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arxiv: 2606.31625 · v1 · pith:Y4XPJO22new · submitted 2026-06-30 · ⚛️ physics.chem-ph

An Additive Reference Correction Scheme for the Transcorrelated Method

Johannes Hauskrecht , Kristoffer Simula , Yifan Cheng , Evelin Martine Corvid Christlmaier , Daniel Kats , Ali Alavi This is my paper

Pith reviewed 2026-07-01 03:05 UTC · model grok-4.3

classification ⚛️ physics.chem-ph
keywords transcorrelated methodreference correctionxTCatomization energiesdouble-zeta basisHEAT setCCSD(T)
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The pith

Replacing the reference energy in xTC calculations with a larger-basis value improves atomization energies in double-ζ bases while keeping the small-basis correlation energy.

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

The paper introduces an additive reference correction for the transcorrelated method and its xTC approximation to address inaccuracies in energy differences when using small orbital basis sets. It keeps the correlation energy computed in the small basis but replaces the corresponding reference energy with the value obtained from a larger basis. This targets the observation that reference errors dominate over correlation errors for xTC atomization energies in double-ζ bases. A sympathetic reader would care because the approach delivers better results at modest extra cost, making high-accuracy computations feasible without immediately moving to larger, more expensive bases. Benchmarks on the non-relativistic HEAT set confirm substantial gains over standard xTC and competitive or better performance than F12a methods in the small-basis regime.

Core claim

The central claim is that for xTC atomization energies the dominant error in double-ζ bases originates from the reference contribution rather than from the correlation energy. In the reference-corrected scheme the small-basis correlation energy is retained while the TC reference energy is replaced by its larger-basis counterpart. Benchmark calculations for the HEAT set with the Dunning family show that this RC-xTC scheme substantially improves both total and atomization energies relative to standard xTC in double-ζ bases. At the CCSD(T) level RC-xTC yields better atomization energies than CCSD(T)-F12a in the double-ζ regime while preserving the favorable total-energy accuracy of xTC; at the

What carries the argument

The RC-xTC scheme, an additive correction that substitutes the small-basis TC reference energy with its larger-basis value while retaining the small-basis correlation energy.

If this is right

  • RC-xTC improves both total and atomization energies relative to standard xTC in double-ζ bases on the HEAT set.
  • At the CCSD(T) level, RC-xTC produces better atomization energies than CCSD(T)-F12a in the double-ζ regime while retaining xTC total-energy accuracy.
  • At the CCSD level, RC-xTC improves atomization energies relative to F12a across the full basis-set sequence.
  • As the basis set enlarges, RC-xTC converges to standard xTC by construction.

Where Pith is reading between the lines

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

  • The same reference-swap idea could be tested on other energy differences such as reaction barriers where reference contributions might similarly dominate.
  • Applying the correction to even smaller bases such as single-ζ could check whether the reference-error dominance persists and how far the scheme remains useful.
  • The construction suggests that separating reference and correlation treatments can be an efficient route for transcorrelated methods when basis-set limitations are the main bottleneck.

Load-bearing premise

The dominant error for xTC atomization energies in double-ζ bases originates from the reference contribution rather than from the correlation energy.

What would settle it

A decomposition of the xTC atomization energy error in double-ζ bases that shows the correlation-energy contribution exceeds the reference-energy contribution would falsify the premise for the correction.

Figures

Figures reproduced from arXiv: 2606.31625 by Ali Alavi, Daniel Kats, Evelin Martine Corvid Christlmaier, Johannes Hauskrecht, Kristoffer Simula, Yifan Cheng.

Figure 1
Figure 1. Figure 1: Basis set dependent mean absolute errors for [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: System-resolved total-energy (left) and atomization-energy errors (right) for xTC-CCSD(T) and RC [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 1
Figure 1. Figure 1: Thus, both the CABS correction and the present [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: Atomization-energy errors for the HEAT systems at the CCSD(T) level, comparing CCSD(T)-F12 (top [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Basis-set error statistics for the Dunning basis-set family at the CCSD(T) level. Shown are the MAEs [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Basis-set error statistics for the Dunning basis-set family at the CCSD level. Shown are the MAEs of the [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
read the original abstract

