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arxiv: 2606.31117 · v1 · pith:F5WXYTYInew · submitted 2026-06-30 · ⚛️ physics.chem-ph · quant-ph

Radical-Fragment Many-Body Expansion for Linear Alkane Quantum Chemistry

Daniel Sierra-Sosa , Jorge Saavedra , Santiago Solares , Gregorio Toscano-Pulido This is my paper

Pith reviewed 2026-07-01 03:26 UTC · model grok-4.3

classification ⚛️ physics.chem-ph quant-ph
keywords many-body expansionradical fragmentslinear alkanesquantum chemistryVQEqubit reductionfragmentationROHF
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The pith

A two-body radical-fragment expansion reconstructs linear alkane energies from four unique calculations, cutting qubit needs by over 12 times for C26H54.

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

The paper presents a many-body expansion at the two-body level that uses homolytic cleavage of C-C bonds to create open-shell radical fragments. These fragments are computed separately with restricted open-shell Hartree-Fock and then assembled through a fixed formula to recover the full molecular energy. Symmetry among the fragments means only four distinct calculations are ever required, no matter how long the alkane chain becomes. The approach is checked against classical and quantum solvers up to hexacosane and shows that the reconstructed energies track direct calculations while lowering the qubit count from hundreds to tens.

Core claim

Linear alkane total energies can be assembled from two-body interactions of homolytic radical fragments (CH3 and CH2) computed in isolation with ROHF, using an assembly formula that requires only four unique fragment calculations independent of chain length.

What carries the argument

The two-body MBE2 assembly formula applied to energies of homolytic C-C cleavage radical fragments treated without capping atoms or embedding.

If this is right

  • Total energies for linear alkanes of any length are obtained from four unique fragment calculations.
  • Maximum qubit requirement drops with fragment size rather than full molecule size, yielding a 12.3x reduction for C26H54.
  • MBE2-VQE and MBE2-SQD executed on IBM hardware closely track their classical MBE2 reference values.
  • The same four-fragment decomposition works across RHF, CCSD, VQE, ADAPT-VQE, and SQD solvers for chains from C4 to C26.

Where Pith is reading between the lines

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

  • The fixed four-calculation count could extend to other linear chain molecules if similar radical symmetry holds.
  • Hardware runs on fragments suggest the method lowers the barrier for applying current quantum devices to molecules larger than those feasible today.
  • If the radical-fragment choice avoids the need for electrostatic embedding, the same pattern may simplify other fragmentation schemes that currently rely on capping and embedding.

Load-bearing premise

That two-body interactions of isolated radical fragments are enough to reconstruct accurate total energies without higher-order corrections or embedding terms for linear alkanes.

What would settle it

A direct full-molecule calculation for an alkane such as C30H62 that deviates from the MBE2 energy by more than chemical accuracy using any of the tested solvers.

Figures

Figures reproduced from arXiv: 2606.31117 by Daniel Sierra-Sosa, Gregorio Toscano-Pulido, Jorge Saavedra, Santiago Solares.

Figure 1
Figure 1. Figure 1: Intrinsic MBE2 fragmentation error for the two classical methods. (a) Total reconstruction error (kcal/mol) vs. number of carbon atoms for MBE2-RHF (relative to full RHF) and MBE2-CCSD (relative to full CCSD). (b) Error normalized per carbon atom, showing convergence toward a stable per-carbon penalty as chain length increases. Unlike VQE and ADAPT-VQE, which solve reduced 8-qubit CASSCF Hamiltonians on a … view at source ↗
Figure 2
Figure 2. Figure 2: Comprehensive error comparison. (a) Total error (kcal/mol) for all three quantum methods against their respective full-molecule references, overlaid with the pure fragmentation baselines MBE2-RHF and MBE2-CCSD. (b) Error per carbon atom, showing convergence toward stable per-carbon asymptotes for long chains [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Qubit requirements. Side-by-side bar chart of full-molecule qubit count vs. the constant MBE2 maximum fragment (30 qubits) for each alkane. 9 [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Fragment qubit costs and symmetry exploitation. (a) Qubit count for each unique fragment type: CH• 3 monomer (16q), •CH• 2 monomer (14q), CH3–CH2 dimer (30q), and CH2–CH2 dimer (28q), with the full-molecule range (60–368q) shown as a shaded band. (b) Total fragment count (brute force) vs. unique fragment count (exploiting translational symmetry), showing the gap widening from 7 vs. 4 at butane to 51 vs. 4 … view at source ↗
read the original abstract

We introduce a radical-fragment many-body expansion at the two-body level (MBE2) for quantum chemistry of linear alkanes. Instead of heterolytic bond cleavage with hydrogen capping atoms and electrostatic embedding like in Fragment Molecular Orbital (FMO), we perform homolytic C-C bond cleavage to produce open-shell radical fragments (CH3, CH2) treated with restricted open-shell Hartree-Fock (ROHF) in isolation. The two-body MBE2 assembly formula reconstructs total alkane energies from only four unique fragment calculations regardless of chain length, reducing the maximum qubit requirement. We benchmark this framework against five energy solvers (RHF, CCSD, VQE, ADAPT-VQE, and SQD) across 11 linear alkanes from butane (C4H10) to hexacosane (C26H54). The MBE2 decomposition achieves a 12.3x qubit reduction for C26H54 (from 368 to 30 qubits) and a 12.8x reduction in unique calculations via symmetry exploitation. MBE2-VQE and MBE2-SQD (executed on IBM quantum hardware) closely track their respective classical MBE2 references, demonstrating that fragmentation-based quantum chemistry is viable for scaling quantum solvers to large molecular systems.

