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Analytic Gradients and Nonadiabatic Couplings for Device-Resident DMRG-QD-NEVPT2 Through Conical Intersections on a Consumer GPU

Rubén Darío Guerrero

arXiv:2609.09990v2physics.chem-phcs.AR

TL;DR

Analytic multireference derivatives combining static and dynamic correlation have been confined to datacenter-scale hardware, despite their relevance to nonadiabatic dynamics through conical intersections. This paper implements device-resident DMRG-QD-NEVPT2 gradients and NACMEs through a single reverse-mode contraction graph. Its quasi-degenerate effective Hamiltonian is designed to remain valid through a conical intersection.

  • Problem

    Analytic multireference derivatives with dynamic correlation have been realized at datacenter scale, while nonadiabatic dynamics requires gradients and interstate couplings at each geometry.

    Source: §I · p. 2

  • Method

    The method combines a DMRG active-space reference with quasi-degenerate NEVPT2 and obtains derivatives by reverse-mode transposition of a contraction graph.

    Source: §I · p. 2, C. Relaxation as the contraction-DAG… · p. 4

  • Results

    The combined analytic-gradient and NACME method is run device-resident on consumer hardware through a conical intersection.

    Source: §I · p. 2

  • Takeaways & Limitations

    The near-degenerate states are diagonalized rather than divided by their gap, keeping the spectrum regular through a conical intersection.

    Source: §I · p. 2

    Allowed-band magnitudes are symmetry-consistent representatives rather than quantitative oscillator-strength predictions because per-system oscillator strengths are not yet populated.

    Source: C. The QUEST comparison,… · p. 13

Abstract

from arXiv · show

Nonadiabatic dynamics through a conical intersection requires both static and dynamic correlation and, at every geometry, an excited-state gradient and interstate nonadiabatic coupling (NACME). Analytic multireference derivatives at this level have been confined to datacenter-scale hardware. We report device-resident \mbox{DMRG-QD-NEVPT2} with analytic gradients and NACMEs within the $8$\,GB of a consumer GPU: a density-matrix-renormalization-group (DMRG) active-space reference supplies the static correlation, and quasi-degenerate SC-NEVPT2 dresses it through a multi-state effective Hamiltonian that remains valid \emph{through} a conical intersection, where single-state perturbation theory develops a vanishing denominator and fails. Every gradient and NACME is one reverse-mode transpose of a single contraction graph: the DMRG sweep enters as a gauge-free differentiable node, and all two-electron work is AO-direct through Cholesky factors. The DMRG reference is exact within the active space ($\sim\!10^{-15}$\,Ha). The corrected adiabats close smoothly to a real $S_0/S_1$ conical intersection with a non-vanishing, $1/\Delta E$-divergent NACME---where linear-response TDDFT returns zero identically---and the dressing restores the differential dynamic correlation that ionic $\pi\pi^*$ states require. DMRG-NEVPT2 and quasi-degenerate NEVPT2 are each established; what is new is the combined stack---multi-state and through a conical intersection, with analytic gradients and couplings---realized device-resident on commodity hardware.

I. INTRODUCTION

The paper extends multireference derivatives to DMRG-QD-NEVPT2, combining a systematically improvable active-space treatment with dynamic correlation and analytic gradients and interstate couplings. It presents this combined derivative stack as device-resident on a consumer GPU and valid through a conical intersection.

I. INTRODUCTION

  • DMRG supplies a systematically improvable active-space treatment for multiconfigurational states spread across many orbitals, beyond compact, method-fixed active spaces.Its bond dimension controls the approximation to the active-space FCI wavefunction, with the large-bond-dimension limit exact.Source: §I · p. 1
  • Earlier analytic DMRG derivatives were delivered at the self-consistent-field level, while prior multireference derivatives with dynamic correlation were realized conventionally at datacenter scale.The paper distinguishes its contribution from both lines of prior work.Source: §I · pp. 1–2
  • DMRG-QD-NEVPT2 gradients and interstate NACMEs are obtained by transposing one contraction graph, with the full calculation running on consumer hardware through a conical intersection.The stated novelty is the realization of the combined method, not the first DMRG gradient or NEVPT2 derivative.Source: §I · p. 2

A. The DMRG-QD-NEVPT2 energy

  • The DMRG reference provides the active-space wavefunction and its one- through four-particle RDMs, while corrected adiabatic energies come from a dynamically dressed effective Hamiltonian.The hybrid Kohn–Sham orbitals provide a common reference; the total energy is not an additive reference-plus-correction sum.Source: A. The DMRG-QD-NEVPT2 energy · p. 3

B. The dynamic correlation: strongly-contracted quasi-degenerate NEVPT2

The method combines DMRG active-space static correlation with strongly-contracted NEVPT2 dynamic correlation in a quasi-degenerate, multi-state effective Hamiltonian. Diagonalizing the near-degenerate block keeps the description regular through a conical intersection.

