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REVIEW 4 major objections 4 minor 1 cited by

Electronic structure calculation for superheavy elements Livermorium (Lv, Z=116) and Tennessine (Ts, Z=117) and their lighter analogs Te, I, Po, and At

T0 review · 4 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Coupled many-body calculations predict spectra and properties of elements 116 and 117 at about one-percent accuracy.

desk verdict Useful, honestly benchmarked calculation of Lv/Ts spectra and properties; the numbers are new and mostly credible, but the superheavy error bars are overstated, especially the ~1% IP claim. read the letter →

arxiv 2505.22895 v2 pith:TZ6RCIZ7 submitted 2025-05-28 physics.atom-ph

V. A. Dzuba , V. V. Flambaum , G. K. Vong This is my paper
classification physics.atom-ph
keywords superheavyelementslivermoriumtennessinecoupled-clustermethodconfiguration-interactionperturbationtheoryionizationpotentialelectronaffinityatomicpolarizability
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper predicts the low-energy spectra and key atomic properties of the two least-studied superheavy elements, livermorium ($Z=116$) and tennessine ($Z=117$), for which no spectroscopic measurements exist. The authors combine a linearized coupled-cluster single-double treatment of core and core-valence correlations with configuration-interaction perturbation theory for the valence $p$-shell, and benchmark the same method on the lighter analogs tellurium, iodine, polonium, and astatine. Agreement with measured energy levels is at the few-percent level for the lighter atoms, and the paper argues the same accuracy should carry over to the superheavies. The new results include complete low-energy level schemes, ionization potentials, electron affinities, field isotope shifts, and static dipole polarizabilities, with the ionization potentials claimed accurate to about 1% and the electron affinities to about 10%.

What carries the argument

The load-bearing mechanism is the combination of the linearized coupled-cluster single-double (SD) method with configuration-interaction perturbation theory (CIPT). SD generates the one-electron correlation operator $\hat{\Sigma}_1$ and the two-electron screened-Coulomb operator $\hat{\Sigma}_2$, which are added to a configuration-interaction Hamiltonian built on a relativistic Hartree-Fock core described by the $V^{N-M}$ approximation; CIPT then keeps the low-energy part of the configuration space exactly and treats the high-energy part perturbatively through an energy-dependent effective matrix. The same machinery, with the random-phase approximation for external fields, yields energy levels, $g$-factors, electric-dipole amplitudes, field isotope shifts, and static polarizabilities.

What would settle it

Measure the ionization potential or the energy of the lowest optical transition of Lv or Ts, for instance by laser spectroscopy of trapped ions or atoms; if the measured value differs from the predicted $54433\,\mathrm{cm}^{-1}$ (Lv) or $61643\,\mathrm{cm}^{-1}$ (Ts) by more than about 2-3%, the assumed transferability of accuracy breaks down. In the near term, a precise measurement of the electron affinity of astatine or the polarizability of polonium would test the 1.1 correction factor applied to the superheavy polarizabilities.

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Extended reading notes

Core claim

The central claim is that a hybrid SD+CIPT calculation using the $V^{N-M}$ approximation, with the $ns^2$ subshell frozen into the core and only the four or five open-shell $p$ electrons treated explicitly, produces quantitatively reliable electronic-structure predictions deep into the relativistic regime, where $(Z\alpha)^2$ reaches 0.73 for $Z=117$. Validated on Te and I, the method reproduces measured energy levels with average absolute deviations around $300\,\mathrm{cm}^{-1}$ and $1000\,\mathrm{cm}^{-1}$; applied to Lv and Ts it predicts ground configurations $7p^4$ and $7p^5$, the fine-structure splittings, several strong optical electric-dipole transitions whose spin suppression is lifted by relativity, field-isotope-shift constants around 160-340 GHz/fm$^2$, ionization potentials of $54433\,\mathrm{cm}^{-1}$ (Lv) and $61643\,\mathrm{cm}^{-1}$ (Ts), electron affinities of $5623\,\mathrm{cm}^{-1}$ and $11579\,\mathrm{cm}^{-1}$, and static dipole polarizabilities of 76.0 and 71.6 atomic units after applying a 1.1 correction factor.

Load-bearing premise

The load-bearing premise is that the accuracy shown for the lighter analogs Te, I, Po, and At transfers unchanged to Lv and Ts, because no experimental data exist for the superheavies to check the extrapolation.

