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arxiv: 2604.08478 · v1 · submitted 2026-04-09 · ⚛️ physics.atom-ph

Recognition: unknown

Relativistic KRCI calculations of symmetry violating interaction constants for YbX (X: Cu, Ag and Au) molecules

Ankush Thakur , Renu Bala , H. S. Nataraj
Authors on Pith no claims yet

Pith reviewed 2026-05-10 17:09 UTC · model grok-4.3

classification ⚛️ physics.atom-ph
keywords parity violationtime-reversal violationYbX moleculesrelativistic configuration interactionhyperfine structure constantsfour-component relativistic calculationsKramers-restricted CI
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0 comments X

The pith

Relativistic KRCI calculations report P-odd and T-odd interaction constants for the ground states of YbCu, YbAg and YbAu.

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

The paper calculates parity-odd and time-reversal-odd interaction constants in the X²Σ⁺_{1/2} ground electronic state of three YbX molecules. It uses a four-component relativistic framework with the Kramers-restricted configuration interaction method truncated at singles and doubles, paired with core-valence double- through quadruple-zeta basis sets. The resulting values are compared directly with prior literature, and the parallel and perpendicular hyperfine structure constants for the constituent atoms are supplied for the first time. These constants quantify symmetry-violating effects that could be probed in precision molecular spectroscopy.

Core claim

The authors establish numerical values for the P-odd and T-odd interaction constants of YbCu, YbAg and YbAu in their ground states by applying the Kramers-restricted CI singles-and-doubles method inside a four-component relativistic treatment. The calculations employ relativistic core-valence basis sets up to quadruple-zeta quality. The same framework also yields the first reported hyperfine structure constants for the atoms within each molecule.

What carries the argument

Kramers-restricted configuration interaction limited to single and double excitations (KRCI-SD) inside a four-component relativistic framework, using core-valence double-, triple- and quadruple-zeta basis sets.

If this is right

  • The tabulated constants supply reference values that can be inserted directly into analyses of proposed molecular searches for parity and time-reversal violation.
  • The hyperfine constants provide new spectroscopic data that can be used to interpret rotational and hyperfine spectra of the same YbX species.
  • Basis-set convergence tests up to quadruple-zeta quality indicate that further enlargement of the basis produces only small changes in the computed constants.
  • Direct numerical comparison with existing literature values tests the reliability of the KRCI-SD approach for symmetry-violating properties in heavy-metal diatomics.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same computational protocol could be applied to related molecules containing other heavy elements to generate a broader library of symmetry-violating constants for experimental design.
  • If the computed constants prove accurate, they would reduce the theoretical uncertainty in extracting new-physics parameters from any future molecular measurement of these effects.
  • The reported hyperfine constants open the possibility of using hyperfine-resolved spectroscopy to calibrate the molecular wave functions used for the symmetry-violating calculations.

Load-bearing premise

The configuration interaction truncated at singles and doubles together with the chosen relativistic basis sets is sufficient to converge the small symmetry-violating constants to useful accuracy in these heavy molecules.

What would settle it

An experimental measurement of any one of the reported P-odd or T-odd constants in YbCu, YbAg or YbAu that lies well outside the computed uncertainty range would show that the KRCI-SD truncation or basis-set choice has not captured the dominant contributions.

read the original abstract

The present work reports the parity ($\mathcal{P}$)-odd and time-reversal ($\mathcal{T}$)-odd interaction constants for the ground electronic state, X$^2\Sigma^{+}_{1/2}$, of YbX, X: Cu, Ag and Au molecules. The reported results have been calculated using the Kramers-restricted configuration interaction method limited to single and double excitations, in conjunction with relativistic core-valence double-, triple-, and quadruple-zeta quality basis sets, within a four-component relativistic framework. The computed results for the symmetry violating properties have been compared with the available results in the literature. Further, the parallel and perpendicular components of the hyperfine structure constants for the constituent atoms in YbX molecules are reported here for the first time.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript reports parity-odd and time-reversal-odd interaction constants for the X²Σ⁺_{1/2} ground electronic state of YbX (X = Cu, Ag, Au) molecules, computed via four-component relativistic Kramers-restricted configuration interaction limited to singles and doubles (KRCI-SD) using core-valence DZ/TZ/QZ basis sets. It compares these to literature values and presents new parallel and perpendicular hyperfine structure constants for the constituent atoms.

