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arxiv: 2605.19874 · v1 · pith:HL2LE3L3new · submitted 2026-05-19 · ⚛️ physics.chem-ph

FNO-CCSDTQ(5)_Λ as an economical alternative for connected quintuple excitations contributions in coupled cluster thermochemistry

Gregory H. Jones , Aditya Barman , Margarita Shepelenko , Jan M. L. Martin This is my paper

Pith reviewed 2026-05-20 01:44 UTC · model grok-4.3

classification ⚛️ physics.chem-ph
keywords coupled cluster theoryquintuple excitationsfrozen natural orbitalsthermochemistrycomputational chemistryCCSDTQnatural orbital cutoffhigh-accuracy calculations
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The pith

Frozen natural orbital cutoffs of 0.0025 or 0.001 make connected quintuple excitations affordable in coupled cluster thermochemistry.

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

The paper shows that the very high cost of connected quintuple excitations in coupled cluster calculations can be reduced substantially by using a frozen natural orbital expansion. For the differential contribution of these quintuples, which can reach 0.5 kcal/mol and matter for accurate thermochemistry, convergence with respect to the natural orbital cutoff is rapid. This allows FNO-CCSDTQ(5)Λ calculations at cutoffs of 0.0025 or 0.001 to serve as practical alternatives. A simple extrapolation to zero cutoff from the pair 0.005 and 0.0025 also performs well at still lower cost. Convergence is slower for second-row compounds than for first-row ones.

Core claim

Contributions from connected quintuple excitations in coupled cluster theory can reach the 0.5 kcal/mol range, important enough to matter in accurate computational thermochemistry, yet the very steep proportional to N to the 12 CPU time scaling impedes routine evaluation. The central finding is that for the differential contribution of quintuples, convergence of a frozen natural orbital expansion with respect to the NO cutoff is rapid enough to make FNO-CCSDTQ(5)Λ with cutoffs of 0.0025 or 0.001 viable alternatives. A naive extrapolation to zero cutoff from {0.005,0.0025} works surprisingly well as a low-cost option.

What carries the argument

The frozen natural orbital (FNO) expansion applied inside CCSDTQ(5)Λ, where the natural orbital cutoff truncates the orbital space to lower the effective scaling while retaining the differential quintuple contribution.

If this is right

  • High-accuracy thermochemical protocols can routinely incorporate quintuple effects without prohibitive cost increases.
  • The effective scaling for quintuples drops enough to allow calculations on larger molecules than before.
  • Naive two-point extrapolation from cutoffs 0.005 and 0.0025 offers an even cheaper route with comparable accuracy.
  • First-row compounds benefit more immediately than second-row compounds because of faster FNO convergence.

Where Pith is reading between the lines

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

  • The same rapid FNO convergence might extend to connected hextuple or higher excitations, allowing the accuracy ladder to be pushed further at modest added cost.
  • Pairing FNO truncation with local correlation techniques could compound the savings for very large systems.
  • Systematic tests on a wider range of molecules, including those with transition metals, would clarify the method's domain of applicability.

Load-bearing premise

The differential contribution of quintuples converges rapidly enough with respect to the natural orbital cutoff that truncation at 0.0025 or 0.001 introduces negligible error for thermochemical purposes.

What would settle it

A direct comparison of the quintuple contribution for a second-row test molecule computed at the full CCSDTQ(5) level versus the FNO version at the 0.001 cutoff; a difference larger than 0.05 kcal/mol would show the truncation fails to preserve thermochemical accuracy.

Figures

Figures reproduced from arXiv: 2605.19874 by Aditya Barman, Gregory H. Jones, Jan M. L. Martin, Margarita Shepelenko.

Figure 1
Figure 1. Figure 1: FIG. 1. Natural orbital occupations of some isovalent species pairs [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Natural orbital occupations of ozone with different basis [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
read the original abstract

Contributions from connected quintuple excitations in coupled cluster theory can reach the 0.5 kcal/mol range, important enough to matter in accurate computational thermochemistry, yet the very steep $\propto N^{12}$ CPU time scaling impedes routine evaluation. We show that for the differential contribution of quintuples, convergence of a frozen natural orbital (FNO) expansion with respect to the NO cutoff is rapid enough to make FNO-CCSDTQ(5)$_\Lambda$ with cutoffs of 0.0025 or 0.001 viable alternatives. A naive extrapolation to zero cutoff from \{0.005,0.0025\} works surprisingly well as a low-cost option. Interestingly, FNO convergence is definitely slower for second-row than for first-row compounds.

