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arxiv: 2606.12272 · v1 · pith:ZGP3KQTJnew · submitted 2026-06-10 · ⚛️ physics.chem-ph

Excited-state Properties Beyond the Excitation Energy from Orbital-Optimized Density Functional Calculations I: Dipole Moments of Rydberg States

Lorenzo Restaino , Jukka John , Diego Llorena Prieto , Yorick L. A. Schmerwitz , Elvar \"Orn J\'onsson , Gianluca Levi This is my paper

Pith reviewed 2026-06-27 08:00 UTC · model grok-4.3

classification ⚛️ physics.chem-ph
keywords Rydberg statesdipole momentsorbital-optimized DFTplane wavesatomic basis setsPBEself-interaction correction
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0 comments X

The pith

Orbital-optimized DFT with plane waves reveals that atomic basis sets produce inaccurate dipole moments for Rydberg states even when excitation energies are correct.

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

The paper shows that orbital-optimized density functional theory calculations performed with a plane-waves basis can compute dipole moments for several Rydberg excited states of molecules. This reveals that a commonly used single-augmented atomic basis set gives wrong dipole moments even in cases where the excitation energy itself is insensitive to the choice of basis. The calculations compare several functionals and find that PBE matches higher-level results while PBE0 improves further, whereas adding explicit self-interaction correction increases the errors. A reader would care because dipole moments are a key excited-state property that has received far less benchmarking than energies, especially for states beyond the lowest one.

Core claim

Orbital-optimized density functional calculations with a plane waves basis set are used to compute the dipole moments of several Rydberg states of a set of molecules. Plane waves provide a flexible representation of the diffuse Rydberg orbitals, revealing limitations of atomic orbitals basis sets. A commonly used single-augmented atomic basis set yields inaccurate dipole moments even when the excitation energy is insensitive to the basis representation, and discrepancies with plane waves calculations persist for the most diffuse states even when extra augmented diffuse functions are added. The generalized gradient approximation functional PBE gives good agreement with higher-level calculatio

What carries the argument

Orbital-optimized density functional calculations with a plane-waves basis set used to represent diffuse Rydberg orbitals when evaluating dipole moments.

If this is right

  • A commonly used single-augmented atomic basis set yields inaccurate dipole moments even when the excitation energy is insensitive to the basis representation.
  • Discrepancies with plane waves calculations persist for the most diffuse states even when extra augmented diffuse functions are added.
  • The PBE functional gives good agreement with higher-level calculations for the dipole moments.
  • The hybrid functional PBE0 further improves the dipole-moment results.
  • PBE with globally scaled explicit Perdew-Zunger self-interaction correction leads to larger errors and overestimation of the dipole moment.

Where Pith is reading between the lines

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

  • Properties other than energy may require more flexible basis representations for Rydberg states than what suffices for energies alone.
  • The same basis limitations could appear in other diffuse-state observables such as transition dipole moments or polarizabilities.
  • Plane-wave OO-DFT could be tested on additional molecular excited-state properties to check whether the pattern holds.

Load-bearing premise

The plane-wave calculations with the chosen cutoff and k-point sampling form a converged reference against which atomic-basis errors can be measured.

What would settle it

A new plane-wave run with substantially higher cutoff energy or denser k-point grid that changes the computed dipole moments by more than the reported discrepancies would falsify the reference.

Figures

Figures reproduced from arXiv: 2606.12272 by Diego Llorena Prieto, Elvar \"Orn J\'onsson, Gianluca Levi, Jukka John, Lorenzo Restaino, Yorick L. A. Schmerwitz.

Figure 1
Figure 1. Figure 1: Cartesian coordinate frames used for the molecules investigated in this manuscript. [PITH_FULL_IMAGE:figures/full_fig_p011_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Effect of the basis set on the dipole moments of ground and singlet excited states of [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Comparison of the optimized 3px orbital obtained in a mixed-spin calculation of the S4 state of water obtained with different atomic orbitals basis sets and with plane waves. (a) 3px amplitude along an axis perpendicular to the molecular plane and containing the oxygen atom calculated with aug (red), d-aug (orange), and PWs (blue). (b) Three-dimensional plot of the difference density, ∆norb = nd-aug−nPW, b… view at source ↗
Figure 4
Figure 4. Figure 4: Spin-purified dipole moments of the singlet excited states of water (a), formalde [PITH_FULL_IMAGE:figures/full_fig_p017_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Signed (a) and absolute (b) relative percentage errors in the magnitude of singlet [PITH_FULL_IMAGE:figures/full_fig_p021_5.png] view at source ↗
read the original abstract

Rydberg excited states are challenging to describe due to their highly diffuse character. Orbital-optimized density functional calculations provide a better description of Rydberg states than time-dependent density functional theory. However, benchmarks have so far focused on the excitation energy, while assessments of dipole moments remain limited to the lowest excited state. Here, orbital-optimized density functional calculations with a plane waves basis set are used to compute the dipole moments of several Rydberg states of a set of molecules. Plane waves provide a flexible representation of the diffuse Rydberg orbitals, revealing limitations of atomic orbitals basis sets. A commonly used single-augmented atomic basis set yields inaccurate dipole moments even when the excitation energy is insensitive to the basis representation, and discrepancies with plane waves calculations persist for the most diffuse states even when extra augmented diffuse functions are added. The generalized gradient approximation functional PBE gives good agreement with higher-level calculations where available. The hybrid functional PBE0 further improves the results, while PBE with globally scaled explicit Perdew-Zunger self-interaction correction leads to larger errors and an overestimation of the dipole moment, despite restoring the correct asymptotic $-1/r$ behavior of the effective Kohn--Sham potential.

