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arxiv: 2605.28637 · v2 · pith:GHB4EN7Gnew · submitted 2026-05-27 · ⚛️ physics.chem-ph

Excited States from Restricted Open Shell Plane-Wave DFT

Michael J. Sahre , Marco Romanelli , Martijn Marsman , Leticia Gonz\'alez , Georg Kresse This is my paper

Pith reviewed 2026-06-29 09:26 UTC · model grok-4.3

classification ⚛️ physics.chem-ph
keywords ROKSexcited statesplane-wave DFTTDDFTVASPMgOoxygen vacancysinglet excitations
0
0 comments X

The pith

Plane-wave restricted open-shell Kohn-Sham DFT computes spin-pure singlet excitations and forces with accuracy comparable to TDDFT.

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

The paper implements restricted open-shell Kohn-Sham (ROKS) DFT inside the plane-wave projector augmented-wave framework to obtain excited states at ground-state cost. It recovers spin-pure singlet energies by variationally minimizing a weighted combination of mixed-spin and triplet configurations, with analytical forces derived for geometry changes. Validation against a Gaussian-basis reference code on eight organic molecules produces mean deviations of roughly 30 meV. In MgO containing a neutral oxygen vacancy, ROKS and TDDFT differ by 0.21 eV on vertical excitation energies, 0.14 eV on Franck-Condon shifts, and 0.12 amu^{1/2} Ang on mass-weighted displacements when using a dielectric-dependent hybrid functional, with weaker functional dependence observed for ROKS.

Core claim

The central claim is that the ROKS functional, implemented via preconditioned conjugate-gradient or DIIS optimization in the plane-wave PAW setting, yields excitation energies and excited-state forces whose accuracy is similar to that of TDDFT while preserving the scaling of ordinary ground-state DFT, as demonstrated by close numerical agreement on both molecular test cases and the MgO oxygen-vacancy defect.

What carries the argument

The ROKS energy functional, formed as a weighted average of mixed-spin and triplet configurations and minimized in the plane-wave PAW representation, together with the derived analytical atomic forces.

If this is right

  • ROKS excitation energies for the eight organic molecules agree with the Q-Chem reference to a mean deviation of approximately 30 meV.
  • For the MgO oxygen vacancy, vertical excitation energies from ROKS and TDDFT differ by 0.21 eV on average with a dielectric-dependent hybrid functional.
  • Franck-Condon shifts and mass-weighted displacements between excited and ground states differ by 0.14 eV and 0.12 amu^{1/2} Ang on average between the two methods.
  • Excited-state properties exhibit weaker dependence on the underlying DFT functional for ROKS than for TDDFT when the PBE functional is used.
  • ROKS supplies both energies and forces at the computational cost of ground-state DFT, enabling simulations of excited states in extended systems.

Where Pith is reading between the lines

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

  • The availability of analytical forces would permit routine excited-state geometry optimization and molecular dynamics in periodic defect systems where TDDFT scaling becomes prohibitive.
  • Weaker functional dependence could reduce the need for expensive hybrid functionals in large supercell calculations of excited states.
  • The method could be tested on additional point defects, surfaces, or low-dimensional materials to map its range of applicability beyond the MgO vacancy example.
  • Direct comparison of ROKS results against higher-level wavefunction methods on the same periodic systems would quantify remaining systematic errors.

Load-bearing premise

The plane-wave PAW implementation of the ROKS functional converges to the same spin-pure singlet energies obtained by the Gaussian-basis ROKS code, without substantial extra errors from the basis representation or pseudopotential choice.

What would settle it

A side-by-side calculation of the eight organic-molecule excitation energies with both the new plane-wave code and the established Gaussian-basis ROKS implementation would show whether mean deviations remain near 30 meV or grow systematically.

Figures

Figures reproduced from arXiv: 2605.28637 by Georg Kresse, Leticia Gonz\'alez, Marco Romanelli, Martijn Marsman, Michael J. Sahre.

