REVIEW 2 major objections 6 minor 2 cited by
Excited-state Properties Beyond the Excitation Energy from Orbital-Optimized Density Functional Calculations I: Dipole Moments of Rydberg States
T0 review · 2 major / 6 minor · reviewed 2026-08-02 · deepseek-v4-flash
Pith's one-line read Dipole moments are a stricter test than excitation energies for orbital-optimized DFT calculations of Rydberg states, and plane-wave bases reveal biases hidden in atom-centered basis sets.
desk verdict A worthwhile OO-DFT benchmark: dipole moments of Rydberg states are much harder to converge than energies, and plane waves expose LCAO limits—but the plane-wave reference itself lacks a box-size test, so the dramatic sign-error claims are not yet fully anchored. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The central object is the excited-state dipole moment evaluated from state-specific orbital-optimized densities, with open-shell singlet values obtained by spin purification (µ_S = 2µ_M − µ_T). The key tool is the plane-wave/projector-augmented-wave (PAW) representation, which provides a flexible, non-atom-centered description of diffuse Rydberg orbitals. The basis-set comparison is aided by the variance of the electron position operator, σ(r), which quantifies the spatial extent of the excited-state density and shows that matching σ(r) does not guarantee an accurate dipole moment.
What would settle it
Recompute the most diffuse Rydberg states (e.g., water S4 and S5) with a much larger simulation cell (e.g., 15–20 Å vacuum) and a tighter grid; if the plane-wave dipole moments shift by more than ~0.1 D relative to the 10.5 Å results, the claimed PW reference would be compromised.
Extended reading notes
Core claim
Using orbital-optimized DFT with a plane-wave basis, the authors compute dipole moments for a set of Rydberg excited states of water, formaldehyde, ammonia, and methanol. They find that the dipole moment is far more sensitive to basis-set choice than the excitation energy. A singly-augmented atom-centered basis (aug-cc-pVDZ) overconfines the Rydberg density, causing large magnitude errors and sometimes wrong orientation of the dipole, even when the excitation energy is nearly basis-set independent. Adding a second diffuse function set (d-aug) improves radial extent but leaves persistent errors for the most diffuse states, because the atom-centered form cannot fully capture the anisotropic de
Load-bearing premise
The plane-wave calculations are treated as the converged reference without a demonstrated test that the chosen vacuum size and grid spacing are fully converged for dipole moments, and the coupled-cluster references themselves use atom-centered basis sets that the paper argues can be unreliable for the most diffuse states.
Editorial extensions
If this is right
- Benchmarking OO-DFT Rydberg states solely by excitation energies is insufficient; dipole moments (and likely other one-electron properties) expose basis-set deficiencies hidden by variational energy stationary points.
- Plane-wave or otherwise delocalized basis representations should be preferred for computing properties of diffuse Rydberg states, especially when accurate reference values are sought.
- Adding more diffuse Gaussian functions does not systematically eliminate dipole errors; the atom-centered anchoring itself is a limitation, not just the radial extent.
- PBE0 emerges as a reliable low-cost functional for Rydberg-state dipole moments, while a globally scaled self-interaction correction, despite its correct asymptotic potential, systematically overestimates dipole magnitudes.
- High-level coupled-cluster references that use atom-centered bases may themselves be biased for the most diffuse Rydberg states, so new benchmark data with flexible basis representations are needed.
Reading between the lines
- The same atom-centered basis bias likely affects other properties (e.g., oscillator strengths, polarizabilities) of diffuse excited states, not just dipole moments.
- Locally scaled self-interaction corrections, which reduce the correction in regions of overlapping orbital densities, could plausibly resolve the overestimation seen here, but this is a testable conjecture beyond the paper.
- The finding that matching σ(r) does not ensure accurate dipole moments suggests that anisotropic basis flexibility—not just diffuseness—should be a design criterion for future basis sets for Rydberg states.
- The spin-purification procedure assumes the mixed-spin and triplet states have identical spatial orbitals; the paper notes SIC-induced symmetry breaking that prevents purification in some cases, implying this assumption can fail and may affect other states where it was applied.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. This paper reports orbital-optimized (OO) density functional calculations of excited-state dipole moments for Rydberg states of water, formaldehyde, ammonia, and methanol. The authors compare plane-wave/PAW and atom-centered (aug-cc-pVDZ+sz, d-aug-cc-pVDZ+sz) basis sets with PBE, PBE0, and globally scaled Perdew–Zunger SIC functionals, and benchmark against high-level coupled-cluster reference values where available. The central claim is that dipole moments are a much stricter test than excitation energies for OO calculations of diffuse Rydberg states: a single-augmented basis can give large errors or even sign errors in the dipole moment while the excitation energy remains close to the plane-wave result, and residual errors persist with double augmentation for the most diffuse states. The authors further report that PBE/PW agrees well with reference values, PBE0 improves the statistics, and global SIC overestimates dipole magnitudes despite restoring the correct asymptotic potential.
