pith. machine review for the scientific record. sign in

arxiv: 2605.06013 · v1 · submitted 2026-05-07 · ⚛️ physics.chem-ph

Recognition: unknown

Assessing excited-state geometry optimization strategies for adiabatic photophysical energies

Amrita Bera , Atreyee Majumdar , Raghunathan Ramakrishnan
Authors on Pith no claims yet

Pith reviewed 2026-05-08 04:10 UTC · model grok-4.3

classification ⚛️ physics.chem-ph
keywords adiabatic 0-0 energiesexcited-state geometry optimizationTDDFTUKS DFTssUKSsinglet-triplet gapsphotophysical processesADC(2)
0
0 comments X

The pith

TDDFT-optimized S1 and T1 geometries produce adiabatic 0-0 energies with mean absolute error below 0.1 eV against experiment.

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

The paper benchmarks different geometry-optimization methods for excited singlet and triplet states before computing adiabatic 0-0 energies. It tests TDDFT optimizations against UKS DFT for triplets and state-specific UKS for singlets, then combines the resulting structures with ADC(2) energies and consistent zero-point corrections. The TDDFT geometries match experimental anion photoelectron data most closely, but the UKS and state-specific alternatives deliver nearly identical accuracy. Vertical excitation energies vary strongly with the chosen geometry, whereas S1-T1 gaps remain stable because of partial cancellation of errors. The work focuses on molecules whose excited states have dominant single-determinant character and shows that the cheaper UKS/ssUKS routes remain useful even for larger systems such as rubrene.

Core claim

Adiabatic 0-0 energies evaluated at TDDFT-optimized S1 and T1 geometries show the best agreement with experiment, with a mean absolute error below 0.1 eV. Replacing these geometries with UKS-optimized T1 and ssUKS-optimized S1 structures yields comparable accuracy. Vertical excitation energies are substantially more sensitive to the choice of geometry than the corresponding S1-T1 gaps, which are comparatively more robust because of partial error cancellation.

What carries the argument

Benchmarked comparison of TDDFT, UKS, and ssUKS geometry optimizations, followed by ADC(2) single-point energies plus zero-point vibrational corrections evaluated at those geometries.

If this is right

  • S1-T1 gaps remain stable across geometry choices because errors partially cancel.
  • UKS and ssUKS optimizations supply an efficient alternative to TDDFT for states with single-determinant character.
  • The same geometries remain useful for evaluating singlet-fission energetics in larger molecules such as rubrene.
  • Vertical excitation energies change more with geometry choice than the energy gaps between states.

Where Pith is reading between the lines

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

  • These protocols could lower the computational cost of screening candidate molecules for light-harvesting or emissive applications.
  • The robustness of the gaps suggests the methods may transfer to other difference properties even when absolute energies are less accurate.
  • Testing the same geometry choices with higher-level wavefunction methods would clarify whether the observed accuracy ordering persists beyond ADC(2).
  • The findings imply that initial excited-state structures from simpler DFT optimizations can serve as reliable starting points for more expensive calculations.

Load-bearing premise

The chosen molecules and their anion photoelectron spectroscopy data represent general photophysical processes and the excited states possess dominant single-determinant character.

What would settle it

Adiabatic 0-0 energies computed from these optimized geometries that deviate by more than 0.1 eV from new experimental measurements on an expanded set of molecules would disprove the reported accuracy ranking.

Figures

Figures reproduced from arXiv: 2605.06013 by Amrita Bera, Atreyee Majumdar, Raghunathan Ramakrishnan.

Figure 1
Figure 1. Figure 1: FIG. 1. Frontier MOs of 5AP and their energies from orbital-optimized ground- and excited-state calculations. MOs and their view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Computational workflow used to evaluate adiabatic view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Chemical structures of 5AP, azulene, anthracene, fluoranthene, and pyruvic acid optimized at different electronic view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Torsional energy profiles of pyruvic acid along the view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Frontier molecular orbitals and dominant orbital contributions to the low-lying excited states of the benchmark systems. view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Optimized view at source ↗
read the original abstract