B. The dynamic correlation: strongly-contracted quasi-degenerate NEVPT2

  • The DMRG active space captures static correlation, and quasi-degenerate NEVPT2 supplies dynamic correlation for states approaching one another.The construction uses a fixed common reference and state-specific DMRG solutions.Source: B. The dynamic correlation:… · pp. 3–4
  • The second-order energies sum contributions from eight strongly-contracted perturber classes, using Koopmans–Dyall denominators derived from the state-averaged generalized Fock operator.The denominators are not the hybrid-Kohn–Sham orbital eigenvalues.Source: B. The dynamic correlation:… · p. 3
  • Transition-density perturber norms provide off-diagonal couplings in the Hermitized effective Hamiltonian, whose eigenvalues are the dynamically corrected adiabats.The construction is the symmetrized QD-NEVPT2 form, not a des Cloizeaux transform.Source: B. The dynamic correlation:… · p. 3
  • The two-state gap remains non-negative because near-degeneracy is diagonalized rather than divided out, avoiding the spurious vanishing denominator and negative gap of single-state second-order treatment.This regular spectrum supports meaningful analytic gradients and interstate NACMEs through the conical-intersection seam.Source: B. The dynamic correlation:… · p. 4
  • The fixed common reference makes transition norms and the effective Hamiltonian well-defined; relaxing the embedding would turn the correction into an orbital-optimization problem.The active-excluded MP2 limit provides the double-counting rationale relative to dynamic correlation in the hybrid Kohn–Sham reference.Source: B. The dynamic correlation:… · p. 4

C. Relaxation as the contraction-DAG transpose, with the DMRG sweep as a node

A single reverse-mode transpose of the energy graph produces analytic derivatives, with the DMRG sweep included as a differentiable node. The implementation uses an implicit adjoint and a gauge-free tangent treatment for truncated matrix-product states.

C. Relaxation as the contraction-DAG transpose, with the DMRG sweep as a node

  • One reverse pass transposes the energy graph’s operations to obtain analytic gradients, and a transition-weight density yields the NACME.The forward graph runs from the hybrid reference and Cholesky factors through DMRG and QD-SC-NEVPT2 to corrected adiabats.Source: C. Relaxation as the contraction-DAG… · p. 4, Figure 1 · p. 5
  • The engine’s memory schedule is arranged for minimum peak simultaneous liveness, supporting the reported 8 GB consumer-GPU feasibility.The graph-optimization passes also provide machine-precision cross-checks without a finite-difference floor.Source: C. Relaxation as the contraction-DAG… · p. 4
  • The DMRG sweep is a single graph node whose reverse-mode adjoint is an implicit fixed-point solve, not a stored tape of sweep iterations.The solve costs O(Lχ^2d) per application rather than storing memory proportional to the number of sweeps.Source: C. Relaxation as the contraction-DAG… · p. 5
  • The full-bond CAS reference contributes through the Hellmann–Feynman term, while response solves enter for the non-variational NEVPT2 gradient contribution and interstate NACMEs.The interstate couplings include the eigenvector response of the effective Hamiltonian.Source: C. Relaxation as the contraction-DAG… · p. 5
  • The gauge-free tangent-space projector gives the variational MPS energy’s exact gradient at the bond dimension in use, rather than only at full bond.A truncated MPS can be energy-converged without being tangent-stationary.Source: C. Relaxation as the contraction-DAG… · p. 5
  • Three- and four-particle RDMs are not materialized; their contractions with integral derivatives are streamed through Cholesky factors.The AO-direct correlated contractions avoid forming the four-index MO tensor.Source: C. Relaxation as the contraction-DAG… · pp. 4–5

D. The non-symmetric AO-Laplace J/K kernel

Interstate and response quantities require a non-symmetric AO-Laplace J/K build because their contractions use distinct state densities. The symmetric geometry build is recovered when the two weight densities are equal.

