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REVIEW 3 major objections 4 minor 27 references

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

T0 review · 3 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read A relativistic many-body method predicts the missing spectra and ionization potentials of superheavy ions Lv and Ts, with accuracy benchmarked on Te and I.

desk verdict First predictions for Lv/Ts ions are worth having, but a 13.5% iodine IP1 discrepancy undercuts the accuracy claim and needs a fix. read the letter →

arxiv 2507.16268 v1 pith:QDQUEA5U submitted 2025-07-22 physics.atom-ph

G. K. Vong , V. A. Dzuba , V. V. Flambaum This is my paper
classification physics.atom-ph
keywords superheavyelementsionizationpotentialsenergylevelslivermoriumtennessineconfigurationinteractioncoupled-clustermethodrelativisticeffects
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 aims to establish that a combined linearised coupled-cluster, configuration-interaction, and perturbation-theory approach (SD+CIPT) can predict accurate energy levels and successive ionization potentials for ions of the superheavy elements livermorium and tennessine, as well as their lighter homologues polonium and astatine. The method is validated on tellurium and iodine ions, where experimental data exist, and the average deviations are about 1.4% for excitation energies and about 3% for ionization potentials. If that error rate carries over, the paper's tables supply the first reliable electronic-structure predictions for Lv and Ts ions. The results show the expected growth of relativistic effects down the group, most visibly through a strongly stabilised $7p_{1/2}$ subshell and large spin-orbit splittings that leave characteristic jumps in the ionization-potential ladders.

What carries the argument

The central machinery is SD+CIPT: linearised coupled-cluster single-double equations generate the one- and two-electron correlation operators $\hat\Sigma_1$ and $\hat\Sigma_2$ that describe core-valence correlations, and configuration-interaction perturbation theory then builds the valence-electron Hamiltonian, treating high-energy configurations perturbatively to keep the CI matrix manageable. A frozen-core $V^{N-M}$ potential is used so that core-valence correlations are treated reliably and subtraction diagrams are avoided, while a B-spline basis supplies the single-electron states. Breit and QED corrections are included through a radiative potential. The method produces ground-state energies for successive charge states, whose differences are the ionization potentials, and also yields the level spectra and Land\'e $g$-factors tabulated for each ion.

What would settle it

Measure the 17,968 cm$^{-1}$ interval between the ground state and first excited level of Po II ($6s^2 6p^3 \, {}^4S^o_{3/2}$ to $6s^2 6p^3 \, {}^2P^o_{3/2}$) by laser spectroscopy on trapped Po$^{+}$ ions; if the measured interval deviates from the prediction by much more than the about 1.4% benchmark deviation, the claimed accuracy transfer to the heavier homologues is falsified.

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Extended reading notes

Core claim

The paper claims that the SD+CIPT method, benchmarked on Te and I ions, extends successfully to Po, At, Lv, and Ts ions with the same level of accuracy: roughly 1.4% for excitation energies and 3% for successive ionization potentials. For Lv and Ts, where no experimental or reliable theoretical data exist for the ionic spectra, the computed levels presented in Tables XXIV to XXXIV are put forward as the first predictions of the electronic structure of these ions. The calculations also reproduce the expected trend of growing relativistic effects down the group, with the $7p_{1/2}$ subshell strongly lowered in energy so that, for example, the jump between IP2 and IP3 of Lv and between IP3 and IP4 of Ts marks the removal of a $7p_{1/2}$ electron.

Load-bearing premise

The whole accuracy claim rests on the assumption that the error rate measured for the lighter homologues tellurium and iodine, where relativistic effects are mild, transfers to livermorium and tennessine, where relativistic effects are strong and no experiment is available to check.

Editorial extensions

If this is right

  • Tables XIII to XXXIV become reference data for the spectra and successive ionization potentials of Po, At, Lv, and Ts ions until experiments on these species become feasible.
  • The predicted Lv and Ts ionization potentials fall within the spread of earlier advanced calculations, so they help narrow the expected values for quantities such as chemical reactivity and charge-state behaviour of superheavy elements.
  • The large predicted spin-orbit jumps in the ionization ladders, between IP2 and IP3 for Lv and between IP3 and IP4 for Ts, give a clear experimental signature to look for in future ionization or mass-spectrometric measurements.
  • The calculated Land\'e $g$-factors deviate from non-relativistic values, indicating strong configuration mixing, so the tables offer level identifications rather than energies alone.
  • The benchmark agreement on Te and I, if it transfers, supports treating the new superheavy-ion tables as accurate to roughly 1.4% in excitation energies and 3% in ionization potentials.

