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arxiv: 2606.13243 · v1 · pith:W5RFQL3Jnew · submitted 2026-06-11 · ⚛️ physics.chem-ph

Excited-state Properties Beyond the Excitation Energy from Orbital-Optimized Density Functional Calculations II: Absorption Spectra

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

Pith reviewed 2026-06-27 05:29 UTC · model grok-4.3

classification ⚛️ physics.chem-ph
keywords orbital-optimized DFToscillator strengthsabsorption spectranonorthogonal determinantsprojector augmented-waveexcited statesdensity functional theory
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The pith

Orbital-optimized density functional calculations reproduce absorption spectra from high-level multireference methods across a molecular set.

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

The paper extends Löwdin's formalism for nonorthogonal determinants to the projector augmented-wave method with plane-wave basis sets. This extension enables computation of oscillator strengths for multiple valence and Rydberg excited states obtained from orbital-optimized density functional theory. The resulting spectra qualitatively match reference absorption spectra even when a basic generalized-gradient approximation functional is used. Agreement in peak intensities holds well for states with single-determinant character but deviates for states with strong multi-configurational character. No systematic gain in accuracy appears when exact exchange or explicit self-interaction correction is added, and errors show no clear link to ground-state overlaps.

Core claim

Orbital-optimized density functional calculations describe each excited state with its own variationally optimized orbitals and, after extension of Löwdin's formalism to the projector augmented-wave framework, yield oscillator strengths that allow reconstruction of absorption spectra. These spectra qualitatively match those from high-level multireference methods for the tested molecules even with a simple generalized-gradient approximation, with excellent intensity agreement for single-determinant states and larger discrepancies for multi-configurational states. Inclusion of exact exchange or self-interaction correction brings no systematic improvement, and nonzero overlaps between ground an

What carries the argument

Extension of Löwdin's formalism to the projector augmented-wave framework with plane-wave basis for oscillator strengths between nonorthogonal orbital-optimized states.

If this is right

  • Absorption spectra become accessible from orbital-optimized density functional theory for sets of molecules without requiring advanced multireference methods.
  • Peak intensities in the computed spectra match reference data well when the excited state is dominated by a single determinant.
  • States with strong multi-configurational character produce substantial discrepancies in intensities that persist across different functionals.
  • Adding exact exchange or explicit self-interaction correction does not systematically reduce errors in oscillator strengths.
  • The magnitude of ground-excited state overlap does not predict the size of errors in the absorption peaks.

Where Pith is reading between the lines

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

  • The method could enable spectrum calculations for larger molecules where multireference approaches remain computationally prohibitive.
  • Focus on improving the underlying functional description for multi-configurational states may be needed to reduce remaining discrepancies.
  • The absence of correlation with overlaps suggests the nonorthogonality treatment remains stable for the tested systems and basis sets.

Load-bearing premise

The extension of Löwdin's formalism to the projector augmented-wave framework with plane-wave basis accurately computes oscillator strengths without introducing uncontrolled errors from nonorthogonality handling or basis representation.

What would settle it

Direct numerical comparison of oscillator strengths computed for a strongly multi-configurational excited state against values from experiment or a higher-level multireference calculation would test whether the qualitative reproduction holds.

Figures

Figures reproduced from arXiv: 2606.13243 by Diego Llorena Prieto, Elvar \"Orn J\'onsson, Gianluca Levi, Jukka John, Lorenzo Restaino, Yorick L. A. Schmerwitz.

Figure 1
Figure 1. Figure 1: Calculated absorption spectrum of water. (a) OO density-functional and (b) LR [PITH_FULL_IMAGE:figures/full_fig_p022_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Calculated absorption spectrum of formaldehyde. (a) OO density functional and [PITH_FULL_IMAGE:figures/full_fig_p023_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Calculated absorption spectrum of ammonia. (a) OO density functional and [PITH_FULL_IMAGE:figures/full_fig_p024_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Calculated absorption spectrum of methanol. (a) OO density functional and [PITH_FULL_IMAGE:figures/full_fig_p025_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Calculated absorption spectrum of ethylene. (a) OO density functional and (b) LR [PITH_FULL_IMAGE:figures/full_fig_p026_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Relative percentage errors in oscillator strengths categorized by xc-functional. [PITH_FULL_IMAGE:figures/full_fig_p027_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Relative percentage errors in oscillator strengths categorized by state character (a) [PITH_FULL_IMAGE:figures/full_fig_p028_7.png] view at source ↗
read the original abstract