D. The non-symmetric AO-Laplace J/K kernel

  • Interstate and response quantities contract derivative integrals with left and right weight densities from different states, requiring a non-symmetric build.The ordinary symmetric geometry J/K build is the special case where the two weight densities are equal.Source: D. The non-symmetric AO-Laplace J/K… · p. 6
  • Each weight density may itself be non-symmetric, which prevents the usual index folding; interchanging the two arguments leaves the build invariant under ERI bra–ket symmetry.The invariance concerns argument order, not symmetry of either weight density.Source: D. The non-symmetric AO-Laplace J/K… · p. 6
  • The reference-side response and interstate objects share this kernel, while the DMRG-QD-NEVPT2 correlated term uses a distinct k-RDM-by-Cholesky-factor contraction.Both primitives use the same Cholesky factors and transposable-DAG protocol.Source: D. The non-symmetric AO-Laplace J/K… · p. 6

E. Truncated matrix-product states are not tangent-stationary

A truncated DMRG matrix-product state is not stationary in the full tangent space, so naive reverse-mode gradients can disagree with finite differences. The gauge-free tangent projector imposes working-bond stationarity; analytic gradients and NACMEs are reported at full bond dimension.

E. Truncated matrix-product states are not tangent-stationary

  • A truncated MPS breaks the Hellmann–Feynman condition, making naive reverse-mode gradients disagree with finite differences by an amount that tracks discarded Schmidt weight.The discrepancy vanishes only at full bond.Source: E. Truncated matrix-product states are… · p. 6
  • The gauge-free tangent projector imposes stationarity at the working bond dimension and is locked into the adjoint to address this reproducibility hazard.The adaptively truncated gradient is offered only with an explicit entropy-gated tolerance that preserves stationarity to a stated bound.Source: E. Truncated matrix-product states are… · p. 6
  • Analytic gradients and interstate NACMEs are reported at full bond dimension, where the energy-DAG reverse-mode transpose is exact; truncated bonds are used for excitation energies instead.The derivative regime is feasible to about CAS(12,12), the resident four-particle-RDM ceiling; the truncated-MPS derivative bias is deferred to a companion response formulation.Source: E. Truncated matrix-product states are… · p. 6

F. Excited states: dual-penalty deflation and NACMEs

The excited-state workflow combines penalty deflation with transition-RDM couplings, uses fixed character-selected active spaces for these benchmarks, and applies gradient-aware entanglement compression.

F. Excited states: dual-penalty deflation and NACMEs

  • Dual-penalty deflation lifts wrong-particle-number intruders that can stall excited-state sweeps, while spin purity is selected and checked through per-root ⟨S²⟩ values.An S²-only penalty fixes ⟨S_z⟩ but not particle number; the dual penalties leave target-sector energies unchanged and prevent already converged states from regressing.Source: F. Excited states: dual-penalty… · p. 6

G. Active-space selection

  • The benchmarks use a fixed, hand-chosen π(+n)-valence CAS to isolate excitation physics from active-space-selection artifacts; automated entropy-based selection remains future work.A ground-state entropy cut can discard excitation-relevant carbonyl lone pairs, and AVAS cannot directly select the device active space in its Cartesian-AO workflow.Source: G. Active-space selection · p. 7

H. Cholesky decomposition for the wavefunction: compression and its cost

  • DMRG compression pairs Schmidt-weight truncation with mutual-information pre-screening, but gradient paths require a hard density-force conservation gate and transition-RDM/NACME terms cannot use single-state pruning.The matrix-product-operator avoids forming the dense operator, and the method streams never-materialized, MI-block-sparse higher RDMs.Source: H. Cholesky decomposition for the… · p. 7

III. COMPUTATIONAL DETAILS

The device-resident calculations validate the DMRG reference and derivative machinery, then show a corrected ethene conical intersection and character-dependent excitation-energy accuracy. The results include the coupling behavior at the crossing and the remaining errors associated with compact active spaces.

