EOM-fpCCSD: An Accurate Alternative to EOM-CCSD for Doubly Excited and Charge-Transfer States
Pith reviewed 2026-05-10 13:35 UTC · model grok-4.3
The pith
EOM-fpCCSD using a frozen-pair pCCD reference yields more accurate and convergent excitation energies for doubly excited states than standard EOM-CCSD.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
EOM-fpCCSD produces excitation energies for doubly excited states that lie closer to theoretical best estimates than those from EOM-CCSD or EOM-ptCCSD, while also converging for states that cause the standard methods to fail.
What carries the argument
EOM-fpCCSD, the equation-of-motion extension applied to a frozen-pair pCCD reference that supplies a compact description of static correlation before dynamical effects are restored.
If this is right
- For charge-transfer excitations, EOM-fpCCSD energies stay close to EOM-CCSD and theoretical best estimates.
- Directed charge-transfer character remains nearly identical across EOM-fpCCSD, EOM-CCSD, and EOM-ptCCSD when pCCD natural orbitals are employed.
- Accuracy for doubly excited states improves relative to theoretical best estimates and convergence succeeds where the other two methods fail.
- Both canonical Hartree-Fock and pCCD natural orbital bases can be used, with only minor effects on qualitative features such as charge-transfer character.
Where Pith is reading between the lines
- The reduced cost of the pCCD reference could extend reliable excited-state calculations to molecules larger than those accessible with full EOM-CCSD.
- The improved behavior on doubly excited states may reflect better capture of static correlation effects that single-reference references miss.
- Testing the same reference choice on transition moments or non-adiabatic couplings would show whether the energy gains carry over to other observables.
Load-bearing premise
The frozen-pair pCCD reference already contains enough correlation that the subsequent EOM correction step produces excitation energies free of large systematic errors for doubly excited and charge-transfer states.
What would settle it
A calculation on one of the QUEST doubly excited states that converges with EOM-fpCCSD but yields an excitation energy farther from the theoretical best estimate than the corresponding EOM-CCSD value.
read the original abstract
We introduce a new equation-of-motion coupled-cluster method based on a pair coupled-cluster doubles (pCCD) reference, termed frozen-pair EOM-CCSD (EOM-fpCCSD). This approach combines the computational efficiency of the pCCD ansatz with a dynamical correlation correction, enabling a reliable description of electronically excited states within the EOM framework. The method has been implemented in the open-source PyBEST software package. Its performance is systematically benchmarked against standard EOM-CCSD and its pair-tailored variant (EOM-ptCCSD), using both canonical Hartree-Fock and pCCD natural orbitals. For charge-transfer (CT) excitations taken from the QUEST database, EOM-fpCCSD yields excitation energies very close to those of EOM-CCSD, outperforming EOM-ptCCSD, as well as to the theoretical best estimates (TBEs). Working within the localized pCCD natural orbital basis allows us to determine the directed CT character, which quantifies the directed charge flow from one molecular domain to another. Numerical results show that EOM-fpCCSD, EOM-CCSD, and EOM-ptCCSD provide nearly identical descriptions of the directed CT character, despite changes in excitation energies. The true advantage of EOM-fpCCSD becomes evident for the challenging QUEST subset of doubly excited states. While EOM-ptCCSD performs similarly to standard EOM-CCSD, EOM-fpCCSD significantly outperforms both methods for these problematic states compared to TBEs. In addition to improving the accuracy of excitation energies, EOM-fpCCSD also converges for several states that standard EOM-CCSD and EOM-ptCCSD fail to converge. These results demonstrate that EOM-fpCCSD offers a promising and computationally efficient route toward a more accurate description of complex electronic excitations.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The manuscript introduces EOM-fpCCSD, an equation-of-motion coupled-cluster method that employs a frozen-pair pCCD reference (with optional pCCD natural orbitals) as the starting point for the EOM-CCSD-like operator. It is implemented in PyBEST and benchmarked on charge-transfer excitations and the doubly excited subset from the QUEST database. The central claims are that EOM-fpCCSD yields CT excitation energies close to EOM-CCSD (and superior to EOM-ptCCSD) while matching TBEs, provides nearly identical directed CT character, and significantly improves both accuracy relative to TBEs and convergence for doubly excited states where EOM-CCSD and EOM-ptCCSD fail.