Orbital-optimized density functional calculations describe each excited state using its own set of variationally optimized orbitals. While this state-specific optimization improves the description of excited states, it also results in nonorthogonal electronic states, which complicates the evaluation of transition properties. Existing benchmarks have primarily targeted the excitation energy, whereas estimates of oscillator strengths have largely been restricted to the first excited state only. In this study, L\"owdin's formalism for nonorthogonal determinants is extended to the projector augmented-wave framework. It is then used with a plane-wave basis set to compute the oscillator strengths of several valence and Rydberg excited states in a set of molecules. Orbital-optimized density functional calculations qualitatively reproduce absorption spectra from high-level multireference reference methods across the molecular set, even when using a simple generalized-gradient approximation. The agreement in peak intensities is excellent for states dominated by a single determinant, whereas substantial discrepancies arise for states with strong multi-configurational character. Analysis of the exchange--correlation functional shows that the inclusion of exact exchange and explicit self-interaction correction does not provide a systematic improvement in the accuracy of oscillator strengths. Moreover, no clear correlation emerges between the errors in the absorption peaks and the nonzero overlap between the ground state and the orbital-optimized excited states.

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

3 major / 2 minor

Summary. The manuscript extends Löwdin's formalism for transition matrix elements between nonorthogonal determinants to the projector augmented-wave (PAW) representation in a plane-wave basis. Orbital-optimized DFT calculations are then performed for valence and Rydberg excited states across a molecular test set, with oscillator strengths used to generate absorption spectra that are compared to high-level multireference reference data. The central claim is that even a simple GGA yields qualitative agreement with the reference spectra, with excellent intensity agreement for single-determinant states but larger discrepancies for multi-configurational states; no correlation is reported between ground-excited overlap and spectral errors, and inclusion of exact exchange or self-interaction correction does not systematically improve results.

Significance. If the Löwdin-PAW extension proves accurate, the work would show that state-specific orbital optimization in DFT can deliver reliable oscillator strengths beyond excitation energies, providing a parameter-free and computationally efficient route to absorption spectra that makes falsifiable predictions against external multireference benchmarks. This would be a useful advance for systems where multireference methods remain prohibitive.

major comments (3)
  1. [Theory section (Löwdin-PAW extension)] The extension of Löwdin's nonorthogonal-determinant formalism to the PAW plane-wave representation (described in the Theory section) is load-bearing for every reported oscillator strength and intensity. The manuscript supplies no numerical validation of this extension against analytically known oscillator strengths for nonorthogonal test cases, nor any convergence tests with respect to plane-wave cutoff or supercell size; without such checks, apparent agreement with multireference spectra could arise from uncontrolled basis or projector artifacts rather than the quality of the orbital-optimized densities.
  2. [Abstract and Results section] Abstract and Results section: the claim that peak intensities show 'excellent' agreement for single-determinant states and that the method 'qualitatively reproduces' the reference spectra is unsupported by any quantitative metric (e.g., mean absolute deviation, root-mean-square error, or integrated intensity ratios). Only qualitative language is used, which prevents a proportionate assessment of whether the Löwdin-PAW implementation is reliable enough to support the headline result.
  3. [Results section] Results section: the diagnostic that overlap magnitude does not correlate with error is presented, yet this test does not address possible systematic errors internal to the PAW implementation of the nonorthogonal transition formula (e.g., handling of nonorthogonality inside the projectors). A direct validation of the formalism itself remains necessary before the lack of correlation can be interpreted as evidence of robustness.
minor comments (2)
  1. [Abstract] The number of molecules, total states, and specific functionals employed should be stated explicitly in the abstract to give immediate context for the scope of the claimed qualitative agreement.
  2. [Figures] Figure captions and axis labels for the absorption spectra should include the precise definition of the broadening function and the units of the oscillator strength axis for reproducibility.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments, which have identified important ways to strengthen the validation and presentation of our results. We address each major comment below and will incorporate the suggested improvements in a revised manuscript.

