Calculation of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>3</mml:mn><mml:mn /></mml:math>intrashell resonance states of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">He</mml:mi></mml:mrow><mml:mrow><mml:mi>−</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math>and of isoelectronic atoms

Piangos, Nicos A.; Nicolaides, Cleanthes A.

doi:10.1103/physreva.67.052501

Cited by 9 publications

(18 citation statements)

References 36 publications

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“…Theoretically, a 570-term 25 angular component wave function gives an energy of −1.043414 a.u., and the position at 174.11 eV, in an SP calculation with R-matrix approximation [13], which agrees quite well with the recent CCR result of −1.043 a.u., involving correlated basis sets [53], and the state specific result [55] for the latter matches closely with the state specific result of −1.0393859 a.u. [55]. No other results are available for any of these states for further comparison and these results may be useful in future studies of these resonances.…”

Section: Resultssupporting

confidence: 77%

“…This ordering is in keeping with the CCR findings of [56] for He − as well as that of the CI calculation for N 4+ [22]. However it differs from that of [55], who find in a large scale state specific calculation that as in the n=2 resonances, the 3s 2 3p 2 P o lies below At this stage it is worthwhile to make a few pertinent remarks on the status of excited state calculations within DFT. Although founded in the 1920s and later rejuvenated in the 1960s in the works of Hohenberg, Kohn and Sham [58,59], DFT has been a very powerful and successful tool for the electronic structure calculation of atoms, molecules, solids in their ground states [60,61], inherent difficulties were encountered for the excited states and consequently in areas such as spectroscopy, its success has been relatively less conspicuous.…”

Section: Resultssupporting

confidence: 70%

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Studies on the hollow states of atomic lithium using a density functional approach

Roy¹

2004

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

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Density functional calculations are performed for twelve 2l2l ′ nl ′′ (n≥2) triply excited hollow resonance series of Li, viz., 2s 2 ns 2 S e , 2s 2 np 2 P o , 2s 2 nd 2 D e , 2p 2 ns 2 D e , 4 P e , 2s2pns 4 P o , 2s2pnp 4 D e , 2p 2 np 2 F o , 4 D o , 2p 2 nd 2 G e , 4 F e and 2s2pnd 4 F o , covering a total of about 270 low-, moderately highand high-lying states, with n as high as up to 25. The work-function-based exchange potential and the nonlinear gradient plus Laplacian included Lee-Yang-Parr correlation energy functional is used.The relevant Kohn-Sham-type equation is solved numerically using the generalized pseudospectral method offering nonuniform, optimal spatial discretization to obtain the orbitals and densities. The present single determinantal approach yields fairly accurate results for the nonrelativistic energies, excitation energies as well as the radial densities and other expectation values. Except for the one state, the discrepancy in the calculated state energies remains well within 0.98%, whereas the excitation energies deviate by 0.02-0.58% compared to the available experimental and other theoretical results. Additionally companion calculations are also presented for the 37 3l3l ′ nl ′′ (n≥3) doubly hollow states (seven are n=3 intrashell type) of Li with both K and L shells empty (up to n=6) in the photon energy range 175.63-180.51 eV, with varying symmetries and multiplicities.Our calculation shows good agreement with the recent literature data for the only two such doubly hollow states reported so far, viz., 3s 2 3p 2 P o and 3s3p 2 4 P e . The resonance series are found to be inextricably entangled to each other, leading to complicated behavior in their positions. Many new states are reported here for the first time. This provides a simple, efficient and general scheme for the accurate calculation of these and other multiply excited Rydberg series of many-electron atomic systems within density functional theory.

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Section: Resultssupporting

confidence: 77%

Section: Resultssupporting

confidence: 70%

Studies on the hollow states of atomic lithium using a density functional approach

Roy¹

2004

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

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“…[173]. Critical issues in the theory and computation of the lowest three n=3 intrashell states, viz., 3s 2 3p 2 P o , 3s3p 2 4 P e and 3s3p 2 2 D e of Z=2-7 in the light of state specific theory, has been published [168]. Energies, widths and Auger branching ratios for eight He − 3l3l ′ 3l ′′ states are calculated by complex rotation method [168].…”