Accurate prediction of adiabatic $0$-$0$ excited-state energies is crucial for modeling molecular photophysical processes. Here, we benchmark computational strategies for evaluating excited-state energies and singlet-triplet gaps obtained using different geometry-optimization strategies, including time-dependent density functional theory (TDDFT), spin-unrestricted Kohn-Sham (UKS) DFT for triplet states (${\rm T}_1$), and state-specific orbital-optimized UKS (ssUKS) DFT for singlet excited states (${\rm S}_1$). Zero-point vibrational energy corrections are evaluated consistently at the optimized geometries and combined with ADC(2) excitation energies for comparison with experimental anion photoelectron spectroscopy data for a representative set of molecules. Among the protocols considered, adiabatic $0$-$0$ energies evaluated at TDDFT-optimized ${\rm S}_1$ and ${\rm T}_1$ geometries show the best agreement with experiment, with a mean absolute error below 0.1 eV. Replacing these geometries with UKS-optimized ${\rm T}_1$ and ssUKS-optimized ${\rm S}_1$ structures yields comparable accuracy. Vertical excitation energies are substantially more sensitive to the choice of geometry than the corresponding ${\rm S}_1$-${\rm T}_1$ gaps, which are comparatively more robust because of partial error cancellation. As a larger case study, we examine rubrene and find that UKS/ssUKS-based geometries remain useful for evaluating singlet-fission energetics. Overall, UKS/ssUKS-based workflows provide an efficient and accurate route to excited-state geometry optimization and to the evaluation of adiabatic $0$-$0$ energies for states with dominant single-determinant character.

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 / 3 minor

Summary. The paper benchmarks computational strategies for excited-state geometry optimization to obtain adiabatic 0-0 energies and S1-T1 gaps. Protocols using TDDFT, UKS DFT (for T1), and ssUKS DFT (for S1) geometries are evaluated with consistent ZPVE corrections and ADC(2) single-point energies, benchmarked directly against experimental anion photoelectron spectroscopy data for a representative molecular set, plus a rubrene case study on singlet-fission energetics. The central finding is that TDDFT-optimized S1/T1 geometries yield the best experimental agreement (MAE below 0.1 eV), with UKS/ssUKS geometries providing comparable accuracy; vertical energies are more geometry-sensitive than gaps, which benefit from partial error cancellation.

Significance. If the performance claims hold, the work supplies practical, efficiency-oriented guidance for photophysical modeling by showing that orbital-optimized DFT geometries can substitute for TDDFT without substantial loss of accuracy for single-determinant states. The explicit experimental validation, consistent ZPVE treatment, and error-cancellation analysis for gaps are strengths that support broader applicability to processes such as singlet fission.

major comments (2)
  1. [Computational Methods] Computational Methods section: explicit selection criteria, inclusion/exclusion rules, and the complete list of molecules with references to the anion PES experimental sources are not provided. This information is load-bearing for verifying the robustness of the reported MAE < 0.1 eV and the claim that the set is representative.
  2. [Results] Results section: statistical uncertainties or error bars on the MAE values for each geometry protocol are not reported. Without them, the assertion that TDDFT geometries are best and that UKS/ssUKS are comparable cannot be assessed for statistical significance.
minor comments (3)
  1. A table summarizing the benchmark molecules, their experimental 0-0 energies, and the computed values for each protocol would improve readability and reproducibility.
  2. [Conclusion] The conclusion's caveat on applicability to 'states with dominant single-determinant character' would benefit from a short operational definition or reference to how such character is diagnosed (e.g., via natural orbital occupation numbers).
  3. Figure legends and axis labels should explicitly name the geometry-optimization method (TDDFT, UKS, ssUKS) rather than using abbreviations alone.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments, which have helped us identify areas for improvement. We address each major comment point by point below and outline the revisions we will make.

read point-by-point responses

  1. Referee: [Computational Methods] Computational Methods section: explicit selection criteria, inclusion/exclusion rules, and the complete list of molecules with references to the anion PES experimental sources are not provided. This information is load-bearing for verifying the robustness of the reported MAE < 0.1 eV and the claim that the set is representative.

    Authors: We agree that these details are essential for full reproducibility and for allowing readers to assess the representativeness of the benchmark set. In the revised manuscript, we will expand the Computational Methods section to explicitly state the selection criteria and inclusion/exclusion rules used to assemble the molecular set. We will also include the complete list of molecules together with the original references to the anion photoelectron spectroscopy experiments from which the adiabatic energies were taken. revision: yes

  2. Referee: [Results] Results section: statistical uncertainties or error bars on the MAE values for each geometry protocol are not reported. Without them, the assertion that TDDFT geometries are best and that UKS/ssUKS are comparable cannot be assessed for statistical significance.

