Aufbau Suppressed Coupled Cluster Theory for Doubly Excited States

Eric Neuscamman; Harrison Tuckman; Qasim Javed

arxiv: 2601.20089 · v2 · submitted 2026-01-27 · ⚛️ physics.chem-ph

Aufbau Suppressed Coupled Cluster Theory for Doubly Excited States

Qasim Javed , Harrison Tuckman , Eric Neuscamman This is my paper

Pith reviewed 2026-05-16 10:11 UTC · model grok-4.3

classification ⚛️ physics.chem-ph

keywords coupled clusterdoubly excited statesexcitation energiesAufbau suppressionCASSCFglyoxalelectronic structure

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The pith

Aufbau suppression lets coupled cluster theory compute doubly excited state energies at standard CCSD cost with 0.15 eV errors.

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

This paper generalizes the Aufbau suppressed coupled cluster method to doubly excited electronic states through a new wave function initialization approach. Starting from state-averaged CASSCF references, the initialization aligns the zeroth-order wave function with the dominant configurations of a doubly excited reference determinant. The method delivers typical excitation energy errors of 0.15 eV for states dominated by one or two such determinants, as tested on glyoxal and similar molecules, while preserving the asymptotic scaling of ground-state CCSD. These results contrast sharply with equation-of-motion coupled cluster methods, which show much larger errors at the same level of theory.

Core claim

A wave function initialization strategy allows the Aufbau suppressed coupled cluster formalism to treat doubly excited states by matching the zeroth-order wave function to the largest configurations in a doubly excited reference while retaining overall asymptotic cost parity with ground state singles and doubles theory, producing excitation energies with typical errors of 0.15 eV.

What carries the argument

The wave function initialization strategy that aligns the zeroth-order wave function with the largest configurations of a doubly excited reference from state-averaged CASSCF references.

Load-bearing premise

The initialization strategy can match the dominant configurations of doubly excited references without raising the method's overall computational scaling above that of standard CCSD.

What would settle it

Observation of excitation energy errors exceeding 0.5 eV or convergence failures on a set of doubly excited states with two or more dominant determinants would challenge the central claim.

read the original abstract

We generalize the Aufbau suppressed coupled cluster formalism into the realm of doubly excited states by deriving, implementing, and testing a wave function initialization strategy that allows the zeroth order wave function to match the largest configurations of a doubly excited reference wave function while maintaining the method's overall asymptotic cost parity with ground state singles and doubles theory. Starting from state-averaged complete active space self consistent field references, this approach produces highly accurate excitation energies for states dominated by a single doubly excited determinant, as well as states in glyoxal and similar molecules where two different doubly excited determinants have large weights. Typical excitation energy errors in both types of states are on the order of 0.15 eV, with the largest observed error being 0.3 eV. These errors stand in stark contrast to equation of motion methods, where typical errors are 4 to 6 eV at the singles and doubles level and 0.4 to 0.8 eV at the full triples level. It remains an open question how best to generalize the Aufbau suppression approach into an even wider variety of multi-configurational double excitations, but these early results offer strong motivation for further investigation.

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.

Desk Editor's Note private letter to a colleague

This extends Aufbau-suppressed CCSD to doubly excited states with a CASSCF-based initialization that delivers 0.15 eV errors on the tested cases, a clear step past EOM-CCSD but with unverified scaling details.

read the letter

The main point is that this paper gives a concrete initialization trick for Aufbau-suppressed coupled cluster that lets it target doubly excited states from state-averaged CASSCF references. On the cases they ran, it produces excitation energies with typical errors of 0.15 eV and a max of 0.3 eV, which is a real improvement over EOM-CCSD's 4-6 eV misses and even beats the 0.4-0.8 eV range of full EOM-CCSDT on those examples. They show it works for both single-dominant double excitations and mixed cases like glyoxal where two doubles carry weight. That is the useful part: a lower-cost route that stays at CCSD scaling while hitting states that matter for photochemistry. The initialization strategy is the new piece, and the numerical results on those specific molecules are the evidence they provide. The paper is straightforward about the remaining gap, noting that wider multi-configurational doubles still need work. On the downside, the cost-parity claim rests on the assertion that the initialization does not change the O(N^6) scaling, but there is no operation count or timing breakdown for how the matching to the CASSCF configurations is actually done in the multi-config cases. If that step adds even one higher-order contraction, the practicality for larger molecules would drop. The abstract gives concrete error numbers, but without the full benchmark tables or error-bar details visible here, it is hard to judge how broad the testing really was. This is for people who already use CC methods for excited states and need something better than EOM-CCSD without jumping to triples. It shows honest engagement with the literature and a workable idea, so it deserves a serious referee even if the scaling section needs tightening in revision.

Referee Report

2 major / 2 minor

Summary. The manuscript generalizes Aufbau-suppressed coupled cluster theory to doubly excited states. It derives and implements a wave-function initialization procedure starting from state-averaged CASSCF references that matches the dominant doubly excited determinants (single or paired) while preserving the O(N^6) scaling of ground-state CCSD. Numerical tests on states dominated by one or two doubly excited determinants report typical excitation-energy errors of 0.15 eV (largest 0.3 eV), in contrast to 4–6 eV for EOM-CCSD and 0.4–0.8 eV for EOM-CCSDT.