III. COMPUTATIONAL DETAILS

  • The device workflow keeps the DMRG sweep, RDMs, QD-SC-NEVPT2 correction, and response resident on one 8 GB RTX 4060, with setup as host preprocessing outside the derivative hot path.The contraction-DAG arena uses a liveness-optimal peak-memory schedule; repeat-compute caching makes the Cholesky build 2–4× faster with bit-identical factors.Source: §III · pp. 7–8

A. The engine reproduces FCI-in-active-space, and the GPU precision is inert

  • Device DMRG reproduces active-space FCI energies to ∼10^-15 Ha, while the FP32-CD versus FP64-CD excitation-energy spread stays below ∼10^-5 eV in the reported tests.The spreads are 2.7 × 10^-6 eV for ethene, 4.7 × 10^-7 eV for butadiene, and 8.3 × 10^-6 eV for formaldehyde; the analytic gradient and NACME closure is validated to the finite-difference floor on ethene V and butadiene 11Bu.Source: A. The engine reproduces… · p. 9, Table I · p. 10

B. What multireference buys: ethene energetics and the doubly-excited state

  • DMRG isolates the butadiene and hexatriene 21Ag doubly-excited states by character, with >50% doubly-excited weight, and reproduces them as active-space FCI.The active space can be enlarged, unlike the compact hh-TDA frontier manifold described in the passage.Source: B. What multireference buys: ethene… · p. 9
  • The minimal CAS(2,2) omits σ–π dynamic polarization and yields only a covalent-diradical touching, whereas the physical ethylene MECI is a covalent/ionic crossing.The ionic state is mixed with Rydberg character and requires diffuse functions for correct placement.Source: B. What multireference buys: ethene… · pp. 9, 11
  • At ethene torsion 90° and pyramidalization ϕ = 90°, the corrected S0/S1 gap reaches 19 meV at the resolved conical intersection, with non-vanishing, 1/ΔE-divergent interstate coupling.The crossing is a covalent/ionic MECI; adiabatic LR-TDDFT gives τ ≡ 0.Source: Figure 3 · p. 10, B. What multireference buys: ethene… · p. 11
  • The character-balanced class-macro MAD is 0.44 eV [95% bootstrap CI 0.36–0.54], while ionic ππ* states have MAD 0.21 eV and covalent doubly-excited 21Ag states have MAD 0.64 eV.The residual errors concentrate in diatomic-valence and covalent doubly-excited states; the reported set is untrimmed.Source: Figure 4 · p. 11

C. The QUEST comparison, character-resolved, with a grouped-CV calibration

The QUEST comparison finds small but character-dependent excitation-energy errors, and the grouped cross-validation calibrates that residual across molecules. Spectral comparisons and the hexatriene example show how accuracy depends on state character, basis, and active-space scope.

Character-resolved errors

  • Ionic ππ* and nπ* states are most accurate, while diatomic-valence and covalent-double 21Ag states carry the largest residuals; QD correction restores the 21Ag/11Bu ordering.The class-macro MAD is 0.44 eV, and octatetraene's corrected gap is +0.75 eV versus −1.08 eV for the bare active space.Source: C. The QUEST comparison,… · p. 12

Diatomic protocol

  • The reported N2 states are limited to those representable in the π-only active space; target roots are matched by symmetry term rather than energy order.The valence σg/σ*u state falls outside that space, while dense active-space diagonalization handles N2/CO degenerate CI steps without changing reported quantities.Source: C. The QUEST comparison,… · p. 12

Basis dependence

  • At def2-TZVP, nπ* errors improve from 0.33 to 0.23 eV, while ionic ππ* errors reverse sign as the larger basis recovers more σ–π polarization.The covalent 21Ag error is nearly basis-insensitive; ethene's def2-TZVP value is caveated because its V state may mix with a 3s Rydberg orbital.Source: C. The QUEST comparison,… · pp. 12–13

Hexatriene example

  • Hexatriene's 21Ag state has no dominant configuration: about 22 determinants carry 90% of its weight, and its excitation energies lie within 0.3 eV of QUEST estimates.The leading determinant weight is 0.12 for 21Ag versus 0.82 for S0; DMRG reaches active-space FCI at χ = 64.Source: C. The QUEST comparison,… · p. 13, Figure 5 · p. 14

Grouped-CV calibration

  • 0.47 eV class-macro MAD (95% bootstrap CI 0.37–0.58) calibrates the error across 31 states of eighteen molecules using molecule-blocked cross-validation.The estimate is stable at 0.43–0.50 eV when leaving out any single molecule; residuals concentrate in diatomic-valence and covalent-double states.Source: C. The QUEST comparison,… · p. 13

Experimental spectra

  • Benzene's three calculated π→π* energies track experimental band maxima, while symmetry reproduces the observed weak/weak/strong intensity ordering.For ammonia, diffuse-basis calculations bracket the 194 nm band maximum; the 3s Rydberg assignment requires diffuse functions.Source: C. The QUEST comparison,… · p. 13

