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arxiv: 2606.26941 · v1 · pith:PIDXXUQJnew · submitted 2026-06-25 · ⚛️ physics.chem-ph

Perturbatively Corrected Linear Response Selected Configuration Interaction

Peter Reinholdt , Erik Kjellgren , Jacob Kongsted This is my paper

Pith reviewed 2026-06-26 02:26 UTC · model grok-4.3

classification ⚛️ physics.chem-ph
keywords selected configuration interactionlinear responseEpstein-Nesbet perturbation theorystatic polarizabilitiesfull configuration interactionmolecular response properties
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0 comments X

The pith

Perturbative corrections to linear response SCI preserve pole structure and improve static polarizabilities toward FCI.

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

This paper develops perturbative corrections using Epstein-Nesbet theory up to second order for the linear response selected configuration interaction method. The corrections are shown to keep the pole structure intact from the variational parent method, restricting use to static properties. Numerical tests on polarizabilities of water, ethene, boron hydride, and hydrogen chloride reveal that second-order terms give better accuracy and smoother convergence to the full CI limit than the uncorrected version. With extrapolation, results align closely with coupled cluster benchmarks for both ground and excited states.

Core claim

The authors establish that finite-order Epstein-Nesbet perturbative corrections applied to the LR-SCI equations preserve the exact pole structure of the variational theory. This property enables the method to compute static polarizabilities with improved accuracy over the parent variational LR-SCI, showing systematic convergence to FCI and reduced oscillatory behavior when second-order corrections are included.

What carries the argument

Order-by-order Epstein-Nesbet perturbation expansion through second order applied to the linear response SCI equations, which preserves the pole structure while correcting the response properties.

If this is right

  • First-order corrections yield only marginal improvements while second-order corrections substantially enhance accuracy.
  • Second-order corrections diminish the oscillatory convergence behavior of the parent variational LR-SCI method.
  • The corrected method achieves systematic convergence toward the FCI limit for ground and excited state polarizabilities.
  • Combined with extrapolation techniques, LR-SCI-PT matches high-level coupled-cluster references closely.

Where Pith is reading between the lines

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

  • If the pole preservation holds generally, similar perturbative corrections could apply to other variational response methods for static properties.
  • The method's success on small molecules suggests it may scale to larger systems where full FCI is infeasible.
  • Testing the approach on other static properties like dipole moments could reveal broader applicability.

Load-bearing premise

Finite-order Epstein-Nesbet perturbative corrections preserve the exact pole structure of the parent variational LR-SCI theory without new singularities.

What would settle it

Demonstration that the perturbatively corrected response function develops additional poles or singularities not present in the variational LR-SCI, or lack of convergence improvement in the benchmarks.

Figures

Figures reproduced from arXiv: 2606.26941 by Erik Kjellgren, Jacob Kongsted, Peter Reinholdt.

Figure 1
Figure 1. Figure 1: Convergence of the LR-SCI-PT polarizability of water/cc-pVDZ (8e, 23o) towards [PITH_FULL_IMAGE:figures/full_fig_p015_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Convergence of the zz component of the ground-state polarizability of water/cc￾pVDZ (8e, 23o) as a function of the perturbative accuracy parameter ε2. The three panels show results for different choices of the variational space parameter ε1. The black lines show a version in which the parameter ε2 controls both the accuracy of the fluctuation operator matrix-vector multiplication and the size of the pertur… view at source ↗
Figure 3
Figure 3. Figure 3: The αzz component of the polarizability of ethene/cc-pVDZ (12e, 46o). The polarizability is computed using LR-SCI-PT for a set of increasingly tight thresholds ε1. The inset shows a zoomed region around ε1 = 0. The black dashed line shows an extrapolation towards ε1 = 0. Results obtained using CCSD, CCSDT, and CCSDTQ are indicated with dashed lines. well as density-functional-based methods. Here, we repeat… view at source ↗
Figure 4
Figure 4. Figure 4: Convergence of LR-SCI methods towards the FCI limit for the isotropic ground- [PITH_FULL_IMAGE:figures/full_fig_p020_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Convergence of LR-SCI methods towards the FCI limit for the isotropic ground- [PITH_FULL_IMAGE:figures/full_fig_p022_5.png] view at source ↗
read the original abstract