Figure 1
Figure 1. Figure 1: FIG. 1. Panel A: Electronic configurations after HOMO to LUMO [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. A: Structure of MgO with oxygen vacancy [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The radial distribution function of Mg (left) and oxygen (middle) around the oxygen vacancy in the ground state and the optimized [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
read the original abstract

Variational excited-state density functional theory (DFT) enables the calculation of excited states at a cost comparable to ground-state calculations, but single-configuration approaches often suffer from spin contamination. We implement restricted open-shell Kohn-Sham (ROKS) DFT, which recovers spin-pure singlet excitation energies via the variational minimization of a weighted combination of mixed-spin and triplet configurations, within the plane-wave projector augmented-wave framework of VASP. The energy functional is optimized using a preconditioned conjugate-gradient or a direct inversion in the iterative subspace algorithm, and analytical atomic forces are derived. The implementation is validated for eight organic molecules by comparison to the Q-Chem quantum chemistry code, yielding mean deviations of approximately $30\,\mathrm{meV}$. As a solid-state application, we investigate the three lowest lying excitations of MgO with a neutral oxygen vacancy. For a dielectric-dependent hybrid functional, vertical excitation energies from ROKS and time-dependent density functional theory (TDDFT) differ on average by about $0.21\,\mathrm{eV}$. The Franck-Condon shifts deviate on average by $0.14\,\mathrm{eV}$ between the two methods and mass-weighted displacements between the excited states and the ground state by $0.12\,\mathrm{amu}^{1/2}$ Ang. Additional calculations at the PBE level reveal that these properties depend less strongly on the DFT functional for ROKS than for TDDFT. These results demonstrate that ROKS provides excitation energies and excited-state forces with an accuracy similar to TDDFT while retaining the favorable scaling of ground-state DFT, making it a promising approach for affordable excited-state simulations in extended systems.

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

0 major / 3 minor

Summary. The manuscript implements restricted open-shell Kohn-Sham (ROKS) DFT in the plane-wave PAW framework of VASP for variational excited-state calculations. It optimizes the ROKS energy functional with PCG or DIIS, derives analytical atomic forces, validates the implementation on eight organic molecules against Q-Chem (mean deviation ~30 meV), and applies it to the three lowest excitations of MgO with a neutral oxygen vacancy. Vertical excitation energies, Franck-Condon shifts, and mass-weighted displacements are compared to TDDFT (average differences 0.21 eV, 0.14 eV, 0.12 amu^{1/2} Å) using a dielectric-dependent hybrid functional; additional PBE calculations show weaker functional dependence for ROKS than TDDFT. The central claim is that ROKS achieves TDDFT-comparable accuracy at ground-state DFT cost for extended systems.

Significance. If the implementation and validations hold, the work is significant for enabling affordable excited-state simulations (including forces) in periodic systems with defects, where TDDFT scaling is often prohibitive. Explicit cross-code validation on molecules, direct comparison to TDDFT on a solid-state example, and functional-dependence tests provide concrete grounding. The derivation of analytical forces is a notable strength for geometry optimization and dynamics applications.

minor comments (3)
  1. [Abstract] Abstract: the unit is written as 'amu^{1/2} Ang'; standardize to 'amu^{1/2} Å' for consistency with standard notation in the field.
  2. [MgO application section] The manuscript should include a brief statement on the specific PAW potentials and plane-wave cutoff used for the MgO calculations to allow direct reproduction of the reported 0.21 eV deviation.
  3. [Implementation section] Clarify in the methods whether the ROKS singlet energy is obtained from the same weighted combination formula as in the Gaussian-basis reference implementation, or if any adjustment was made for the PAW representation.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive and constructive review of our manuscript on the ROKS implementation in VASP. The recommendation for minor revision is noted, and we will incorporate appropriate updates in the revised version.

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained via external benchmarks

full rationale

The paper's central claims rest on implementing ROKS within VASP's plane-wave PAW framework, deriving analytical forces, and validating via direct numerical comparison to the independent Q-Chem Gaussian-basis ROKS implementation (mean deviation ~30 meV across eight molecules) plus side-by-side comparison to TDDFT for MgO excitations (differences quantified at 0.21 eV, 0.14 eV, 0.12 amu^{1/2} Å). No equations, fitted parameters, or self-citations are shown that reduce reported energies or forces to the inputs by construction; the derivation chain is externally grounded rather than tautological.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only the abstract is available; no explicit free parameters, new entities, or non-standard axioms are stated. The work rests on the standard ROKS construction and the usual DFT approximations already present in VASP.

axioms (1)
  • domain assumption The weighted mixed-spin plus triplet functional yields a spin-pure singlet when minimized
    This is the defining premise of ROKS and is invoked to justify the variational procedure described in the abstract.

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