Molecular Structure Eval

molecular-structure-eval

Accurate and Efficient Quantum Computations of Molecular Properties Using Daubechies Wavelet Molecular Orbitals: A Benchmark Study against Experimental Data — Hong et al. (2022) (arXiv:2205.14476, 2022)

What this evaluates

Evaluates the accuracy of quantum chemistry methods in predicting equilibrium molecular geometries and vibrational properties against experimental benchmarks. It probes the ability of different basis sets and ansatzes to capture electron correlation and potential energy surface curvature.

Datasets

• Small Molecule Benchmark (H2, LiH, BeH2, H2O) — total 4; splits: test (4)

Metrics

• vibrational_frequency_error_pct (primary) — range: percent
  • Percentage error of the calculated vibrational frequency (ω) relative to the experimental value: |ω_calc - ω_exp| / ω_exp × 100%. Lower is better.
• nonparallelity_error_mhatree — range: other
  • Nonparallelity error (NPE) measured in milli-Hartree. Defined as the absolute difference between the maximum and minimum errors relative to a reference potential energy curve across the sampled geometry range.
• bond_length_error_ang — range: other
  • Absolute difference between the calculated equilibrium bond length and the experimental value, measured in Angstroms (Å).

Input / output format

Input: Molecular composition and initial geometry parameters; basis set specification (e.g., Daubechies wavelet, STO-3G, cc-pVDZ) and solver method (UCCSD, FCI).

Output: Calculated equilibrium bond length (Å), vibrational frequency (cm⁻¹), bond angle (°), and potential energy curve data points.

Scoring recipe

def compute_metrics(pred, gold):
    freq_err = abs(pred['vib_freq'] - gold['exp_freq']) / gold['exp_freq'] * 100
    bond_err = abs(pred['bond_len'] - gold['exp_len'])
    angle_err = abs(pred['angle'] - gold['exp_angle'])
    pec_errs = [e - ref for e, ref in zip(pred['pec'], gold['ref_pec'])]
    npe = abs(max(pec_errs) - min(pec_errs))
    return {'freq_err_pct': freq_err, 'bond_err_ang': bond_err, 'angle_err_deg': angle_err, 'npe_mhatree': npe}

Common pitfalls

• Vibrational frequency is highly sensitive to basis set quality and potential energy surface curvature near the minimum; small geometry perturbations can cause large frequency errors.
• Bond length alone is not a reliable indicator of method accuracy, as methods can yield correct bond lengths but incorrect curvatures (frequencies).
• NPE depends heavily on the reference curve choice (here cc-pVTZ/FCI); changing the reference changes the metric value.

Evidence (verbatim from paper)

Note that we choose to focus on the bond length and vibrational frequency because they are measurable molecular properties of which accurate experimental data are available... The error is defined as the absolute energy difference with respect to the ground-state energy value from the exact diagonalization (FCI) in the largest affordable Gaussian basis set of cc-PVTZ... Nonparallelity error (NPE), defined as the absolute difference between the maximum and minimal errors with respect to a reference on a given potential energy surface, could be another accuracy metric to describe the full potential energy curve properties.

Citation

@misc{hong2022daubechies,
  title={Accurate and Efficient Quantum Computations of Molecular Properties Using Daubechies Wavelet Molecular Orbitals: A Benchmark Study against Experimental Data},
  author={Hong et al. (2022)},
  year={2022},
  note={arXiv:2205.14476}
}

• arXiv: 2205.14476