read point-by-point responses

  1. Referee: [Theory section (Löwdin-PAW extension)] The extension of Löwdin's nonorthogonal-determinant formalism to the PAW plane-wave representation (described in the Theory section) is load-bearing for every reported oscillator strength and intensity. The manuscript supplies no numerical validation of this extension against analytically known oscillator strengths for nonorthogonal test cases, nor any convergence tests with respect to plane-wave cutoff or supercell size; without such checks, apparent agreement with multireference spectra could arise from uncontrolled basis or projector artifacts rather than the quality of the orbital-optimized densities.

    Authors: We agree that explicit numerical validation of the Löwdin-PAW extension is necessary to confirm its accuracy independent of the molecular applications. In the revised manuscript we will add a dedicated subsection to the Theory section containing benchmark calculations against analytically known oscillator strengths for simple nonorthogonal determinant pairs, together with convergence tests with respect to plane-wave cutoff and supercell size. These additions will demonstrate that the reported spectral features are not dominated by basis-set or projector artifacts. revision: yes

  2. Referee: [Abstract and Results section] Abstract and Results section: the claim that peak intensities show 'excellent' agreement for single-determinant states and that the method 'qualitatively reproduces' the reference spectra is unsupported by any quantitative metric (e.g., mean absolute deviation, root-mean-square error, or integrated intensity ratios). Only qualitative language is used, which prevents a proportionate assessment of whether the Löwdin-PAW implementation is reliable enough to support the headline result.

    Authors: The referee correctly observes that the manuscript relies on qualitative descriptors without accompanying quantitative error metrics. We will revise the Abstract and Results sections to report mean absolute deviations, root-mean-square errors, and integrated intensity ratios for the oscillator strengths relative to the multireference reference data, separately for single-determinant and multi-configurational states. This will enable a more objective evaluation of the method's performance. revision: yes

  3. Referee: [Results section] Results section: the diagnostic that overlap magnitude does not correlate with error is presented, yet this test does not address possible systematic errors internal to the PAW implementation of the nonorthogonal transition formula (e.g., handling of nonorthogonality inside the projectors). A direct validation of the formalism itself remains necessary before the lack of correlation can be interpreted as evidence of robustness.

    Authors: We acknowledge that the overlap analysis alone does not exclude possible systematic errors arising from the PAW implementation of the nonorthogonal transition formula. The validation subsection added in response to the first comment will include targeted tests of nonorthogonality handling within the projectors and direct comparisons of transition matrix elements against known analytic results. These tests will provide the direct validation required to support the robustness of the reported lack of correlation. revision: yes

Circularity Check

0 steps flagged

No circularity; central results rest on external multireference benchmarks and established formalism extension

full rationale

The paper's core claim—that orbital-optimized DFT qualitatively reproduces absorption spectra—is validated by direct numerical comparison to independent high-level multireference reference methods on a molecular test set. The Löwdin nonorthogonal-determinant formalism is extended to the PAW plane-wave setting, but this extension is presented as a technical implementation step resting on prior established work rather than a self-referential fit or definition. No equations reduce a reported oscillator strength or spectral feature to a fitted parameter by construction, no uniqueness theorem is imported from the same authors to force the method, and no ansatz is smuggled via self-citation. Overlap diagnostics and functional comparisons are post-hoc analyses, not load-bearing inputs. The derivation chain therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The work relies on standard DFT approximations and the validity of the Löwdin extension without introducing new fitted parameters or postulated entities; main assumptions concern the accuracy of the nonorthogonal transition formalism in the PAW context.

axioms (2)
  • domain assumption Löwdin's formalism for nonorthogonal determinants can be accurately extended to the projector augmented-wave method without additional uncontrolled approximations.
    Invoked when applying the extended formalism to compute oscillator strengths in the PAW framework.
  • domain assumption Orbital-optimized DFT provides a valid description of excited states even with simple GGA functionals for the purpose of transition properties.
    Underlies the claim of qualitative reproduction using a simple generalized-gradient approximation.

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Reference graph

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