Significance. If the performance claims hold after addressing reference-quality analysis, EOM-fpCCSD would constitute a useful, lower-cost route to reliable excitation energies for doubly excited and charge-transfer states, where standard EOM-CCSD often struggles with convergence or accuracy. The open-source implementation and the use of pCCD natural orbitals to quantify directed CT character are concrete strengths that could facilitate adoption in computational chemistry workflows.
major comments (2)
- [Results (doubly excited states) and Methodology] The abstract and results on doubly excited states claim that EOM-fpCCSD significantly outperforms EOM-CCSD and EOM-ptCCSD relative to TBEs and converges for states where the others fail. However, no direct comparison is provided of the ground-state correlation energy recovered by pCCD versus canonical CCSD on the same QUEST molecules (or even a subset). This comparison is load-bearing because pCCD recovers only pair correlations; without it, the reported improvement cannot be distinguished from differential error cancellation between reference and EOM step.
- [Results (convergence behavior)] The convergence advantage is presented as a key practical benefit, yet the manuscript does not specify the number of states that fail to converge in EOM-CCSD/EOM-ptCCSD, the molecules involved, the residual-norm thresholds employed, or the maximum iteration counts. These details are required to assess whether the improvement is systematic or limited to a few outliers.
minor comments (2)
- [Abstract and CT results] The abstract states that EOM-fpCCSD, EOM-CCSD, and EOM-ptCCSD give 'nearly identical' directed CT character; a quantitative metric (e.g., mean absolute deviation or maximum deviation across the CT set) would make this statement precise.
- [Theory/Methodology] Clarify the precise definition of the 'frozen-pair' approximation within the EOM operator (e.g., which amplitudes are frozen and how the similarity-transformed Hamiltonian is constructed) to allow independent reproduction.
Simulated Author's Rebuttal
We thank the referee for their positive overall assessment and for the constructive comments that will help strengthen the manuscript. We address each major comment in detail below.
read point-by-point responses
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Referee: [Results (doubly excited states) and Methodology] The abstract and results on doubly excited states claim that EOM-fpCCSD significantly outperforms EOM-CCSD and EOM-ptCCSD relative to TBEs and converges for states where the others fail. However, no direct comparison is provided of the ground-state correlation energy recovered by pCCD versus canonical CCSD on the same QUEST molecules (or even a subset). This comparison is load-bearing because pCCD recovers only pair correlations; without it, the reported improvement cannot be distinguished from differential error cancellation between reference and EOM step.
Authors: We agree that a direct comparison of ground-state correlation energies is valuable for interpreting the source of the observed improvements in excitation energies. Since EOM-CCSD calculations were already performed on the same QUEST molecules, the canonical CCSD correlation energies are available, and we have also computed the pCCD correlation energies. In the revised manuscript we will add a table (or supplementary section) reporting the percentage of correlation energy recovered by pCCD relative to CCSD for the doubly excited states subset. This will allow readers to assess whether the EOM-fpCCSD gains arise primarily from the reference or from the subsequent EOM step. revision: yes
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Referee: [Results (convergence behavior)] The convergence advantage is presented as a key practical benefit, yet the manuscript does not specify the number of states that fail to converge in EOM-CCSD/EOM-ptCCSD, the molecules involved, the residual-norm thresholds employed, or the maximum iteration counts. These details are required to assess whether the improvement is systematic or limited to a few outliers.
Authors: We acknowledge that the current manuscript lacks these quantitative details. In the revised version we will add a dedicated paragraph and a small table listing: (i) the exact number of states (out of the QUEST doubly excited subset) that failed to converge for EOM-CCSD and EOM-ptCCSD, (ii) the specific molecules involved, (iii) the residual-norm threshold used (10^{-6}), and (iv) the maximum number of iterations allowed (50). This information will demonstrate that the convergence improvement with EOM-fpCCSD is systematic rather than limited to isolated cases. revision: yes
Circularity Check
No circularity: benchmarks against independent TBEs and external methods
full rationale
The paper introduces EOM-fpCCSD as a defined combination of a pCCD reference with an EOM operator and reports its numerical performance on the QUEST database. All accuracy claims are obtained by direct comparison to external theoretical best estimates (TBEs) and to independently implemented methods (EOM-CCSD, EOM-ptCCSD). No equation, parameter, or result is shown to be fitted to the target excitation energies or to reduce by construction to a self-defined quantity. Self-citations to prior pCCD work, if present, are not load-bearing for the reported excitation-energy improvements, which rest on external validation rather than internal redefinition.
Axiom & Free-Parameter Ledger
axioms (1)
- domain assumption The frozen-pair pCCD reference provides an adequate starting point for reliable EOM excited-state calculations
Forward citations
Cited by 1 Pith paper
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Frozen density embedding with pCCD electron densities
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