Selected configuration interaction (SCI) methods have emerged as powerful, lower-cost alternatives to full configuration interaction (FCI) for ground- and excited-state energies. Still, calculating molecular response properties with SCI remains a significant challenge. In this work, we introduce perturbative corrections to the linear response selected configuration interaction (LR-SCI) framework, using an order-by-order Epstein-Nesbet perturbation expansion through second order. We demonstrate that in this theoretical framework, the finite-order perturbative treatment preserves the pole structure of the parent variational LR-SCI theory, which means that although the method can be useful for static properties, it is not suitable for frequency-dependent molecular response properties. Numerical benchmarks targeting the static polarizabilities of water, ethene, boron hydride, and hydrogen chloride demonstrate systematic convergence toward the FCI limit for both ground and excited electronic states. While first-order corrections yield marginal improvements, the inclusion of second-order corrections substantially enhances accuracy over underlying variational treatments and diminishes oscillatory convergence behavior present in the parent variational LR-SCI method. Combined with extrapolation techniques, LR-SCI-PT achieves excellent agreement with high-level coupled-cluster references, establishing a powerful route toward near-FCI quality molecular properties for systems otherwise inaccessible to exact FCI treatments.

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 paper introduces finite-order Epstein-Nesbet perturbative corrections (through second order) to the linear response selected configuration interaction (LR-SCI) framework. It asserts that these corrections preserve the pole structure of the parent variational LR-SCI theory, rendering the method suitable for static polarizabilities but unsuitable for frequency-dependent response. Numerical benchmarks on the static polarizabilities of water, ethene, BH, and HCl demonstrate systematic convergence to the FCI limit for ground- and excited-state properties, with second-order corrections improving accuracy over variational LR-SCI and reducing oscillatory behavior; extrapolation yields agreement with coupled-cluster references.

Significance. If the pole-preservation property holds and the benchmarks are robust, the work provides a practical route to near-FCI static response properties for systems beyond direct FCI reach, extending SCI methods while addressing convergence issues in the variational parent method.

major comments (1)
  1. [Theoretical framework / pole-structure argument] The central claim that finite-order Epstein-Nesbet corrections preserve the exact pole structure of variational LR-SCI (without new singularities or artifacts) is load-bearing for both the static-property restriction and the validity of all reported polarizabilities. The abstract states this preservation is demonstrated, yet the algebraic argument establishing that the corrected response function retains the parent poles at finite order must be supplied explicitly; any shift or artifact would undermine the entire framework.
minor comments (1)
  1. The abstract refers to benchmarks on four molecules but does not list the basis sets, active-space definitions, or reference FCI values used; these details are needed to assess the convergence claims.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting the importance of rigorously establishing the pole-preservation property. We agree that an explicit algebraic argument is essential and will revise the manuscript to supply it in full detail.

read point-by-point responses

  1. Referee: The central claim that finite-order Epstein-Nesbet corrections preserve the exact pole structure of variational LR-SCI (without new singularities or artifacts) is load-bearing for both the static-property restriction and the validity of all reported polarizabilities. The abstract states this preservation is demonstrated, yet the algebraic argument establishing that the corrected response function retains the parent poles at finite order must be supplied explicitly; any shift or artifact would undermine the entire framework.

    Authors: We agree that the manuscript would benefit from an explicit algebraic derivation rather than a summary statement. The original text notes that the Epstein-Nesbet corrections are applied order-by-order to the linear-response equations without introducing new frequency-dependent denominators, thereby inheriting the parent poles; however, the step-by-step matrix algebra was not written out. In the revised manuscript we will add a dedicated subsection deriving the first- and second-order corrected response function, showing that the effective response matrix retains the same secular equation structure and pole locations as variational LR-SCI. This addition will also clarify why the approach remains restricted to static properties. revision: yes

Circularity Check

0 steps flagged

No significant circularity in LR-SCI-PT derivation

full rationale

The paper applies standard order-by-order Epstein-Nesbet perturbation theory to the existing LR-SCI response equations and states that finite-order corrections preserve the parent pole structure as an algebraic property of the framework. This demonstration is presented directly from the equations rather than by fitting parameters or reducing to self-citations. Benchmarks compare to independent FCI and CC references. No self-definitional, fitted-input, or load-bearing self-citation patterns appear in the provided abstract or description.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard quantum-chemistry assumptions about the applicability of Epstein-Nesbet partitioning to linear-response equations and the compatibility of configuration selection with perturbative corrections; no new entities are postulated.

axioms (1)
  • domain assumption Epstein-Nesbet perturbation theory can be applied order-by-order to the linear response equations of selected configuration interaction while preserving the parent pole structure
    Invoked when the paper states that finite-order corrections preserve the pole structure of variational LR-SCI.

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