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Rh-Enamide

Rh-enamide is the clearest literature-reproduction case in the repo: a complete Rh(I)-diphosphine asymmetric hydrogenation TSFF with 9 training structures.

Scope

  • Type: Transition state (Rh-catalyzed asymmetric hydrogenation)
  • Molecules: 9 TS structures
  • Parameters: 182 (OPT substructure: 8 bonds, 23 angles, 48 torsions)
  • QM reference: B3LYP/LACVP**

Publication

Property Value
Paper Donoghue, P. J. et al. J. Chem. Theory Comput. 2008, 4, 1313–1323
DOI 10.1021/ct800132a
System Rh(I)-diphosphine asymmetric hydrogenation of enamides
Training set 9 transition-state structures
Engine MacroModel MM3*

What the paper fitted and reports

What the original Q2MM workflow fitted

The original Q2MM workflow fit a multi-target penalty function, not just Hessian eigenvalues.1

  • Bond lengths
  • Bond angles
  • Torsions
  • The full Hessian matrix
  • Partial charges
  • Relative energies

The paper reports penalty-function tolerances of 0.01 Å for bonds, 0.5° for angles, 1° for torsions, and 0.02 e for charges, with Newton-Raphson plus Simplex refinement inside MacroModel MM3*.1

The authors also describe two fitted variants:

  • RhH — the standard fit
  • RhH-E — an energy-emphasized fit

What the paper reports

Donoghue et al. report strong structural and energetic agreement between QM and MM for the fitted force field.1

  • Bond RMSD: ≤ 0.03 Å (Table 5)
  • Angle RMSD: < 2° (Table 6)
  • Relative-energy RMSD: 0.3–0.5 kcal/mol (Table 7)
  • External selectivity validation: MUE = 0.6 kcal/mol across 18 test points

The 2008 paper does not report an eigenvalue R² directly. It reports structural and energetic agreement (bond RMSD, angle RMSD, relative-energy RMSD).

Our reproduction

Metric Value
Overall eigenvalue R² 0.991
Overall slope 0.986
Aggregate frequency RMSD 259.9 cm⁻¹ (per-molecule avg: 85.5)

Our analytical QFUERZA starting point reproduces 99.1% of the variance in the QM eigenspectrum (R² = 0.991) with slopes near 1.0 across all 9 transition states, without any iterative optimization.

TS Atoms Eig R² Slope Freq RMSD
1 36 0.990 1.000 93.9
2 38 0.995 0.986 86.0
3 38 0.993 0.987 87.1
4 62 0.985 0.975 97.5
5 62 0.985 0.975 98.2
6 58 0.994 0.989 76.6
7 58 0.993 0.989 76.3
8 58 0.994 0.990 77.2
9 58 0.993 0.989 76.9

Benchmark results

Multi-target objective

Eigenmatrix-diagonal + geometry refs, 182 frozen-scoped active params, invert_ts_curvature=True, SciPy L-BFGS-B with JaxLoss analytical gradients on RTX 5090 GPU:

Metric Value
Ratio check 1.07 (pass)
Initial score 4.86 × 10⁵
Final score 2.71 × 10⁵
Reduction 44.66 % (vs ~0.6 % per-call ObjectiveFunction noise floor — 77× above noise)
Iterations (L-BFGS-B nit) 15
ObjectiveFunction evaluations 2
Gradient source jac="auto" resolved to jac_mode="jax_loss" (JaxLoss analytical)
Wall time 739 s (12 min)

Per-category fit of the optimized force field (post-L-BFGS-B):

Category n_refs R²
bond_length 500 0.989
bond_angle 1,050 0.954
eig_diagonal 1,395 0.968

These numbers are from the published-start baseline. Reproduce with scripts/regenerate_convergence_results.py --starting-point published; raw JSON output with provenance lives at q2mm-data/benchmarks/rh-enamide/from-published/. The canonical QFUERZA-start results (current default since q2mm#290) live at convergence/ and are summarized in the QFUERZA-recovery doc.