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 / 0 minor

Summary. The manuscript introduces a radical-fragment many-body expansion at the two-body level (MBE2) for linear alkanes, using homolytic C-C bond cleavage to generate open-shell radical fragments (CH3, CH2) treated in isolation with ROHF. An assembly formula is claimed to reconstruct total energies from only four unique fragment calculations independent of chain length. The approach is benchmarked on 11 alkanes (C4H10 to C26H54) using RHF, CCSD, VQE, ADAPT-VQE, and SQD solvers, reporting a 12.3x qubit reduction for C26H54 (368 to 30 qubits) and close tracking of MBE2-VQE/MBE2-SQD (on IBM hardware) to classical MBE2 references.

Significance. If the two-body radical-fragment MBE2 is shown to accurately reproduce full-molecule energies, the method would offer a concrete route to reduce qubit counts and unique circuit evaluations for quantum chemistry on linear systems, potentially extending the reach of near-term quantum solvers without embedding or higher-order corrections.

major comments (2)
  1. [Abstract] Abstract: the central reconstruction claim requires that the two-body MBE2 formula (homolytic cleavage, isolated ROHF fragments, no embedding) accurately recovers total alkane energies, yet the reported benchmarks compare only MBE2-VQE and MBE2-SQD to classical MBE2 references; no errors versus non-fragmented full-molecule RHF or CCSD are supplied for any of the 11 alkanes, leaving the sufficiency of the two-body truncation unverified.
  2. [Abstract] Abstract: the qubit-reduction and symmetry-exploitation claims (12.3x and 12.8x for C26H54) rest on the assembly formula using only four unique fragments, but without an explicit equation for the MBE2 energy expression or a demonstration that higher-order terms remain negligible for linear alkanes, the scaling advantage cannot be assessed against full-molecule references.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their detailed and constructive review. We address each major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central reconstruction claim requires that the two-body MBE2 formula (homolytic cleavage, isolated ROHF fragments, no embedding) accurately recovers total alkane energies, yet the reported benchmarks compare only MBE2-VQE and MBE2-SQD to classical MBE2 references; no errors versus non-fragmented full-molecule RHF or CCSD are supplied for any of the 11 alkanes, leaving the sufficiency of the two-body truncation unverified.

    Authors: The manuscript's primary objective is to validate that quantum solvers applied to the radical fragments reproduce the classical MBE2 reference energies, thereby establishing the viability of the fragmentation strategy for quantum hardware. The two-body reconstruction formula itself is presented in the main text (Eq. 1) and is constructed to recover the total energy exactly within the MBE2 approximation for the chosen homolytic cleavage. Direct MBE2 vs. full-molecule errors are not reported because the focus is on the quantum-classical agreement on the fragments rather than re-benchmarking the classical MBE2 truncation. We agree this comparison would strengthen the abstract claim and will add a supplementary table of MBE2-RHF versus full RHF energies for the smaller alkanes (C4–C10) where full calculations remain tractable. revision: yes

  2. Referee: [Abstract] Abstract: the qubit-reduction and symmetry-exploitation claims (12.3x and 12.8x for C26H54) rest on the assembly formula using only four unique fragments, but without an explicit equation for the MBE2 energy expression or a demonstration that higher-order terms remain negligible for linear alkanes, the scaling advantage cannot be assessed against full-molecule references.

    Authors: Equation 1 in Section II explicitly states the MBE2 assembly: the total energy is recovered from only four unique open-shell fragment calculations (two distinct CH3 radicals and two distinct CH2 radicals) with appropriate coefficients independent of chain length. The qubit counts (368 → 30 for C26H54) follow directly from solving these fixed-size fragments rather than the full molecule. For linear alkanes the two-body truncation is justified by the localized C–C interactions; the consistent agreement between MBE2-VQE/SQD and classical MBE2 across eleven chain lengths provides indirect support that omitted higher-order terms do not grow with length. We will add a brief clarifying sentence in the revised abstract and a footnote referencing Eq. 1 to make the scaling basis unambiguous. revision: partial

Circularity Check

0 steps flagged

No circularity: derivation is self-contained by explicit construction of MBE2

full rationale

The paper explicitly defines the radical-fragment MBE2 procedure (homolytic cleavage to CH3/CH2 radicals, isolated ROHF, two-body assembly from four unique fragments) and applies it to linear alkanes. It then compares quantum solvers (VQE, SQD) directly to classical MBE2 references computed on the identical fragments. Qubit and calculation reductions follow immediately from the fragmentation definition itself. No parameters are fitted to a data subset and renamed as predictions, no self-citations justify load-bearing uniqueness or ansatze, and no equations reduce to their inputs by construction. The reported tracking of references is therefore a direct consequence of solving the same defined subproblems, rendering the chain self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The reconstruction claim depends on the unstated two-body assembly formula being accurate for these systems; no free parameters, new entities, or ad-hoc axioms are described in the abstract.

axioms (1)
  • domain assumption Standard quantum chemistry solvers (RHF, CCSD, VQE) applied to isolated radical fragments yield energies that combine correctly via the MBE2 formula.
    The paper applies these solvers to fragments without additional justification or error analysis in the abstract.

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Reference graph

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