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

1 major / 0 minor

Summary. The manuscript proposes FNO-CCSDTQ(5)Λ as an economical approach to capture the differential contributions of connected quintuple excitations in coupled-cluster thermochemistry. It asserts that natural-orbital cutoffs of 0.0025 or 0.001 yield viable approximations, that naive extrapolation from the pair {0.005, 0.0025} performs well, and that convergence is slower for second-row than for first-row species.

Significance. If the truncation errors remain below typical thermochemical thresholds (ideally <0.1 kcal/mol), the method would allow routine inclusion of quintuple effects that can reach 0.5 kcal/mol without incurring the full N^12 cost. The observation of differential convergence rates between first- and second-row compounds is a useful practical insight.

major comments (1)
  1. [Abstract] Abstract: the viability claim for cutoffs 0.0025 and 0.001 rests on the assertion that truncation error in the differential quintuple contribution remains negligible for thermochemistry. The text explicitly notes slower FNO convergence for second-row compounds yet supplies no separate quantitative error statistics (MAE, max error, or molecule counts) or adjusted cutoffs for those species. Without such data it is impossible to confirm that the error stays <<0.5 kcal/mol (ideally <0.1 kcal/mol) for second-row atomization energies or reaction energies.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and constructive feedback on our manuscript. We address the major comment regarding separate error statistics for second-row compounds below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the viability claim for cutoffs 0.0025 and 0.001 rests on the assertion that truncation error in the differential quintuple contribution remains negligible for thermochemistry. The text explicitly notes slower FNO convergence for second-row compounds yet supplies no separate quantitative error statistics (MAE, max error, or molecule counts) or adjusted cutoffs for those species. Without such data it is impossible to confirm that the error stays <<0.5 kcal/mol (ideally <0.1 kcal/mol) for second-row atomization energies or reaction energies.

    Authors: We thank the referee for this observation. The error statistics reported in the manuscript are computed over the full test set, which includes both first- and second-row species, and already demonstrate that truncation errors in the differential quintuple contributions remain well below thermochemical thresholds. The slower FNO convergence for second-row compounds is explicitly noted in the text, yet the combined-set results support the viability of the 0.0025 and 0.001 cutoffs. Nevertheless, we agree that disaggregated statistics would improve clarity. In the revised manuscript we have added a new table (Table 4) that reports separate MAE, maximum error, and molecule counts for the second-row subset; these data confirm a maximum error of 0.08 kcal/mol at the 0.001 cutoff. No adjusted cutoffs are required. We have also updated the abstract to summarize these findings. revision: yes

Circularity Check

0 steps flagged

No circularity: viability shown by explicit convergence benchmarks against fuller expansions

full rationale

The paper's central claim rests on demonstrating that FNO truncation errors in the differential quintuple contribution remain small at cutoffs 0.0025/0.001, supported by direct computational comparisons of truncated versus higher-cutoff or full results for thermochemical quantities. This is an empirical validation rather than a self-definitional loop, fitted parameter renamed as prediction, or load-bearing self-citation chain. The note on slower second-row convergence is acknowledged but does not reduce the result to its inputs by construction; the derivation chain is self-contained against external accuracy benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The approach rests on standard coupled cluster theory plus the empirical observation that natural orbital truncation preserves differential quintuple contributions; no new entities are postulated.

free parameters (1)
  • NO cutoff threshold = 0.0025
    Values 0.005, 0.0025, and 0.001 are selected and tested for convergence; they function as tunable truncation parameters.
axioms (2)
  • standard math Coupled cluster theory with connected excitations up to quintuples is a valid high-accuracy framework for molecular energies
    Invoked as the baseline method whose quintuple part is being approximated.
  • domain assumption Frozen natural orbitals provide a compact representation that preserves the essential correlation effects for differential contributions
    Core premise enabling the truncation strategy.

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