    Authors: We acknowledge that the absence of statistical uncertainties makes it difficult to judge whether the observed differences in MAE are statistically meaningful. Although the benchmark set is modest in size, we will add the standard deviation of the signed errors and, where appropriate, bootstrap-derived standard errors on the MAE values for each geometry-optimization protocol in the revised Results section. This will allow a quantitative evaluation of the robustness of the conclusion that TDDFT geometries perform best while UKS/ssUKS geometries remain comparable. revision: yes

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper benchmarks geometry optimization protocols (TDDFT, UKS for T1, ssUKS for S1) by computing adiabatic 0-0 energies and S1-T1 gaps via ADC(2) on top of those geometries, then directly compares the results to independent experimental anion photoelectron spectroscopy data for a representative molecular set. Reported MAEs (<0.1 eV), gap robustness via error cancellation, and the rubrene case study are all external validations; no equations, fitted parameters, or self-citations reduce these quantities to quantities defined inside the paper. The single-determinant caveat is stated explicitly rather than used to force agreement. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claims rest on standard domain assumptions in computational chemistry rather than new free parameters or invented entities; the paper combines established methods with external experimental data.

axioms (2)
  • domain assumption ADC(2) provides sufficiently accurate excitation energies when combined with ZPVE corrections at DFT-optimized geometries
    Invoked to generate the adiabatic energies compared to experiment
  • domain assumption The test set of molecules and experimental anion photoelectron data are representative for systems with single-determinant excited states
    Stated as basis for general conclusions on UKS/ssUKS utility

pith-pipeline@v0.9.0 · 5615 in / 1483 out tokens · 49227 ms · 2026-05-08T04:10:21.348687+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

65 extracted references

  1. [1]

    Wilson, Kenneth D and Styers, William H and Wood, Samuel A and Woods, R Claude and McMahon, Robert J and Liu, Zhe and Yang, Yang and Garand, Etienne , journal=jacs, year=

  2. [2]

    Vossk. Phys. Chem. Chem. Phys. , volume=. 2015 , url=

    2015

  3. [3]

    2013 , url=

    Krylov, Anna I and Gill, Peter MW , journal=. 2013 , url=

    2013

  4. [4]

    2018 , url=

    Neese, Frank , journal=WireCMS, volume=. 2018 , url=

    2018

  5. [5]

    2012 , url=

    Neese, Frank , journal=WireCMS, volume=. 2012 , url=

    2012

  6. [6]

    2016", note=

    M. J. Frisch and others , year="2016", note="

    2016

  7. [7]

    2016 , url=

    Gaussian 16. 2016 , url=

    2016

  8. [8]

    2016 , url=

    Santoro, Fabrizio and Jacquemin, Denis , journal=WireCMS, volume=. 2016 , url=

    2016

  9. [9]

    2018 , url=

    Bremond, Eric and Savarese, Marika and Adamo, Carlo and Jacquemin, Denis , journal=jctc, volume=. 2018 , url=

    2018

  10. [10]

    2018 , url=

    Jacquemin, Denis , journal=jctc, volume=. 2018 , url=

    2018

  11. [11]

    2025 , url=

    Chanda, Shamik and Saha, Subhasish and Sen, Sangita , journal=jcp, volume=. 2025 , url=

    2025

  12. [12]

    2000 , url=

    Tozer, David J and Handy, Nicholas C , journal=pccp, volume=. 2000 , url=

    2000

  13. [13]

    2024 , url=

    Kunze, Lukas and Froitzheim, Thomas and Hansen, Andreas and Grimme, Stefan and Mewes, Jan-Michael , journal=jpcl, volume=. 2024 , url=

    2024

  14. [14]

    2025 , url=

    Burrow, E Michi and Carmona-Garc. 2025 , url=

    2025

  15. [15]

    2018 , url=

    Kregel, Steven J and Thurston, Glen K and Garand, Etienne , journal=jcp, volume=. 2018 , url=

    2018

  16. [16]

