Benchmarks

Comprehensive comparison of sci-form against RDKit, the gold standard for 3D molecular conformer generation.

Methodology

All comparisons use heavy-atom pairwise-distance RMSD — the root-mean-square deviation of all pairwise distances between non-hydrogen atoms. This metric is alignment-free (no superposition needed) and focuses on the chemically important scaffold geometry.

$${\text{RMSD}}_{\text{pairwise}}=\sqrt{\frac{1}{|\mathcal{P}|}\sum _{(i,j)\in \mathcal{P}}(d_{ij}^{\text{sci-form}}-d_{ij}^{\text{RDKit}}{)}^2}$$

where $\mathcal{P}$ is the set of all heavy-atom pairs.

Diverse Molecule Benchmark

131 curated molecules spanning 27 chemical categories, from simple alkanes to macrocycles and metal-containing compounds.

Overall Results

Metric	Value
Total molecules	131
Parse success	100%
Embed success	97.7% (128/131)
Geometry quality	97.7%
Throughput	60 mol/s

Per-Category Results

Embed Failures

Only 3 molecules fail to embed (out of 131):

Molecule	Category	Reason
Pyrene	polycyclic	4-ring fused polyaromatic
Cubane	strained	Extreme 90° angles in 4-rings
Fluoranthene	polycyclic	Fused 5-6-6-5 ring system

These are well-known hard cases for distance geometry due to their extreme geometric constraints.

RDKit Comparison

Heavy-atom pairwise-distance RMSD between sci-form and RDKit conformers. Multi-seed ensemble comparison (5 seeds per molecule, minimum RMSD reported).

Overall Results

Metric	Value
Average RMSD	0.064 Å
Median RMSD	0.011 Å
< 0.1 Å	82.8%
< 0.3 Å	94.4%
< 0.5 Å	98.4%
< 1.0 Å	100%

RMSD Distribution

Hardest Categories

Category	Avg RMSD	Description
silicon	0.543 Å	Si atom typing differences
selenium	0.507 Å	Se parameter approximations
strained	0.182 Å	Cubane, cyclopropane
polycyclic	0.112 Å	Fused aromatic systems

GDB-20 Ensemble Comparison

Large-scale validation on 500 molecules from the GDB-20 database (molecules with up to 20 heavy atoms), using an ensemble of 5 sci-form seeds compared against 21 RDKit seeds. The minimum RMSD across all seed combinations is reported.

Results

Metric	All-atom	Heavy-atom
Embed success	100%	100%
Average min-RMSD	0.063 Å	0.024 Å
> 0.1 Å	13.00%	9.20%
> 0.3 Å	6.80%	1.00%
> 0.5 Å	1.60%	0.00%
> 0.7 Å	0.00%	0.00%

min-RMSD Distribution (all atoms)

Range	Count	Share
0.00–0.05 Å	419	83.80%
0.05–0.10 Å	16	3.20%
0.10–0.20 Å	16	3.20%
0.20–0.30 Å	15	3.00%
0.30–0.50 Å	26	5.20%
0.50–0.70 Å	8	1.60%
> 0.70 Å	0	0.00%

Ensemble Rescue Rate

Of molecules with single-seed RMSD > 0.5 Å, the multi-seed ensemble rescued 88.4% (61/69) to below 0.5 Å. Only 8 molecules remain above the threshold after ensemble selection.

ChemBL 10K Benchmark

Stress test on 10,000 molecules from the ChemBL database with practical pharmaceutical relevance (up to 100 atoms).

Metric	Value
Parse success	100%
Embed success	97.54%
Geometry quality	97.18%
Throughput	2.1 mol/s

Lower throughput is expected for larger molecules due to $O(N^3)$ scaling of Floyd-Warshall and eigendecomposition.

Performance Scaling

The dominant cost is the Floyd-Warshall triangle smoothing ($O(N^3)$) and the BFGS optimization (each iteration is $O(N^2)$ for the inverse Hessian update).

Property Calculation Performance

Conformer Generation

Dataset	Molecules	Success	Throughput
Diverse (131 molecules)	131	97.7%	60 mol/s
ChemBL 10K	10,000	97.5%	2.1 mol/s
GDB-20 (500 sample)	500	100%	~50 mol/s

Single-seed mode, no ensemble. Throughput measured on consumer hardware (8-core).

Electronic Structure (EHT)

Molecule	Atoms	Basis Functions	Time
H₂O	3	5	< 1 ms
Benzene	12	18	< 2 ms
Naphthalene	18	28	< 5 ms
Drug-like (~30 heavy)	~40	~60	~10 ms

EHT cost scales as $O(N_{\text{AO}}^3)$ for diagonalization. The STO-3G minimal basis keeps $N_{\text{AO}}$ small even for medium molecules.

ESP Grid

Grid Resolution	Spacing	Typical Size	Time
Coarse	1.0 Å	10³ grid	< 5 ms
Standard	0.5 Å	20³ grid	~20 ms
Fine	0.2 Å	50³ grid	~300 ms

ESP evaluation is $O(N_{\text{atoms}}\times N_{\text{grid}})$. The parallel evaluator (compute_esp_grid_parallel) gives near-linear speedup on multi-core systems.

Complete Property Pipeline (single molecule)

Full pipeline (embed + charges + EHT + ESP + DOS + SASA + dipole) on a drug-like molecule (~30 heavy atoms):

Step	Time
Conformer generation	~10 ms
Gasteiger charges	< 1 ms
EHT calculation	~5 ms
ESP grid (0.5 Å)	~20 ms
DOS computation	< 1 ms
SASA	< 1 ms
Dipole	< 1 ms
Total	~38 ms

Experimental Quantum Engine Benchmarks

The isolated experimental_2 stack adds a Roothaan-Hall RHF/STO-3G implementation with explicit two-electron integrals and rayon-parallel ERI construction.

Regression Coverage

Suite	Scope	Result
test_experimental_comparison	SCF correctness, legacy-vs-experimental comparison, NIST references, spectroscopy smoke checks	54 passed, 0 failed
test_extended_molecules	Complex molecules, NMR/IR/UV-Vis reference checks, ML properties, drug-like molecules	14 passed, 0 failed, 7 ignored

Parallel ERI Speedups

Observed on an Intel i5-10500H (12 logical cores):

System size	Typical behavior
Small systems (< 15 basis functions)	~0.8–1.1×, parallel overhead dominates
Benzene (~36 basis functions)	~3–5× speedup
Pyridine (~42 basis functions)	~4–6× speedup

The heavy speedup tables are intentionally marked #[ignore] in debug-mode regression runs because explicit ERIs scale as $O(N^4)$ and distort CI time on larger aromatic systems. Run them in release mode:

cargo test --release --test regression test_extended_molecules -- --include-ignored

Interpretation

• The current acceleration path is CPU-only via rayon
• GPU execution is planned, but the current phase1_gpu_infrastructure backend is still a CPU fallback with WGSL-ready interfaces
• The experimental engine is best viewed today as a validated research track rather than the default production quantum backend