Editorial extensions

If this is right

  • The predicted strong optical electric-dipole transitions in Lv and Ts give experimentalists concrete lines to search for with laser spectroscopy once sufficient quantities of these isotopes can be produced.
  • The ionization potentials and electron affinities provide reference values for classifying Lv and Ts chemically, for example their volatility and tendency to form anions, before any bulk chemistry exists.
  • The large field-isotope-shift constants imply that isotope-shift measurements on the predicted transitions would be sensitive probes of the nuclear charge radii of superheavy nuclei, including candidates in the island of stability.
  • The result that Breit and QED corrections shift excitation energies by less than $100\,\mathrm{cm}^{-1}$ even at $Z=117$ means omitting them would not change the qualitative level order in future calculations of these atoms.
  • The trend of shrinking energy intervals between configurations as $Z$ grows brings more electric-dipole transitions into the optical region, making the predicted spectra more accessible to experiment than one might expect.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper, if the 1% accuracy holds for one measured Lv or Ts line, the entire calculated level scheme could be anchored to that line, because all levels share the same core and correlation treatment.
  • Beyond the paper, the constant 1.1 polarizability correction fitted to lighter analogs could be tested and possibly made $Z$-dependent by measuring the polarizability of astatine or polonium; a constant correction may not hold at the extreme relativistic end.
  • Beyond the paper, the same SD+CIPT pipeline should transfer to neighboring superheavy elements such as moscovium ($Z=115$) and oganesson ($Z=118$), whose open $p$-shell structures are closely related to those treated here.
  • Beyond the paper, the predicted relaxation of spin-selection rules implies that some excited states in Lv and Ts will have markedly shorter radiative lifetimes than their nonrelativistic counterparts, a testable prediction once level lifetimes can be measured.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 4 minor

Summary. The manuscript presents relativistic electronic-structure calculations for the superheavy elements Lv (Z=116) and Ts (Z=117) and their lighter homologs Te, I, Po, and At, using a hybrid method that combines relativistic Hartree-Fock, linearized coupled-cluster single-double (SD), and configuration-interaction perturbation theory (CIPT). Results are reported for energy levels and Landé g-factors, ionization potentials, electron affinities, electric-dipole amplitudes and field isotope shifts, and static dipole polarizabilities. The accuracy is calibrated against NIST experimental data for Te, I, Po, and At: average energy-level deviations of about 300 cm^-1 (Te) and 1000 cm^-1 (I), and IP deviations of about 1–2%. For Lv and Ts, where no experimental data exist, the authors compare with previous calculations and assert accuracies of about 1% for IPs, about 10% for EAs and polarizabilities.

Significance. The calibrated ab initio pipeline is a genuine strength, especially the consistent treatment of core-valence correlations via SD + CIPT and the inclusion of Breit and QED corrections. If the accuracy carries over to Z=116,117, the predicted spectra, isotope-shift constants, and polarizabilities would be valuable for future spectroscopy and for astrophysical searches related to the island of stability. The paper is less convincing where it extrapolates the light-atom error bars to the superheavy regime without a quantitative uncertainty budget, and where it presents E1 amplitudes and FIS constants without any benchmark against lighter analogs. These are fixable with additional analysis and should not obscure the value of the Te/I/Po/At calibration.

major comments (4)
  1. [Section VI, Table VIII] The statement in the text that 'It is natural to assume that the IPs of Lv and Ts are now known to an accuracy of ~1%' is not supported by the full set of data shown in the table. For Lv, the other published values span 53470–59600 cm^-1, a spread of roughly 11% around the present 54433 cm^-1, with Ref. [30] disagreeing by 5167 cm^-1; for Ts, the other values span 59520–61730 cm^-1, about 4% around 61643 cm^-1. The ~1% claim relies on agreement with Ref. [6] alone, and a similar issue appears in Table IX for electron affinities, where for Ts the spread of other calculations is about 16% while the text claims ~10%. Please either replace the accuracy claim by a method-specific error estimate that accounts for the spread of independent calculations, or explicitly restrict the claim to agreement with Ref. [6].
  2. [Section VII, Table X] The 'extrapolated' polarizabilities for Lv (76.0 a.u.) and Ts (71.6 a.u.) are obtained by multiplying the ab initio values by a single factor 1.1 that is deduced from comparisons for Te, I, Po, and At. The paper gives no propagated uncertainty for these numbers, and the text itself notes that the accuracy 'may slightly deteriorate for heavier atoms.' The conclusion 'The accuracy for the polarizabilities is about 10%' is therefore an unquantified assertion. I ask the authors to derive and quote an uncertainty for the extrapolated values, e.g. from the scatter of the ratios for the four lighter atoms and the uncertainties of the recommended values, rather than presenting 76.0 and 71.6 as exact outputs.
  3. [Section V.A, Table VII] The electric-dipole amplitudes and field-isotope-shift constants for Lv and Ts are presented as results, but the manuscript contains no validation of the RPA-based procedure against measured E1 transition rates or isotope shifts for any of the lighter homologs. Since the abstract lists field isotope shift among the main outputs, the absence of a benchmark leaves the accuracy of Table VII entirely undetermined. Please add a comparison for at least one known case (e.g. Te or I), or clearly mark these quantities as unbenchmarked predictions and assign conservative uncertainties.
  4. [Section II and Section III] No convergence tests are reported for the single-electron basis (40 B-spline states per partial wave, lmax=6) or for the CIPT truncation (Neff and the number of states in P). Because the claimed accuracy of the Lv and Ts predictions rests entirely on transferring the Te/I benchmark, the paper should show that the basis and Neff are saturated at the level of a few hundred cm^-1 for the lighter atoms before that transfer can be considered reliable.
minor comments (4)
  1. [Section IV heading] The heading appears as 'ENERGY LEVELS OF PO AND A T.'; this should read 'PO AND AT.'
  2. [Table IV caption] The caption contains 'andg-factors' (missing space); please correct the typo.
  3. [Table X] The row for Te lists an ab initio value and a recommended value but no extrapolated value, although Section VII says all ab initio results are multiplied by 1.1; either add the extrapolated Te value or explain the omission.
  4. [Equation (11)] Equation (11) uses J1(kr) while the surrounding text refers to a spherical Bessel function; the notation should be made consistent, for example by using j1(kr) for the spherical Bessel function.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the energy-level, IP, EA, and polarizability calculations are carried out by an ab initio SD/CIPT scheme, with the only calibrated element being an explicitly labeled 1.1 polarizability rescaling factor transferred from lighter analogs to superheavy elements.