The ratio check confirms JaxLoss is a reliable surrogate for this system — the published Donoghue OPT values reproduce QM geometry well so unconstrained geometry relaxation finds the correct local minima. A 44.66 % real-objective improvement against the published starting point — a 77× ratio over the per-call ObjectiveFunction noise floor of ~0.6 % (see "Noise floor caveat" below) — is the largest reduction of any published-FF system in the suite (the published values are good but leave meaningful headroom under the q2mm JAX engine's eigenmatrix-diagonal objective).

Noise floor caveat

Repeated GPU ObjectiveFunction(x0) calls on rh-enamide vary by ~0.6 % across calls (5-call IQR / median). Root cause traced to a combination of scipy L-BFGS-B Fortran internal state and MM3 non-smooth points; see #284 for the full diagnosis. The 44.66 % reduction reported here is 77× the per-call noise band and therefore robust — single-call measurements at this magnitude are scientifically reliable.

Historical frequency-only results

Different objective

Earlier benchmarks used a frequency-only objective with all ~2,742 FF parameters (not the paper's multi-target penalty with 182 OPT-substructure params). These numbers remain useful for optimizer comparison on that specific task, but do not represent literature reproduction.

Under the frequency-only objective, JaxOpt L-BFGS lowered frequency RMSD from 259.9 to 187.7 cm⁻¹ and Optax Adam+cosine reached 199.5 cm⁻¹ — but optimizer improvement on frequency RMSD can trade away eigenspectrum quality (Adam+cosine dropped to R² = 0.843 even as RMSD improved).2

Comparison and gap analysis

Comparison

  • QFUERZA reaches R² = 0.991 with slopes near 1.0 across all 9 TS structures.
  • The 2008 paper does not report eigenvalue R², so a direct comparison is not possible.
  • The original force field was optimized for MacroModel MM3*; our reproduction uses a different engine (JAX). Cross-engine functional-form differences account for any remaining gap.

What q2mm demonstrates

QFUERZA reaches R² = 0.991 in seconds without iteration. The original Q2MM workflow required hours of gradient optimization in MacroModel to reach its final fit.3

The multi-target optimization pipeline runs end-to-end on this 9-molecule system (per-molecule JIT compilation, scipy L-BFGS-B with JaxLoss analytical gradients) and lowers the real ObjectiveFunction by 44.66 % against the published Donoghue OPT starting point (4.86 × 10⁵ → 2.71 × 10⁵ in 15 L-BFGS-B iterations). An earlier baseline reported a 28.68 % reduction; that result depended on an FF whose Donoghue OPT values had been overwritten by QFUERZA. The current loader API preserves the published OPT values, so the optimizer starts from a better point and still finds meaningful headroom.

Gap analysis

To improve further:

  1. Type-normalized penalties — divide each data type's contribution by its count, matching the upstream Q2MM weighting. This is the most impactful change for convergence.
  2. Closer MacroModel MM3* parity — especially any remaining metal-center functional details that do not transfer cleanly to our engine.
  3. Off-diagonal eigenmatrix elements — the current objective uses diagonal-only; the papers use the full lower triangle (weight 0.05).

Reproduce

Configure Q2MM_RH_ENAMIDE as described in External data for published systems before running this command.

# Multi-target (correct methodology)
python -m q2mm.diagnostics.cli --system rh-enamide --backend jax --optimizer scipy-lbfgsb

Raw data: q2mm-data/benchmarks/ → rh-enamide/.

  1. Donoghue, P. J. et al. J. Chem. Theory Comput. 2008, 4, 1313–1323. DOI: 10.1021/ct800132a ↩↩↩

  2. See the later Q2MM/QFUERZA literature discussion in QFUERZA Validation. ↩

  3. QFUERZA Validation summarizes why the analytical start is valuable even before iterative optimization. ↩