Reading between the lines

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

  • Editorial inference: the predicted 17,968 cm$^{-1}$ interval between the ground state and first excited level of Po II is a testable target for laser spectroscopy of trapped Po$^{+}$ ions, and would independently probe the error-transfer assumption before any Lv or Ts experiment is possible.
  • Editorial inference: the same benchmark-on-lighter-homologue strategy should apply to neighbouring superheavy ions such as nihonium, flerovium, and moscovium, where no experimental anchors exist and the $ns^2np$ valence pattern changes gradually.
  • Editorial inference: the strong $7p_{1/2}$ stabilisation implies that the chemistry of Lv and Ts ions may deviate from simple periodicity extrapolations based on lighter Group 16 and 17 elements, potentially affecting predicted oxidation states and volatility.
  • Editorial inference: comparing computed $g$-factors with future measurements would test the method's treatment of configuration mixing separately from its energy-level accuracy, since $g$-factors are sensitive to the wavefunction composition.
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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

3 major / 4 minor

Summary. The manuscript applies the SD+CIPT method (linearised coupled-cluster single-double combined with configuration-interaction perturbation theory) to compute energy levels and successive ionisation potentials of ions of Te, I, Po, At, Lv and Ts. The method is benchmarked against NIST data for Te and I ions, for which the authors report an average deviation of about 1.4% in excitation energies and about 3% in ionisation potentials. On this basis, the paper presents new energy-level tables for Po, At, Lv and Ts ions (Tables XIII–XXXIV) and successive IPs (Table I), concluding that similar accuracy should hold for the superheavy ions.

Significance. If the error-transfer argument were quantitatively supported, the tables for Po, At, Lv and Ts would constitute a valuable first data set for the electronic structure of superheavy ions, complementing the existing theoretical studies cited in Table I. The Te and I benchmark tables contain a large number of levels that agree with NIST data to roughly the stated 1.4%, and the inclusion of Breit and QED corrections is a methodological strength. However, the central accuracy claim is currently weakened by a large unexplained discrepancy in Table I for the first IP of iodine, and by the absence of any direct test of the frozen-core and CIPT truncation errors in the 7p regime. These issues are fixable in revision, but they are load-bearing for the paper's main conclusion.

major comments (3)
  1. [Section III, Table I] The first IP of iodine is listed as 72,925 cm^-1 against the NIST value 84,295 cm^-1, a relative error of about 13.5%. This is incompatible with the statement in the same section that "the relative difference between theory and experiment to be ∼ 3%". Because iodine is one of only two benchmark elements, this single discrepancy directly undermines the stated accuracy level used to justify the extrapolation to At and Ts. The paper must either correct this entry or explain the source of the error, and should quantify how many of the benchmark IPs actually fall within 3%.
  2. [Sections III and IV] The claims "It is natural to assume the same level of accuracy for the IPs of Lv and Ts" and "We should expect similar accuracy for heavier ions of Po, At, Lv, and Ts" are extrapolations without a quantitative error analysis. The two approximations most at risk are the V^(N-M) frozen-core potential of Section II, which uses the same RHF core for all charge stages of an element, and the CIPT partition P/Q of Eq. (5), whose truncation error is not studied in the 7p regime where the paper's own relativistic parameter is about 0.73. A convergence study with respect to the P/Q partition and a test of core relaxation (for example, comparing V^(N-M) with a V^(N) calculation for one of the lighter homologues) would be needed to support the error transfer.
  3. [Table I] Table I contains additional unexplained discrepancies for the direct homologues Po and At that the text does not discuss. The Po II IP is calculated as 129,408 cm^-1 versus 156,000 cm^-1 from the semi-empirical/interpolated value marked with an asterisk, a deviation of about 17%, and the At I IP is 71,254 cm^-1 versus 75,151 cm^-1, a deviation of about 5%. These are the same elements whose spectra are presented as reliable predictions in Tables XIII–XXIII. The paper should either justify why these comparison values are not reliable or explain the deviations, especially since Po and At are the direct lighter homologues of Lv and Ts.
minor comments (4)
  1. [Section I] The sentence "This covers ions with charges from +1 to +6 for the Group 16 elements (Te, Po, Lv) and from +1 to +7 for the Group 17 elements (Te, Po, Lv)" contains a typo: the parenthetical for Group 17 should read (I, At, Ts).
  2. [Section II and Section III] There are minor typographical errors: "celectrons" in Section II and "ocurrs" in Section III should be "electrons" and "occurs", respectively.
  3. [Table I caption] The caption reads "Ionisation potentials (in cm^-1) of I, A and Ts ions"; the symbol "A" should be "At".
  4. [Table X and Table XII] In Table X, row 11, the NIST entry "154 50" appears to be missing a digit. In Table XII, rows 19 and 20 both list the NIST value 495 769 for different levels, which is suspicious and should be checked against the source.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: Lv/Ts predictions are extrapolations benchmarked against external NIST data, not reductions to inputs.