    2012 , url=

    Jacquemin, Denis and Adamo, Carlo , journal=ijqc, volume=. 2012 , url=

    2012

  17. [17]

    2019 , url=

    Loos, Pierre-Fran. 2019 , url=

    2019

  18. [18]

    2009 , url=

    Baba, Masaaki and Saitoh, Motohisa and Taguma, Kunio and Shinohara, Keisuke and Yoshida, Kazuto and Semba, Yosuke and Kasahara, Shunji and Nakayama, Naofumi and Goto, Hitoshi and Ishimoto, Takayoshi and others , journal=jcp, volume=. 2009 , url=

    2009

  19. [19]

    1985 , url=

    Chan, IY and Dantus, Marcos , journal=jcp, volume=. 1985 , url=

    1985

  20. [20]

    2007 , url=

    Melania Oana, C and Krylov, Anna I , journal=jcp, volume=. 2007 , url=

    2007

  21. [21]

    1996 , url=

    Bearpark, Michael J and Bernardi, Fernando and Clifford, Simon and Olivucci, Massimo and Robb, Michael A and Smith, Barry R and Vreven, Thom , journal=jacs, volume=. 1996 , url=

    1996

  22. [22]

    1955 , url=

    Beer, Michael and Longuet-Higgins, HC , journal=jcp, volume=. 1955 , url=

    1955

  23. [23]

    2023 , url=

    Dunlop, David and Ludv. 2023 , url=

    2023

  24. [24]

    2025 , url=

    Zheng, Zong-xiang and Wu, Wang-yang and Wan, Hao-bo and Xie, Wen-bin and Yang, Jun and Wang, Zhou and Yang, Lei and Ran, Xue-qin and Xie, Ling-hai , journal=pccp, volume=. 2025 , url=

    2025

  25. [25]

    2022 , url=

    Vandaele, Eva and Mali. 2022 , url=

    2022

  26. [26]

    2024 , url=

    Tripathy, Vikrant and Flood, Amar H and Raghavachari, Krishnan , journal=jpca, volume=. 2024 , url=

    2024

  27. [27]

    2017 , url=

    Tsunoyama, Hironori and Nakajima, Atsushi , journal=. 2017 , url=

    2017

  28. [28]

    2008 , url=

    Gilbert, Andrew TB and Besley, Nicholas A and Gill, Peter MW , journal=. 2008 , url=

    2008

  29. [29]

    2025 , url=

    Malis, Momir and Luber, Sandra , journal=. 2025 , url=

    2025

  30. [30]

    2023 , url=

    Kimber, Patrick and Plasser, Felix , journal=. 2023 , url=

    2023

  31. [31]

    2012 , url=

    Neese, Frank , journal=. 2012 , url=

    2012

  32. [32]

    2025 , url=

    Neese, Frank , journal=. 2025 , url=

    2025

  33. [33]

    Vahtras, O and Alml. Chem. Phys. Lett. , volume=. 1993 , url=

    1993

  34. [34]

    Kendall, Rick A. and Fr. Theor. Chem. Acc. , volume=. 1997 , url=

    1997

  35. [35]

    , journal=

    Yang, Weitao and Ayers, Paul W. , journal=. 2024 , url=

    2024

  36. [36]

    2021 , publisher=

    Hait, Diptarka and Head-Gordon, Martin , journal=. 2021 , publisher=

    2021

  37. [37]

    2013 , publisher=

    Smith, Millicent B and Michl, Josef , journal=. 2013 , publisher=

    2013

  38. [38]

    Chen, Xian-Kai and Kim, Dongwook and Br. Acc. Chem. Res. , volume=. 2018 , url=

    2018

  39. [39]

    2012 , url=

    Uoyama, Hiroki and Goushi, Kenichi and Shizu, Katsuyuki and Nomura, Hiroko and Adachi, Chihaya , journal=. 2012 , url=

    2012

  40. [40]

    2022 , url=

    Aizawa, Naoya and Pu, Yong-Jin and Harabuchi, Yu and Nihonyanagi, Atsuko and Ibuka, Ryotaro and Inuzuka, Hiroyuki and Dhara, Barun and Koyama, Yuki and Nakayama, Ken-ichi and Maeda, Satoshi and others , journal=. 2022 , url=

    2022

  41. [41]

