energies within the f n configuration are generally known [4,5] from measurements made in the condensed phase. Dipole transition energies f n -f n−1 d are generally not known experimentally, as the d levels in the solid are not very well localized [5]. It also may be noted that most prevalent charge state of the lanthanide/actinide ion in the solid is 3 + [5]. Computationally, these excitation energies are also difficult to obtain [6]. The calculations require the use of a relativistic Hamiltonian (Dirac-Breit) and a correlated wavefunction having at least a first order form, i.e. one that includes all the differentially important single and double subshell excitations from a set of reference functions. At present, a reasonable ab initio accuracy goal for excitations within f n would be to position all levels to ∼1000 cm −1 relative to the ground state. Our recent Gd IV [6] achieved 1257 cm −1 , and we improve this to 838 cm −1 here, accompanied by a drop in calculation time of 67%.

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“…The β's can be determined from "standard" angular momentum theory [12]. Jankowski et al [10] have the 4f 2 's for Yb I 4f 14 , computed at 2nd order, decomposed by angular type. For the NR closed shell case the β = (2S + 1)(2L + 1).…”

Section: Implementation Of Bit-packed Reduce Savings Factormentioning

confidence: 99%

“…We then use the [10] 4. Use of ab initio determined relative shifts for 4f 6 (L p , S p )5d diagonal matrix elements.…”

Section: Implementation Of Bit-packed Reduce Savings Factormentioning

confidence: 99%

Improved RCI techniques for treating 4fⁿ atoms and ions: Application to Gd IV energies

Beck¹,

Domeier²

2009

Can. J. Phys.

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Relativistic configuration interaction results for energy levels and Landé g-values of Gd IV 4f7 J = 7/2 and Gd IV 4f6 5d J = 5/2, 7/2, 9/2, and energies of 51 new levels are presented. The average error between adjacent energy levels in 4f7 is 4.5%. Significant improvements in computational efficiency and accuracy for the difficult-to-treat 4f7 and 4f6 5d states are introduced, including the use of ab initio determined shifts of diagonal matrix elements (ME) for 4f6 parents, neglecting off-diagonal MEs between quadruple (triple) excitations, and a more systematic treatment of radial convergence.PACS Nos.: 31.15.am, 31.15.vj

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Electron correlation effects in the 4f¹⁴ shell

Cited by 12 publications

References 37 publications

Multiple solutions of the valence‐universal coupled‐cluster equations for Be, B⁺, and C²⁺

Multiple solutions of the valence‐universal coupled‐cluster equations for Be, B⁺, and C²⁺

Improved RCI techniques for atomic 4fⁿexcitation energies and polarizabilities

Improved RCI techniques for treating 4fⁿ atoms and ions: Application to Gd IV energies

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Electron correlation effects in the 4f14 shell

Cited by 12 publications

References 37 publications

Multiple solutions of the valence‐universal coupled‐cluster equations for Be, B+, and C2+

Multiple solutions of the valence‐universal coupled‐cluster equations for Be, B+, and C2+

Improved RCI techniques for atomic 4fnexcitation energies and polarizabilities

Improved RCI techniques for treating 4fn atoms and ions: Application to Gd IV energies

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Product

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Electron correlation effects in the 4f¹⁴ shell

Multiple solutions of the valence‐universal coupled‐cluster equations for Be, B⁺, and C²⁺

Multiple solutions of the valence‐universal coupled‐cluster equations for Be, B⁺, and C²⁺

Improved RCI techniques for atomic 4fⁿexcitation energies and polarizabilities

Improved RCI techniques for treating 4fⁿ atoms and ions: Application to Gd IV energies