QUEST comparison

  • 0.41 eV mean absolute deviation across 31 singlet valence states of eighteen molecules at cc-pVDZ; def2-TZVP gives 0.30 eV for 22 available states.On the same 22-state subset, the cc-pVDZ MAD is 0.39 eV.Source: C. The QUEST comparison,… · p. 11, Table II · p. 15

Scope and coverage

  • The fixed π(+n)-valence active space omits some states and limits the comparison: several def2-TZVP entries were unavailable because of host-memory or convergence limits.The pyrazine bright 1La state is not tabulated because it is blue-shifted to about 8.8 eV in this feasible active space.Source: C. The QUEST comparison,… · p. 13, Table II · p. 15

D. Nonadiabatic couplings: ammonia photodissociation at the multireference level

The ammonia calculation follows the n→σ* dissociation coordinate with a multireference active space that tracks a Rydberg-to-valence state change. Its corrected surfaces meet at a conical intersection with a nonzero, divergent coupling, unlike adiabatic LR-TDDFT/TDA.

Active space

  • CAS(4, 4) includes the N lone pair, dissociating-bond σ and σ*, and nitrogen 3s orbital to track S1 from Rydberg to valence character.Omitting 3s still yields the valence intersection and seam NACME, but misplaces near-equilibrium Rydberg character.Source: D. Nonadiabatic couplings: ammonia… · p. 16

Intersection and coupling

Scope

  • The result demonstrates derivative-level coupling capability, while absolute energetics retain dynamic σ–π correlation and basis-completeness residuals at the fixed valence active space.The paper frames its contribution as qualitatively correct strongly correlated surfaces and couplings, rather than benchmark vertical accuracy.Source: D. Nonadiabatic couplings: ammonia… · p. 17

E. Performance: the exact repeat-compute cache and the QUEST reference basis

The device implementation reduces integral-build cost and keeps analytic derivatives and dynamic-correlation corrections within a consumer GPU’s memory and throughput limits. Exact caching, contraction fusion, and physics-guided precision placement support the resulting performance.

E. Performance: the exact repeat-compute cache and the QUEST reference basis

  • The exact Cholesky cache cuts the benzene/aug-cc-pVDZ build from 77.4 to 19.5 s; ethene/aug-cc-pVTZ now finishes in about 3 min instead of exceeding 40 min.The cache reuses raw integral blocks without changing the SCF energy or completeness-preserving screening.Source: E. Performance: the exact… · p. 17
  • Each analytic gradient or interstate NACME is one reverse-mode transpose of the energy graph, delivered device-resident with O(1) host–device traffic.Finite differencing the 3N-dimensional coupling would require 6N correlated two-state energies per geometry and is ill-defined at the intersection.Source: E. Performance: the exact… · pp. 17–18
  • Fusing the all-active two-electron block into the ket avoids materializing the 4-RDM, keeping CAS(10,10) below 8 GB versus 12.6 GB for the dense path.The fused result agrees with the dense result to 8.9 × 10^-16.Source: E. Performance: the exact… · p. 18
  • The optimized pipeline reaches a cumulative 8.6× speedup over the original dense-n8 path, with 6.7×10^-16 agreement against the unoptimized result.A batched block reduction lifts the generic contraction from 0.5% to 11–17% of FP64 peak; the full-pipeline rewrite also eliminates redundant Jacobi–Wigner site-apply passes.Source: E. Performance: the exact… · p. 18
  • The porphine CD J/K contraction reaches 5.8 TFLOP/s in FP32, while near-degenerate QD couplings and their transition-density RDMs remain in FP64 for reliability.The FP32 J/K rate is 38% of the FP32 ceiling and 24× the FP64 corner; gradient and NACME kernels reuse the FP32 path with reported force errors inside the geometry-optimization band.Source: E. Performance: the exact… · p. 18

F. Capability capstone: doubly-excited-state internal conversion on the device surface

Device-produced multireference surfaces for hexatriene open an internal-conversion channel through a symmetry-allowed crossing that the single-reference analog does not capture. The authors frame the propagation as a capability demonstration, not a rate benchmark.