    2023 , url=

    Won, Taehyun and Nakayama, Ken-ichi and Aizawa, Naoya , journal=cprev, volume=. 2023 , url=

    2023

  42. [42]

    2022 , url=

    Li, Jie and Li, Zhi and Liu, Hui and Gong, Heqi and Zhang, Jincheng and Yao, Yali and Guo, Qiang , journal=. 2022 , url=

    2022

  43. [43]

    2019 , url=

    de Silva, Piotr , journal=. 2019 , url=

    2019

  44. [44]

    2020 , publisher=

    Veys, Koen and Escudero, Daniel , journal=jpca, volume=. 2020 , publisher=

    2020

  45. [45]

    2014 , publisher=

    Fang, Changfeng and Oruganti, Baswanth and Durbeej, Bo , journal=jpca, volume=. 2014 , publisher=

    2014

  46. [46]

    2025 , publisher=

    Sinyavskiy, Andrey and Malis, Momir and Luber, Sandra , journal=. 2025 , publisher=

    2025

  47. [47]

    2026 , url =

    Vigneshwaran, V and Basumatary, Swrangsar and Beypi, Chitralekha and Akshay, CP and Ghosh, Soumen , journal=. 2026 , url =

    2026

  48. [48]

    2008 , publisher=

    Cheng, Chiao-Lun and Wu, Qin and Van Voorhis, Troy , journal=. 2008 , publisher=

    2008

  49. [49]

    2019 , url=

    Ehrmaier, Johannes and Rabe, Emily J and Pristash, Sarah R and Corp, Kathryn L and Schlenker, Cody W and Sobolewski, Andrzej L and Domcke, Wolfgang , journal=jpca, volume=. 2019 , url=

    2019

  50. [50]

    2015 , url=

    Kondakov, Denis Y , journal=. 2015 , url=

    2015

  51. [51]

    2012 , url=

    Peach, Michael JG and Tozer, David J , journal=jpca, volume=. 2012 , url=

    2012

  52. [52]

    1997 , url=

    Kendall, Rick A and Fr. 1997 , url=

    1997

  53. [53]

    2017 , url=

    Sutton, Christopher and Tummala, Naga Rajesh and Beljonne, David and Brédas, Jean-Luc , journal=. 2017 , url=

    2017

  54. [54]

    2012 , url=

    Ma, Lin and Zhang, Keke and Kloc, Christian and Sun, Handong and Michel-Beyerle, Maria E and Gurzadyan, Gagik G , journal=pccp, volume=. 2012 , url=

    2012

  55. [55]

    2023 , url=

    Loos, Pierre-Fran. 2023 , url=

    2023

  56. [56]

    1990 , url=

    Jensen, Frank , journal=cpl, volume=. 1990 , url=

    1990

  57. [57]

    2022 , url=

    Froitzheim, Thomas and Grimme, Stefan and Mewes, Jan-Michael , journal=jctc, volume=. 2022 , url=

    2022

  58. [58]

    2016 , url=

    Hait, Diptarka and Zhu, Tianyu and McMahon, David P and Van Voorhis, Troy , journal=jctc, volume=. 2016 , url=

    2016

  59. [59]

    2020 , url=

    Hait, Diptarka and Head-Gordon, Martin , journal=jctc, volume=. 2020 , url=

    2020

  60. [60]

    2025 , url=

    Majumdar, Atreyee and Das, Surajit and Ramakrishnan, Raghunathan , journal=. 2025 , url=

    2025

  61. [61]

    2025 , url=

    Majumdar, Atreyee and Ramakrishnan, Raghunathan , journal=cej, pages=. 2025 , url=

    2025

  62. [62]

    2025 , url=

    Jindal, Komal and Majumdar, Atreyee and Ramakrishnan, Raghunathan , journal=pccp, volume=. 2025 , url=

    2025

  63. [63]

    1977 , url=

    Ziegler, Tom and Rauk, Arvi and Baerends, Evert J , journal=tca, volume=. 1977 , url=

    1977

  64. [64]

    2024 , url=

    Pino-Rios, Ricardo and B. 2024 , url=

    2024

  65. [65]

    and Knott, W

    Schiedt, J. and Knott, W. J. and Le Barbu, K. and Schlag, E. W. and Weinkauf, R. , journal=jcp, volume=. 2000 , doi=

    2000