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arxiv: 2605.19874 · v2 · 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 2026-05-22 09:30 UTC · model grok-4.3

classification ⚛️ physics.chem-ph
keywords coupled clusterquintuple excitationsfrozen natural orbitalsthermochemistrycorrelation energycomputational chemistry
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0 comments X

The pith

Frozen natural orbital truncation makes connected quintuple excitations practical for coupled cluster thermochemistry.

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

Contributions from connected quintuple excitations can reach 0.5 kcal/mol in thermochemical calculations, but the steep N^12 scaling prevents routine use. The paper tests whether a frozen natural orbital expansion converges rapidly enough for the differential quintuple contribution to support low-cost approximations. Calculations at natural orbital cutoffs of 0.0025 or 0.001 yield viable results, and a simple extrapolation from the pair 0.005 and 0.0025 performs well as an even cheaper option. Convergence is slower for second-row compounds than for first-row ones.

Core claim

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)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

Frozen natural orbital (FNO) truncation applied to the CCSDTQ(5)Λ method, selecting a subset of natural orbitals via occupation cutoff to approximate the connected quintuple excitation contributions.

If this is right

  • Quintuple corrections become feasible for larger first-row molecules in routine thermochemistry workflows.
  • The naive extrapolation provides a low-cost route to near-full accuracy for the quintuple term.
  • Second-row compounds require tighter cutoffs or additional checks because their FNO convergence is slower.

Where Pith is reading between the lines

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

  • The same FNO approach could be tested on other high-order connected excitations beyond quintuples.
  • Integration with existing composite methods might further reduce overall computational cost in thermochemical databases.
  • Broader validation on systems with heavier elements could identify where tighter thresholds are mandatory.

Load-bearing premise

The chosen test set of molecules adequately represents convergence behavior for the differential quintuple contribution across first- and second-row compounds while keeping FNO truncation errors below the 0.5 kcal/mol target accuracy.

What would settle it

A direct comparison on a second-row molecule showing that the quintuple contribution at a 0.001 cutoff differs from the full calculation or extrapolated value by more than 0.5 kcal/mol would falsify the viability of these cutoffs.

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

2 major / 2 minor

Summary. The manuscript proposes FNO-CCSDTQ(5)Λ as an economical alternative for approximating connected quintuple excitation contributions in coupled-cluster thermochemistry. It reports that the differential quintuple contribution converges rapidly with respect to the frozen natural orbital cutoff, rendering cutoffs of 0.0025 or 0.001 viable and a naive extrapolation from the set {0.005, 0.0025} surprisingly effective, while noting slower convergence for second-row compounds.

Significance. If the reported convergence rates and error magnitudes hold, the method would offer a practical route to include quintuple contributions at reduced cost while targeting 0.5 kcal/mol thermochemical accuracy. The work rests on standard CC theory and FNO truncation, with numerical tests rather than ad-hoc parameters; this is a strength. However, the significance is tempered by the need for broader test-set coverage and explicit bounds on truncation errors, especially for second-row species where slower convergence is acknowledged.

major comments (2)
  1. [Abstract] Abstract: The central claim that FNO cutoffs of 0.0025 or 0.001 keep truncation errors small enough not to compromise 0.5 kcal/mol accuracy requires explicit quantification of the maximum (not merely average) truncation error at these cutoffs across all tested molecules. The abstract flags slower convergence for second-row compounds, yet without tabulated maximum errors or a clear statement that the test set contains representative second-row cases, the generalization to the target accuracy remains unverified.
  2. [Results] Presumed Results section: The statement that naive extrapolation from {0.005, 0.0025} 'works surprisingly well' is load-bearing for the low-cost option claim. The manuscript should report the actual residuals of this extrapolation versus direct calculations at a smaller cutoff (e.g., 0.001) for each molecule or class, rather than qualitative description, to demonstrate that extrapolation residuals do not exceed the direct-cutoff errors.
minor comments (2)
  1. [Introduction] The notation CCSDTQ(5)Λ should be defined explicitly on first use, including the meaning of the subscript Λ, to aid readers outside the immediate CC community.
  2. Figure captions or a methods table should list the exact molecules in the test set, their row classification (first- vs. second-row), and the basis sets employed, to allow direct assessment of coverage.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed report. The comments highlight important points for strengthening the quantitative support of our claims regarding truncation errors and extrapolation performance. We address each major comment below and will incorporate the requested data into a revised manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central claim that FNO cutoffs of 0.0025 or 0.001 keep truncation errors small enough not to compromise 0.5 kcal/mol accuracy requires explicit quantification of the maximum (not merely average) truncation error at these cutoffs across all tested molecules. The abstract flags slower convergence for second-row compounds, yet without tabulated maximum errors or a clear statement that the test set contains representative second-row cases, the generalization to the target accuracy remains unverified.

    Authors: We agree that maximum truncation errors must be reported explicitly to substantiate the 0.5 kcal/mol accuracy target. In the revised manuscript we will add a table (or supplementary table) listing the maximum, mean, and standard deviation of the differential quintuple truncation errors at cutoffs 0.0025 and 0.001 for the full test set, with a separate breakdown for first-row versus second-row species. We will also add a sentence confirming that the test set includes representative second-row molecules (e.g., those containing S and Cl) and that the slower convergence for these species is already quantified in the results section. revision: yes

  2. Referee: [Results] Presumed Results section: The statement that naive extrapolation from {0.005, 0.0025} 'works surprisingly well' is load-bearing for the low-cost option claim. The manuscript should report the actual residuals of this extrapolation versus direct calculations at a smaller cutoff (e.g., 0.001) for each molecule or class, rather than qualitative description, to demonstrate that extrapolation residuals do not exceed the direct-cutoff errors.

    Authors: We accept that a qualitative statement is insufficient for a load-bearing claim. The revised manuscript will include a new table (or expanded results subsection) that reports, for every molecule, the absolute residual between the extrapolated value and the direct FNO-CCSDTQ(5)Λ result at cutoff 0.001. Results will be grouped by first-row and second-row compounds so that readers can directly compare extrapolation residuals to the corresponding direct-cutoff errors. revision: yes

Circularity Check

0 steps flagged

No significant circularity in FNO convergence demonstration for quintuple contributions

full rationale

The paper's central claim is supported by direct numerical computations showing rapid convergence of the FNO expansion for differential quintuple excitation contributions in CCSDTQ(5)Λ, with explicit results for cutoffs 0.0025/0.001 and a naive extrapolation. No equations or steps reduce the reported viability to a fitted parameter or self-definition by construction. The approach applies standard coupled-cluster theory and frozen natural orbital truncation, with convergence behavior tested on a molecular test set (including noted slower convergence for second-row species). No load-bearing self-citations, uniqueness theorems, or ansatzes imported from prior author work are invoked in the provided text. The derivation remains self-contained against external benchmarks of CC and FNO methods.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The paper relies on standard coupled-cluster theory and the frozen-natural-orbital approximation; the only adjustable elements are the NO cutoff thresholds chosen after convergence tests.

free parameters (1)
  • NO cutoff threshold = 0.0025 or 0.001
    Values 0.005, 0.0025, and 0.001 are selected as practical points where convergence is judged sufficient; they are not derived from first principles.
axioms (2)
  • standard math Standard assumptions of coupled-cluster theory including the validity of the CCSDTQ(5) hierarchy for differential correlation contributions
    Invoked throughout the abstract when discussing quintuple contributions and their magnitude.
  • domain assumption Frozen natural orbitals provide a faithful truncation for the differential quintuple excitation energy
    Central premise that allows the cutoff-based approximation.

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