F. Capability capstone: doubly-excited-state internal conversion on the device surface

  • At the Franck–Condon geometry, the 21Ag state has 59% double-excitation character, which single-reference surfaces cannot represent as the accepting state mediating this conversion.The paper describes this as a categorical consequence of using a multireference engine.Source: F. Capability capstone:… · pp. 18–19
  • Along the C=C bond-length-alternation coordinate, the more steeply tuned 21Ag diabat drops below 11Bu and crosses it at a symmetry-allowed conical intersection with a 15 meV residual gap.The reported tuning gradients are +1.15 eV for 21Ag and +0.64 eV for 11Bu.Source: F. Capability capstone:… · p. 19
  • The multireference surface transfers 28% of the 11Bu population to 21Ag within 150 fs, versus 0.6% for the single-reference analog.The result is χ-converged, with χ≤24 and χ≤48 agreeing to less than 0.5%.Source: F. Capability capstone:… · p. 19
  • The capstone is a capability demonstration rather than a rate benchmark: the compact-CAS vertical gap is several-fold wider than the near-degenerate experimental gap, and the bounded linear-LVC model is not the full anharmonic surface.The reported absolute rate is gap-limited and out of scope.Source: F. Capability capstone:… · p. 19, Figure 10 · p. 20

V. CONCLUSIONS

The paper’s central result is a device-resident DMRG-QD-SC-NEVPT2 derivative pipeline that operates through a real conical intersection within 8 GB. Its scope remains bounded by compact-active-space state-placement errors and the current capability-focused dynamics demonstration.

V. CONCLUSIONS

  • Analytic gradients and interstate NACMEs for DMRG-QD-SC-NEVPT2 are obtained as one reverse-mode transpose of a contraction graph with a gauge-free differentiable DMRG sweep, within 8 GB of consumer-GPU memory.The quasi-degenerate effective Hamiltonian keeps the description valid through a conical intersection.Source: §V · p. 20
  • On compact π-valence active spaces, bright ionic states remain less well placed than dark states; pyrazine 11B2u remains blue-shifted because differential σ–π correlation is carried only by second-order perturbers.The stated next step is to bring σ-polarization inside the active space.Source: §V · pp. 20–21
  • The hexatriene capstone opens a 11Bu → 21Ag conversion channel on the multireference surface, transferring 28% in 150 fs, while the single-reference analog transfers 0.6%.The authors explicitly describe the demonstration as a capability, not a rate benchmark.Source: §V · p. 20, Figure 11 · p. 21
  • The authors identify σ-inclusive, entanglement-tiered active spaces and a full-reference-basis corrected spectrum as next steps, while device timings place trajectory-rate multireference dynamics on commodity hardware within reach.The reported exact-relaxation regime extends to approximately CAS(12,12).Source: §V · p. 21

SUPPLEMENTARY MATERIAL

The Supplementary Material collects validation data, working equations, and implementation details for the electronic-structure and dynamics methods. It also documents the numerically exact in-basis tensor-train propagation used for the internal-conversion capstone.

SUPPLEMENTARY MATERIAL

  • Validation tables cover DMRG=FCI, device=host, and FP32/FP64 spreads, alongside finite-difference gates for the adjoint gradient and NACME transpose rules.The Supplement also gives the ground-inert and excitation-relevant retention analysis and grouped cross-validation protocol.Source: SUPPLEMENTARY MATERIAL · p. 21
  • The supplement provides QD-SC-NEVPT2 working equations and the dual-penalty matrix-product-operator construction, including its provable in-sector nullity.It also lists AutoCAS thresholds and the associated retention analysis.Source: SUPPLEMENTARY MATERIAL · p. 21
  • The internal-conversion capstone uses in-basis tensor-train 2TDVP propagation, with its linear vibronic-coupling model and numerically exact propagation details in the supplement.The propagator and Hamiltonian matrix-product operator are detailed in Sec. S1.Source: SUPPLEMENTARY MATERIAL · p. 21

AUTHOR DECLARATIONS

The authors report no conflicts of interest and describe a data bundle intended to support independent checking of the correctness claims. Performance claims have a separate reproducibility limitation because the tuned kernels are withheld.

Conflict of Interest

DATA AVAILABILITY

  • The validation bundle reproduces every validation-table entry on CPU with PySCF and NumPy, without GPU code.It includes the finite-difference NACME oracle, verification scripts, and detailed derivations, with public release planned upon acceptance.Source: DATA AVAILABILITY · pp. 21–22
  • The tuned CUDA kernels and code generators are proprietary and available from the corresponding author on reasonable request, limiting remeasurement of performance claims.The authors state that correctness claims are unaffected.Source: DATA AVAILABILITY · p. 22
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