full rationale

The paper's derivation chain computes energy levels and ionization potentials from a frozen-core RHF potential, SD correlation operators, and CI+PT treatment of valence electrons, with IPs obtained as differences of ground-state energies of successive ions. The benchmark data for Te and I come from the NIST database and other external calculations, and are not used as inputs to the calculation. The only self-referential elements are citations to the authors' previous method papers and to their earlier neutral-atom first IPs; these do not define the target quantities and are not load-bearing in a circular sense, because the method itself is checked against external experimental data in Tables II-XII. The statement in Section III, 'It is natural to assume the same level of accuracy for the IPs of Lv and Ts,' is an inductive extrapolation of an error budget, not a derivation of predicted values from benchmark values; any concern about whether the Te/I error transfers to the superheavy regime is a correctness or robustness issue, not circularity. No equation defines a predicted level or IP in terms of the same quantity, and no fitted parameter is renamed as a prediction. Therefore there is no specific reduction to exhibit, and the circularity score is 0.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central predictions rest on standard many-body approximations inherited from Refs. [6-9,11] and on a set of numerical truncations. No quantities are fitted to the Lv or Ts results, so the circularity burden is low. The most fragile input is the assumption that Te and I benchmark errors persist for Lv and Ts; the most important numerical choices are the B-spline basis and the P/Q CI split.

free parameters (3)
  • B-spline basis size and order = 40 states, order 9, box radius 40 a_B, l_max = 6
    Chosen to saturate the single-electron basis; not fit to target data but controls convergence and affects every level.
  • CI subspace partition P/Q = not reported
    The split into low-energy P and high-energy Q, with Q treated perturbatively, is a hand-tuned compromise; results depend on it.
  • Fermi nuclear charge distribution = not reported in this text
    Nuclear size parameters enter the RHF potential for each Z; standard choices but not specified here.
assumptions (4)
  • domain assumption A single frozen RHF core potential V^(N-M) is adequate for all ions of an element; core-valence correlations are captured by the SD Sigma operators.
    Section II states the core potential is the same for all ions and relies on Ref. [11] for the V^(N-M) approximation. If the frozen-core picture degrades for highly ionized superheavies, all ionic energy levels would shift.
  • domain assumption Linearized coupled-cluster SD and second-order CIPT truncations converge; neglected higher excitations and off-diagonal Q-space matrix elements are small.
    Section II, Eq. (5) treats high-energy configurations by second-order perturbation. The paper inherits this from Ref. [6] without a dedicated convergence test for 5 to 6 valence electrons in Lv and Ts ions.
  • domain assumption Benchmark accuracy for Te and I transfers to Po, At, Lv, and Ts despite relativistic effects scaling as (Z alpha)^2.
    Sections III to VI assume the roughly 1.4% excitation-energy error and 3% IP error remain similar for heavier homologues; this is extrapolation, not measurement, and is the main source of uncertainty.
  • domain assumption Term assignments from Landé g-factors matched to non-relativistic LS formulas are correct for strongly mixed states.
    Section II, Eqs. (7) and (8) are used to label configurations in all tables; for Lv and Ts with strong configuration mixing, the identification can mislabel levels.

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Cite this review

Pith. "Pith review of Ionisation potentials and energy levels of ions of heavy and superheavy elements Te, I, Po, At, Lv and Ts." pith.science (2026). https://pith.science/paper/QDQUEA5U

@misc{pith2026250716268,
  author       = {Pith},
  title        = {Pith review of: Ionisation potentials and energy levels of ions of heavy and superheavy elements Te, I, Po, At, Lv and Ts},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QDQUEA5U}},
  note         = {Machine review of arXiv:2507.16268}
}
read the original abstract

We calculate the energy levels and successive ionisation potentials (IPs) of ions of the three heaviest known Group 16 and 17 elements using a theoretical approach that combines the linearised coupled-cluster method, configuration interaction, and perturbation theory. Our calculations address critical gaps in the available data on the electronic structure of the superheavy elements livermorium (Lv) and tennessine (Ts), as well as their lighter homologues polonium (Po) and astatine (At). To assess the accuracy of our methods, we perform analogous calculations for the lighter homologues tellurium (Te) and iodine (I), for which both experimental and reliable theoretical data are available for comparison.

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