full rationale

The paper's central results for Lv and Ts are obtained from a method chain (RHF, linearized coupled-cluster SD, CIPT, Breit and QED corrections) that is described by its own equations, and the accuracy claims rest on direct comparisons with experimental NIST data for Te, I, Po, and At in Tables I-IV. The IP and EA values in Tables VIII and IX are not fitted to the target properties; they are energy differences from the same many-electron Hamiltonian, and agreement with experiment is reported as a benchmark, not used to adjust the superheavy predictions. The only fitted ingredient is the uniform 1.1 factor for polarizabilities in Section VII, which is explicitly derived from the comparison of ab initio results with recommended values for lighter atoms and then applied to Lv and Ts; the resulting entries are transparently labeled 'Extrapolated' rather than presented as ab initio predictions. This is an honest extrapolation, not a circular reduction, because the fitted factor is calibrated on distinct atomic species and applied to different targets. The load-bearing assumption that accuracy transfers from Te/I/Po/At to Lv/Ts is an uncertainty-assessment issue and an external-validity risk, not a circularity, since the superheavy quantities are not defined in terms of the lighter-atom benchmarks. Self-references to the CIPT method (Ref. [10]) and the V^N-M approximation (Ref. [16]) are methodological citations accompanied by explicit equations and physical arguments, so the derivation does not reduce to a self-citation chain. No step was found in which a predicted quantity is equivalent by construction to an input parameter or to a cited prior result.

Assumptions & free parameters 1 free parameters · 3 assumptions · 0 invented entities

The calculation relies on standard many-body methods and prior parameterizations; the only new fitted parameter is the global 1.1 polarizability correction. No new physical entities are introduced.

free parameters (1)
  • Polarizability scaling factor = 1.1
    Applied to all ab initio polarizabilities (Section VII, Table X) because comparison with recommended values for Te, Po, I, At shows an underestimate of about 10%. This factor is fitted to benchmark data and then used for Lv and Ts predictions.
assumptions (3)
  • domain assumption The ns2 electrons are treated as core, only open p-shell electrons as valence (V N-M approximation)
    Section II states that no states with excitations from ns2 subshell exist below ~70000 cm-1 for Te and I, and this is assumed to hold for the heavier analogs. This reduces the valence space to 4 or 5 electrons.
  • domain assumption The calculation accuracy for Lv and Ts is similar to that found for Te, I, Po, At
    Section III and V conclude that differences between calculated and experimental levels are similar across Te, I, Po, At and therefore 'We expect similar accuracy for heavier elements Lv and Ts'.
  • domain assumption The B-spline basis (40 states, lmax=6) is sufficiently saturated for the V N-M approximation
    Section II asserts 'This choice of parameters ensures that the basis is sufficiently saturated' and Section III notes that a complete basis is required to compensate the poor initial approximation.

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Cite this review

Pith. "Pith review of Electronic structure calculation for superheavy elements Livermorium (Lv, Z=116) and Tennessine (Ts, Z=117) and their lighter analogs Te, I, Po, and At." pith.science (2026). https://pith.science/paper/TZ6RCIZ7

@misc{pith2026250522895,
  author       = {Pith},
  title        = {Pith review of: Electronic structure calculation for superheavy elements Livermorium (Lv, Z=116) and Tennessine (Ts, Z=117) and their lighter analogs Te, I, Po, and At},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TZ6RCIZ7}},
  note         = {Machine review of arXiv:2505.22895}
}
read the original abstract

Advanced theoretical techniques that combine the linearized coupled-cluster method, configuration interaction method, and perturbation theory are used to calculate energy levels, ionization potentials, electron affinities, field isotope shift, and static dipole polarizabilities of the superheavy elements Lv and Ts, along with their lighter analogs Te, I, Po, and At. Calculations for the heavy elements, Po, At, Lv, and Ts are used to address the gaps in the experimental data. Calculations for the lighter elements, Te and I (and partly Po and At) are used to demonstrate the accuracy of the calculations.

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Ionisation potentials and energy levels of ions of heavy and superheavy elements Te, I, Po, At, Lv and Ts

    physics.atom-ph 2025-07 conditional novelty 5.0 of 10

    Successive ionization potentials and ionic energy levels are predicted for Te, I, Po, At, Lv, and Ts using the SD+CIPT method, with accuracy inferred from Te/I benchmarks.

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