Significance. If the central claim holds, the paper establishes an important new benchmark dimension for OO-DFT Rydberg-state calculations, showing that energy-only validation is insufficient for property predictions. The study is original, uses multiple molecules and functionals, provides state-specific analysis via the variance of the electron density and difference densities, and is implemented in the open-source GPAW code. The plane-wave/PAW approach to diffuse Rydberg dipoles is a useful methodological contribution. However, the strongest conclusions rely on the plane-wave results being converged with respect to simulation cell size, and that convergence is not demonstrated; the functional ranking also rests on a selected subset of states. These issues need to be resolved before the quantitative conclusions can be fully trusted.
major comments (2)
- [§2.4 / Tables 1–2] The plane-wave results are used as the reference for the most dramatic claims (e.g., sign errors in water S4/S5, ammonia S3, methanol S3/S4), but no convergence test is reported for the simulation cell size or the grid/cutoff. The most diffuse states have σ(r) ≈ 80–90 bohr², i.e., an RMS radius of ≈9 bohr, while the stated 'minimum of 10.5 Å of vacuum' puts the cell boundary only ≈20 bohr from the atoms. The Rydberg tail can therefore be sensitive to periodic confinement, and the dipole moment is especially sensitive to the tail density. Since most of the states driving the conclusion have no coupled-cluster reference in Table 2, the PW values are the sole anchor. Please add explicit box-size convergence tests (e.g., vacuum of 10.5, 12, and 14 Å) and cutoff tests for the most diffuse states, and report whether the qualitative LCAO-vs-PW differences survive. Also state precisely how the '
- [§3.2 / Fig. 5] The statistical comparison of functionals in Figure 5 is restricted to states for which the d-aug and PW PBE results differ by less than 5%. This excludes precisely the most diffuse states where basis-set flexibility is the issue and where functional dependence is largest (water S4/S5, ammonia S3, methanol S3/S4). The reported median absolute errors (PBE ≈20%, PBE0 ≈6%, SIC ≈24–26%) therefore characterize a favorable subset, not the Rydberg states that are the paper's main focus. Please report the exact set and number of states used in the statistics, and provide a reference-free analysis (e.g., PW-vs-LCAO differences as a function of functional) to support the claim that PBE0 improves and SIC worsens dipole moments for diffuse Rydberg states.
minor comments (6)
- [§2.3, Eq. (8)] The spin-purification formula for the dipole moment is stated without derivation or citation. Since it is not immediately implied by the energy formula Eq. (4), please provide a justification or a reference showing that the mixed-spin density is the average of the singlet and triplet densities in the OO framework.
- [§3.1 / Table 1] The text says the ammonia S3 dipole is overestimated by 'more than 4.5 D' with aug, but the table gives aug = 4.79 D and PW = 1.07 D, i.e., a difference of 3.72 D. Please correct this numerical value.
- [§4] The statement about two PBE-SIC solutions for the formaldehyde 2p_y→3p_z state gives spin-purified dipole moments of 0.03 and 0.72 D, but Table 2 reports PBE-SIC S3 as 1.21 D. The numbers 0.03 and 0.72 appear to belong to a different state (S4). Please clarify the state labels and the values reported in Table 2.
- [§3.2 / §4] There are several typographical errors: 'Unfortunatley' in §3.2, 'The xcomponent' in §3.1, and inconsistent use of 'SIC/2' vs 'PBE-SIC/2' in a few places. A careful proofreading pass is needed.
- [Table 2 / Ref. [85]] The ammonia reference values are attributed to 'personal correspondence' with the authors of Ref. [12]. For reproducibility, please include these reference values and the underlying calculations in the Supporting Information or make them publicly available in a persistent form.
- [§5] The conclusion states that 'PWs are not affected by confinement effects.' This is only true if the cell is sufficiently large; the manuscript itself acknowledges this in the Introduction. Please rephrase to 'PWs are not affected by confinement effects for the cell sizes used here, as verified by ...' once the convergence test is added.