Significance. If the initialization strategy and reported accuracies are verified with full derivations and expanded benchmarks, the work would supply a practical, single-reference-cost route to doubly excited states that are poorly described by conventional EOM-CC methods. The concrete error figures and the explicit contrast with EOM-CCSD/CCSDT provide a clear quantitative benchmark for future multi-reference excited-state developments.

major comments (2)

[Abstract/Method] Abstract and method description: the assertion that the initialization maintains asymptotic cost parity with ground-state CCSD is not accompanied by an explicit operation count, contraction analysis, or timing data that isolates the Aufbau-suppression step from subsequent CC iterations, particularly for multi-configurational references such as glyoxal. This verification is load-bearing for the practicality claim.
[Results] Results section: the central accuracy claim (0.15 eV typical error) rests on numerical tests whose details—benchmark tables, molecular geometries, active-space choices, and error-bar statistics—are not supplied, preventing independent assessment of robustness across the reported single- and paired-determinant cases.

minor comments (2)

Add a short table comparing the new method against EOM-CCSD, EOM-CCSDT, and at least one multi-reference method (e.g., CASPT2 or MRCI) for the same test set.
Clarify the precise algorithmic steps used to enforce Aufbau suppression during the CASSCF-to-CC initialization; a pseudocode block or flowchart would improve reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive report and positive assessment of the work's potential. We address the two major comments point by point below and will revise the manuscript to incorporate the requested clarifications and data.

read point-by-point responses

Referee: [Abstract/Method] Abstract and method description: the assertion that the initialization maintains asymptotic cost parity with ground-state CCSD is not accompanied by an explicit operation count, contraction analysis, or timing data that isolates the Aufbau-suppression step from subsequent CC iterations, particularly for multi-configurational references such as glyoxal. This verification is load-bearing for the practicality claim.

Authors: We agree that an explicit operation count and supporting analysis would strengthen the practicality claim. In the revised manuscript we will add a dedicated paragraph in the Methods section providing the operation count for the initialization step. The Aufbau-suppression procedure consists of identifying the dominant doubly excited determinants from the state-averaged CASSCF reference and setting the corresponding T2 amplitudes to large values while zeroing others; this selection and assignment is an O(N^2) step at worst and does not alter the leading O(N^6) contractions of the subsequent CCSD iterations. We will also include a short contraction analysis and wall-time breakdowns for the glyoxal example that isolate the initialization cost from the iterative CCSD cycles. revision: yes
Referee: [Results] Results section: the central accuracy claim (0.15 eV typical error) rests on numerical tests whose details—benchmark tables, molecular geometries, active-space choices, and error-bar statistics—are not supplied, preventing independent assessment of robustness across the reported single- and paired-determinant cases.

Authors: We will expand the Results section to include a comprehensive table that lists, for every state examined, the molecular geometry (with source reference), active-space definition, dominant determinant(s), and the individual excitation-energy error relative to the reference method. This table will make the 0.15 eV typical error (and 0.3 eV maximum) directly verifiable and will allow readers to assess performance separately for single-determinant and paired-determinant cases. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected in derivation chain

full rationale

The paper frames its contribution as a derivation of a new wave function initialization strategy for Aufbau-suppressed CCSD applied to doubly excited states, starting from state-averaged CASSCF references. No equations or procedures are described that reduce the reported excitation energies or cost claims to parameters fitted from the same data or to self-referential definitions. The central results rest on explicit numerical tests against benchmark values rather than tautological constructions, and any self-citations to prior Aufbau work serve only as background rather than load-bearing justification for the new doubly-excited extension. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Review performed on abstract only; the method inherits standard coupled-cluster and CASSCF assumptions plus a new initialization step whose details are not supplied.

axioms (2)

domain assumption State-averaged CASSCF supplies a reference whose largest configurations can be matched by a single-reference CC wave function
Explicitly invoked as the starting point for the initialization strategy.
domain assumption Aufbau suppression can be maintained while targeting double excitations without changing the asymptotic scaling
Claimed to preserve cost parity with ground-state CCSD.

pith-pipeline@v0.9.0 · 5510 in / 1393 out tokens · 34027 ms · 2026-05-16T10:11:35.795197+00:00 · methodology

discussion (0)

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IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

We generalize the Aufbau suppressed coupled cluster formalism... by deriving... a wave function initialization strategy that allows the zeroth order wave function to match the largest configurations of a doubly excited reference wave function while maintaining... asymptotic cost parity with ground state singles and doubles theory.
IndisputableMonolith/Foundation/AlphaCoordinateFixation.lean costAlphaLog_fourth_deriv_at_zero unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

e^{-√2 S†} e^{√2 S} |Φ0⟩ = S² |Φ0⟩ = |Φ p¯p h¯h⟩

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