Section: Resultsmentioning

confidence: 99%

A density functional method for general excited states in atoms

Roy

2019

Preprint

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This chapter presents the development of a density functional theory (DFT)-based method for accurate, reliable treatment of various resonances in atoms. Many of these are known to be notorious for their strong correlation, proximity to more than one thresholds, degeneracy with more than one minima. Therefore these pose unusual challenges to both theoreticians and experimentalists. It is well-known that DFT has been one of the most powerful and successful tools for electronic structure calculation of atoms, molecules, solids in the past two decades. While it has witnessed diverse spectacular applications for ground states, the same for excited states, unfortunately, has come rather lately and remains somehow less conspicuous relatively. Our method uses a work-function-based exchange potential in conjunction with the popular gradient-corrected Lee-Yang-Parr correlation functional. The resulting Kohn-Sham equation, in the non-relativistic framework, is numerically solved accurately and efficiently by means of a generalized pseudospectral method through a non-uniform, optimal spatial discretization. This has been applied to a variety of excited states, such as low and high states; single, double, triple as well as multiple excitations; valence and core excitations; autoionizing states; satellites; hollow and doubly-hollow states; very high-lying Rydberg resonances; etc., of atoms and ions, with remarkable success. A thorough and systematic comparison with literature data reveals that, for all these systems, the exchange-only results are practically of Hartree-Fock quality; while with inclusion of correlation, this offers excellent agreement with available experimental data as well as those obtained from other sophisticated theoretical methods. Properties such as individual state energies, excitation energies, radial densities as well as various expectation values are studied. This helps us in predicting many states for the first time. In summary, we have presented an accurate, simple, general DFT method for description of arbitrary excited states of atoms and ions.

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“…This state was examined here in the context of the discussion on hole‐filling electron correlations. Additional results for Cl and the ions Ar + and K ++ , including excited states and oscillator strengths, are given in Reference 38. Following the proposal in the Tables 1 of References 10, 13, pertaining to ground states of neutral atoms of the second row, a reasonable choice for the FS is the set of {3s, 3p, 3d, 4s} orbitals.…”

Section: Comment On Two Concepts and Methods In The Theory And Commentioning

confidence: 99%

“…In this section, the results concern the total energy, the contribution and mixing coefficients of multiple orbital correlations, and the excitation energy KL3s 2 3p 5 2 P o →KL3s3p 6 2 S. Additional analysis and results on transition probabilities for ground as well as excited states of 2 S symmetry, concerning not only Cl but also Ar + and K ++ , will be reported in Reference 38.…”

Section: The CL Kl3s3p6 2s State and Multiple Electron Correlationsmentioning

confidence: 99%

On calculations of correlated wave functions with heavy configurational mixing

Nicolaides¹

2004

Int J of Quantum Chemistry

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ABSTRACT:We discuss aspects of the theory and computation of wave functions and energies of discrete states of polyelectronic atoms that are represented in zero order by configurations with holes in subshells below the valence subshell. Both in zero order and in the remaining correlation components, such wave functions have particularities stemming from the state-specific self-consistent field and the heavy configurational mixing associated with near-degeneracies and hole-filling correlations. By referring to a variety of examples from small-and large-scale calculations, it is noted that appropriate penetration into the many-body problem can provide, in an economic and physically transparent way, reliable interpretations and semi-and fully quantitative understanding of issues related to states with inner holes and to cases of near-degeneracies that result in strongly correlated wave functions. Whenever hole-filling correlations are allowed, multiple correlations (i.e., beyond single-and double-orbital substitutions in the single reference configuration) acquire increased importance relative to that in ordinary electronic structures. This is demonstrated via large-scale multiconfigurational HartreeFock (MCHF) plus configuration interaction (CI) calculations on the Cl KL3s3p 6 2 S discrete state, which is the lowest of its symmetry. The calculations incorporated correlations up to selected sextuple orbital excitations from the M shell. MCHF plus CI calculations at the level of quadruple orbital substitutions were also carried out for the Cl KL3s 2 3p 5 2 P o ground state and the excitation energy at this level of calculation was found to be 85,364 cm Ϫ1 , in excellent agreement with the experimental value of the finestructure-weighted average, 85,385 cm Ϫ1 (10.59 eV). Within the approximations of the calculation, the hole-filling triple and quadruple orbital correlations, which, of course, are absent from the 2 P o state, contribute about 1 eV, which is significant.

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Calculation ofn=3intrashell resonance states ofHe−and of isoelectronic atoms

Cited by 9 publications

References 36 publications

Studies on the hollow states of atomic lithium using a density functional approach

Studies on the hollow states of atomic lithium using a density functional approach

A density functional method for general excited states in atoms

On calculations of correlated wave functions with heavy configurational mixing

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