We introduce an additive reference correction for the transcorrelated (TC) method and its three-body mean-field approximation (xTC), to improve energy differences computed in small orbital basis sets. The correction is motivated by the observation that, for xTC atomization energies, the dominant error in double-{\zeta} bases originates from the reference contribution rather than from the correlation energy. In the proposed reference-corrected scheme (RC-xTC), the small-basis correlation energy is retained, while the corresponding TC reference energy is replaced by its value from a larger basis. Benchmark calculations for the non-relativistic HEAT set with the Dunning basis-set family show that RC-xTC substantially improves both total and atomization energies relative to standard xTC in double-{\zeta} bases. At the CCSD(T) level, RC-xTC yields better atomization energies than CCSD(T)-F12a in the double-{\zeta} regime, while preserving the favorable total-energy accuracy of xTC. At the CCSD level, RC-xTC improves atomization energies relative to F12a throughout the full basis-set sequence. As the basis set is enlarged, xTC and RC-xTC become progressively identical, as expected from the construction of the correction.

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 / 1 minor

Summary. The manuscript introduces an additive reference correction scheme (RC-xTC) for the transcorrelated (TC) method and its three-body mean-field approximation (xTC). The scheme retains the small-basis correlation energy but replaces the TC reference energy with its value computed in a larger basis set. This is motivated by the observation that, for xTC atomization energies, the dominant error in double-ζ bases originates from the reference rather than the correlation contribution. Benchmark calculations on the non-relativistic HEAT set using the Dunning basis-set family demonstrate that RC-xTC substantially improves both total and atomization energies relative to standard xTC in double-ζ bases. At the CCSD(T) level, RC-xTC yields better atomization energies than CCSD(T)-F12a in the double-ζ regime while preserving the favorable total-energy accuracy of xTC. At the CCSD level, improvements over F12a are seen across the basis-set sequence.

Significance. If the central results hold, the RC-xTC scheme offers a computationally efficient way to enhance the accuracy of transcorrelated calculations in small orbital bases without modifying the correlation treatment. The direct comparisons to explicitly correlated F12a methods on the HEAT set provide useful benchmarks for the community. The approach becomes equivalent to standard xTC as the basis set is enlarged, consistent with its construction. The paper provides concrete numerical evidence of improvements in both total and atomization energies.

major comments (1)
  1. [Introduction] Introduction (and results section): The central motivation for retaining the small-basis correlation energy unchanged rests on the claim that reference errors dominate over correlation errors for xTC atomization energies in double-ζ bases. However, no explicit decomposition of basis-set errors into reference and correlation components is provided for the HEAT set molecules, so it remains possible that the reported net improvements arise from a different balance of errors.
minor comments (1)
  1. [Abstract] Abstract: The statement of the motivating observation does not include a cross-reference to the specific results, table, or figure where this dominance is demonstrated.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive feedback. We address the single major comment below.

read point-by-point responses

  1. Referee: [Introduction] Introduction (and results section): The central motivation for retaining the small-basis correlation energy unchanged rests on the claim that reference errors dominate over correlation errors for xTC atomization energies in double-ζ bases. However, no explicit decomposition of basis-set errors into reference and correlation components is provided for the HEAT set molecules, so it remains possible that the reported net improvements arise from a different balance of errors.

    Authors: We agree that an explicit decomposition of the basis-set errors would strengthen the motivation for the RC-xTC scheme. In the revised manuscript we will add this decomposition (as a table in the results section) for the HEAT set at the double-ζ level, separating the reference and correlation contributions to both total and atomization energies. This will directly demonstrate that the reference error dominates for xTC atomization energies and thereby justify retaining the small-basis correlation energy. revision: yes

Circularity Check

0 steps flagged

No significant circularity; scheme is an explicit additive definition with independent benchmarks

full rationale

The RC-xTC method is defined directly by replacing the small-basis TC reference energy with its large-basis counterpart while retaining the small-basis correlation energy; this is a constructional choice, not a derivation that reduces to its own inputs by equation. The paper reports numerical improvements on the external HEAT benchmark set against CCSD(T)-F12a and other methods, providing falsifiable evidence outside the definition itself. No self-citations, fitted parameters renamed as predictions, or uniqueness theorems are invoked in the abstract or described construction. The motivating observation about error dominance is stated but does not create a self-referential loop in the reported results.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The scheme depends on one domain assumption about error partitioning and on the practical availability of larger-basis reference calculations; no free parameters or new entities are introduced.

axioms (1)
  • domain assumption For xTC atomization energies the dominant error in double-ζ bases originates from the reference contribution rather than from the correlation energy.
    Explicitly stated as the motivation for the correction in the abstract.

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