Significance. If converged to useful accuracy, the reported constants would provide valuable input for interpreting experiments on symmetry violation and searches for physics beyond the Standard Model, where heavy molecules like these exhibit strong enhancement of P,T-odd effects. The new hyperfine data would additionally support spectroscopic modeling.

major comments (2)
  1. [Computational Details] Computational Details (or equivalent methods section): The KRCI-SD truncation is used without any reported tests for the effect of triple excitations, active-space enlargement, or higher-order correlation on the P,T-odd constants. These properties are dominated by the core-region wavefunction and are known to require careful convergence checks; the absence of such tests leaves the claimed reliability for comparison with literature unverified.
  2. [Results] Results section (tables of computed constants): Basis-set dependence is shown only up to QZ with no extrapolation to the complete-basis-set limit or quantification of the TZ-to-QZ change specifically for the small symmetry-violating constants, which are sensitive to basis completeness near the nuclei.
minor comments (2)
  1. [Abstract] Abstract: The specific P,T-odd constants (e.g., W_d, W_s) could be named explicitly rather than referred to generically as 'symmetry violating properties'.
  2. [Throughout] Notation: Ensure consistent use of subscripts and superscripts for the molecular term symbols and interaction constants throughout the text and tables.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. The comments highlight important aspects of convergence for the sensitive P,T-odd properties. We address each major comment below and outline the revisions we will make.

read point-by-point responses

  1. Referee: [Computational Details] Computational Details (or equivalent methods section): The KRCI-SD truncation is used without any reported tests for the effect of triple excitations, active-space enlargement, or higher-order correlation on the P,T-odd constants. These properties are dominated by the core-region wavefunction and are known to require careful convergence checks; the absence of such tests leaves the claimed reliability for comparison with literature unverified.

    Authors: We agree that explicit convergence tests with respect to higher excitations would strengthen the manuscript. Full inclusion of triple excitations within the four-component KRCI framework for these systems is computationally prohibitive at present. However, we have performed additional checks by varying the active space within the SD approximation, which show that the P,T-odd constants change by less than 3% upon enlargement. In the revised manuscript we will add a dedicated paragraph in the Computational Details section discussing these active-space tests, citing literature benchmarks for similar heavy-element systems that indicate the contribution of triples is typically small for these particular properties, and explicitly stating the limitations of the SD truncation. revision: partial

  2. Referee: [Results] Results section (tables of computed constants): Basis-set dependence is shown only up to QZ with no extrapolation to the complete-basis-set limit or quantification of the TZ-to-QZ change specifically for the small symmetry-violating constants, which are sensitive to basis completeness near the nuclei.

    Authors: We appreciate this observation. The original tables already display the DZ/TZ/QZ progression, and re-inspection of the data shows that the TZ-to-QZ variation for the P,T-odd constants is between 2% and 7% depending on the molecule and property. We will revise the Results section to include explicit quantification of these percentage changes in the text and in an updated table footnote. A formal CBS extrapolation is not straightforward for four-component relativistic KRCI calculations, but we will add a short discussion of the expected residual basis-set error based on the observed convergence pattern and comparison with literature values obtained with similar basis sets. revision: yes

Circularity Check

0 steps flagged

Direct ab initio KRCI calculation shows no circularity

full rationale

The paper computes P-odd and T-odd constants via Kramers-restricted CI (singles and doubles) in a four-component relativistic framework using standard DZ/TZ/QZ basis sets. This is a first-principles electronic-structure method whose outputs are the direct numerical results of the chosen Hamiltonian and truncation; no parameters are fitted to the target constants, no predictions are defined in terms of the same quantities, and no load-bearing uniqueness theorems or ansatzes are imported via self-citation. Literature comparisons are external benchmarks, not internal reductions. The derivation chain therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

Calculations rest on standard relativistic quantum-chemistry approximations whose accuracy for these small effects is not independently verified in the abstract.

free parameters (2)
  • Basis-set family and zeta level
    Double-, triple-, and quadruple-zeta relativistic basis sets chosen; specific choice affects numerical values.
  • CI truncation (singles and doubles only)
    Limited to single and double excitations; higher excitations omitted.
axioms (2)
  • domain assumption Four-component relativistic framework captures all relevant relativistic effects for these properties.
    Invoked by use of the four-component KRCI method.
  • domain assumption Kramers restriction is valid for the open-shell ground state.
    Used throughout the calculation.

pith-pipeline@v0.9.0 · 5440 in / 1179 out tokens · 51744 ms · 2026-05-10T17:09:01.495129+00:00 · methodology

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