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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 1.05 (pass)
Initial score 3.92 × 10⁵
Final score 2.80 × 10⁵
Reduction 28.68 %
Iterations (L-BFGS-B nit) 6
ObjectiveFunction evaluations 2 (initial + final re-evaluation; JaxLoss calls scipy via the surrogate, not via ObjectiveFunction)
Gradient source jac="auto" resolved to jac_mode="jax_loss" (JaxLoss analytical)
Wall time ~11 min (including per-molecule JIT)

These numbers are reproducible from scripts/regenerate_convergence_results.py (no --skip-optimization); raw JSON output with provenance lives at q2mm-data/benchmarks/rh-enamide/convergence/.

The ratio check confirms JaxLoss is a reliable surrogate for this system — the Seminario starting FF is good enough (R² > 0.93 in every category) that unconstrained geometry relaxation finds the correct local minima.

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 achieves 28.68 % loss reduction.

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

# 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. ↩