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 uses orbital-optimized DFT calculations in a plane-wave basis to compute dipole moments of multiple Rydberg excited states across a set of molecules. It reports that commonly employed single-augmented atomic basis sets produce inaccurate dipoles even when excitation energies are insensitive to basis choice, that adding further diffuse functions does not eliminate discrepancies for the most diffuse states, and that PBE and PBE0 yield good agreement with higher-level references while PBE with Perdew-Zunger SIC overestimates the dipoles despite restoring the correct asymptotic potential.

Significance. If the central comparisons hold, the work is significant because it isolates a clear limitation of standard atomic bases for excited-state properties (dipoles) that is not apparent from excitation energies alone, and it demonstrates the utility of plane-wave representations for diffuse orbitals. The systematic functional comparison (PBE, PBE0, SIC-PBE) against external higher-level data is a positive feature.

major comments (2)
  1. [Methods] The headline claim that single-augmented atomic bases yield inaccurate dipoles (while energies remain stable) and that extra diffuse functions still fail for the most diffuse states (abstract) rests on the plane-wave results constituting a converged reference. However, the Methods section provides no dipole-specific convergence tests (varying cutoff at fixed geometry or increasing k-point density) for the extended Rydberg densities; residual PW incompleteness would produce errors of the same character as the atomic-basis errors being criticized.
  2. [Abstract / Results] The abstract states that PBE gives good agreement with higher-level calculations 'where available' and that PBE0 further improves results, yet no quantitative error statistics, specific molecules, or tabulated deviations with error bars are referenced in the summary of results; without these, the strength of the functional-performance conclusion cannot be assessed.
minor comments (2)
  1. [Abstract] The abstract refers to 'a set of molecules' without naming them or indicating the number of states per molecule; adding this information would improve readability.
  2. Notation for the self-interaction correction (explicitly 'globally scaled explicit Perdew-Zunger') should be defined at first use with a brief equation or reference.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thoughtful review and for recognizing the significance of our findings on the limitations of atomic basis sets for Rydberg dipole moments. We address the major comments below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Methods] The headline claim that single-augmented atomic bases yield inaccurate dipoles (while energies remain stable) and that extra diffuse functions still fail for the most diffuse states (abstract) rests on the plane-wave results constituting a converged reference. However, the Methods section provides no dipole-specific convergence tests (varying cutoff at fixed geometry or increasing k-point density) for the extended Rydberg densities; residual PW incompleteness would produce errors of the same character as the atomic-basis errors being criticized.

    Authors: We agree that demonstrating convergence of the plane-wave dipole moments is essential to support our claims. Although our calculations used a high plane-wave cutoff and Gamma-point sampling with sufficiently large simulation cells, we did not explicitly report dipole convergence tests in the Methods. In the revised manuscript, we will include additional convergence data for the dipole moments with respect to cutoff energy and cell size for representative Rydberg states to confirm that the reported values are converged to within acceptable tolerances. revision: yes

  2. Referee: [Abstract / Results] The abstract states that PBE gives good agreement with higher-level calculations 'where available' and that PBE0 further improves results, yet no quantitative error statistics, specific molecules, or tabulated deviations with error bars are referenced in the summary of results; without these, the strength of the functional-performance conclusion cannot be assessed.

    Authors: The full results section of the manuscript does contain quantitative comparisons, including tables with dipole moments from different methods and deviations from reference values for specific molecules. However, to make this clearer in the summary, we will add a sentence in the results section or abstract referencing the mean absolute deviations or specific error ranges (e.g., PBE0 errors typically below 0.1 D for available cases). We will ensure error bars or statistics are explicitly highlighted. revision: partial

Circularity Check

0 steps flagged

No circularity: direct computational benchmarks against external references

full rationale

The paper computes dipole moments of Rydberg states via orbital-optimized DFT in a plane-wave basis and directly compares the results to atomic-orbital basis sets and to independent higher-level calculations where available. No derivation chain reduces a reported quantity to a fitted parameter or self-citation by construction; the central claims rest on explicit numerical comparisons rather than on any of the enumerated circular patterns. The plane-wave results function as an external reference, not as a quantity derived from the atomic-basis data under test.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The work rests on standard Kohn-Sham DFT approximations and the assumption that orbital optimization improves Rydberg descriptions; no new entities or ad-hoc parameters are introduced beyond the choice of existing functionals and basis representations.

axioms (2)
  • domain assumption Orbital-optimized Kohn-Sham DFT provides a valid description of Rydberg excited states
    Central methodological premise invoked throughout the abstract
  • domain assumption Plane-wave basis sets can be converged to serve as reference for diffuse orbitals
    Implicit in using plane-wave results to benchmark atomic bases

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Forward citations

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