Circularity Check
No significant circularity: the dipole-moment benchmark is anchored on external CC/TBE references and direct calculation, not on fitted inputs or self-referential derivations.
full rationale
This is an empirical benchmark paper, not a derivation whose conclusion is encoded in its inputs. Excited-state dipole moments are computed from optimized orbitals via the stated PAW expression (Eq. 23) and compared across basis sets and functionals; no parameter is fitted to the reported dipole-moment data. The SIC scaling factor alpha=1/2 is imported from prior literature (refs. 74, 75, 63) and applied uniformly, not optimized against the target quantities. The central claim—that dipole moments are a stricter test than excitation energies for Rydberg states—rests on the observed disagreement between LCAO and plane-wave results, with the PW results validated against external high-level CC/TBE references where available (refs. 12, 85). Self-citations (e.g., refs. 11, 38, 63, 71, 72) concern the direct-optimization methodology, the GPAW code, and previously reported excitation-energy insensitivity; they are not load-bearing for the new dipole-moment benchmark, which is independently computed. The absence of a box-size convergence test for the most diffuse PW states is a possible correctness/convergence risk, but it is not circularity: it does not reduce any prediction to its own input by construction. The selective statistical comparison in Fig. 5 is a reporting choice, not a fitted prediction. No quoted equation or step exhibits self-definition, fitted-input prediction, or importation of a uniqueness theorem from the authors' own prior work. Therefore the circularity score is 0.
Assumptions & free parameters
free parameters (1)
- SIC global scaling factor α =
0.5 (PBE-SIC/2) and 1.0 (PBE-SIC)
assumptions (4)
- domain assumption Ziegler-Rauk-Baerends spin purification formulas ES = 2EM - ET (Eq. 4) and µS = 2µM - µT (Eq. 8) hold for the OO single-determinant states.
- domain assumption The frozen-core approximation in the PAW formalism has negligible effect on excitation energies and dipole moments.
- domain assumption The OO stationary points found by the L-SR1 algorithm correspond to the intended non-Aufbau excited states without variational collapse.
- domain assumption Reference CC calculations with d-aug-cc-pVTZ and CBS extrapolations are converged for the states included in the statistical comparison.
Cite this review
Pith. "Pith review of Excited-state Properties Beyond the Excitation Energy from Orbital-Optimized Density Functional Calculations I: Dipole Moments of Rydberg States." pith.science (2026). https://pith.science/paper/ZGP3KQTJ
@misc{pith2026260612272,
author = {Pith},
title = {Pith review of: Excited-state Properties Beyond the Excitation Energy from Orbital-Optimized Density Functional Calculations I: Dipole Moments of Rydberg States},
year = {2026},
howpublished = {\url{https://pith.science/paper/ZGP3KQTJ}},
note = {Machine review of arXiv:2606.12272}
}
abstract
Rydberg excited states are challenging to describe due to their highly diffuse character. Orbital-optimized density functional calculations typically provide more accurate values of the excitation energy of Rydberg states than time-dependent density functional theory approaches. However, the reliability of orbital-optimized methods for properties of Rydberg excited states such as the dipole moment remains much less explored, with existing benchmarks largely limited to the lowest excited states. Here, orbital-optimized density functional calculations with a plane-wave basis set are used to compute the dipole moment of several Rydberg states of a set of small molecules. Plane waves provide a flexible representation of diffuse Rydberg orbitals, overcoming limitations of commonly used atomic orbitals basis sets. Due to overconfinement of the Rydberg orbitals, a single-augmented atomic basis set yields a magnitude of the dipole moment that disagrees with the plane-wave calculations, even when the corresponding excitation energy is in good agreement. For the most diffuse states, the orientation of the dipole moment predicted by the atomic orbitals basis set can also be incorrect, and discrepancies with plane waves calculations persist even when extra augmented diffuse functions are added. The generalized gradient approximation functional PBE used in combination with the plane-wave representation of the orbitals gives good agreement with higher-level coupled-cluster calculations performed with sufficiently diffuse basis sets, when the latter are available. The hybrid functional PBE0 further improves the results, while PBE with globally scaled explicit Perdew-Zunger self-interaction correction generally leads to larger errors and an overestimation of the dipole moment, despite restoring the correct asymptotic $-1/r$ dependence of the effective Kohn--Sham potential.
Figures
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Forward citations
Cited by 2 Pith papers
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Excited-state Properties Beyond the Excitation Energy from Orbital-Optimized Density Functional Calculations II: Absorption Spectra
Orbital-optimized DFT with plane waves yields useful absorption intensities for single-configuration Rydberg states but fails for multi-configurational states, with median errors of ~29% vs ~189%.
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Orbital-optimized density functional calculations of excited electronic states: Recent advances and perspectives
Review summarizing theoretical foundations, recent algorithmic advances, open-shell singlet treatments, transition properties, and applications of orbital-optimized DFT to Rydberg, charge-transfer, and core excitations.
Reference graph
Works this paper leans on
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[1]
Mountaineering strategy to excited states: Highly accurate oscillator strengths and dipole moments of small molecules.J
AmaraChrayteh, AymericBlondel, Pierre-FrançoisLoos, andDenisJacquemin. Mountaineering strategy to excited states: Highly accurate oscillator strengths and dipole moments of small molecules.J. Chem. Theory Comput., 17(1):416–438, January 2021
2021
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[2]
From personal correspondence with the authors of Ref. [1]. 23
Reviewed August 2, 2026 · model on record in the stance chip above.
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