Computation module

Predicting vibrational spectra

How a spectrum is computed sets the accuracy you can expect and the data you can generate. This module covers the theory from the harmonic approximation to anharmonic corrections, and the practical pipeline that produces labelled spectra at scale for the AI program.

From geometry to spectrum

Frequencies come from the mass-weighted Hessian (second derivatives of energy) at an optimised stationary point; intensities come from how the dipole changes along each normal mode (the double-harmonic approximation).

optimise → Hessian ∂²E/∂qi∂qj → diagonalise → {ν̄k} · Ik ∝ |∂μ⃗/∂Qk|²

Harmonic vs anharmonic

LevelCostAccuracy & use
Harmonic + scalinglow–moderateSystematically ~3–5% high; a single empirical scaling factor (~0.96–0.98, method-specific) corrects most of it. Fine for group frequencies and dataset generation.
VPT2 (anharmonic)highSecond-order perturbation theory on a quartic field. Recovers overtones, combination/Fermi bands, and accurate X–H stretches; needed where the fingerprint must match measurement.
VSCF / VCIvery highVariational; for strongly anharmonic/coupled systems and benchmark accuracy on small molecules.
AIMD / VACFhighSpectrum from the dipole autocorrelation of a trajectory — captures temperature, anharmonicity and explicit environment without normal modes.

Scaling-factor discipline

A scaling factor is tied to a specific method/basis and to whether you are fitting fundamentals, ZPE or low-frequency modes. Never transfer one across methods. Report the factor and its source (e.g. the NIST CCCBDB tables); for the fingerprint region a single global factor is a crude fix — anharmonic treatment or region-specific scaling is better.

Environment matters

Gas-phase frequencies can sit tens of cm⁻¹ from condensed-phase values. Continuum solvent shifts polar modes; explicit hydrogen-bond partners are essential for O–H/N–H stretches and for any noncovalent-interaction study. Matching a computed spectrum to a measured one without modelling the environment is a common and avoidable error.

The pipeline used here

The platform generates spectra with GFN2-xTB — a semi-empirical tight-binding method fast enough to run thousands of molecules, while capturing the trends that supervised learning needs. Each structure becomes a fixed-length, automatically-labelled vector:

1. build structure (SMILES → 3D) 2. optimise + Hessian → peak list (ν̄i, Ii) [GFN2-xTB] 3. Lorentzian broaden (FWHM ~20 cm⁻¹) 4. resample → 181-pt vector over [400, 4000] cm⁻¹ 5. auto-label substructures by SMARTS → training pair
ChoiceValueRationale
MethodGFN2-xTBThroughput for dataset-scale generation; consistent systematic error is learnable.
Range / bins400–4000, 20 cm⁻¹181 points; covers fingerprint + functional regions at a tractable width.
BroadeningLorentzianPhysical lineshape for vibrational dephasing; FWHM tunable.
LabelsRDKit SMARTSDeterministic, leak-free functional-group ground truth.

Why this is the keystone

Measured reference libraries are finite and inconsistently conditioned. A computational generator yields arbitrarily large, perfectly-labelled datasets — the prerequisite for training models on the fingerprint region. The trade-off is a method-dependent systematic offset, which models can absorb provided train and test share the same generator. Results: see the fingerprint program.

Open the on-site spectrum simulator →

References

  1. Scott, A. P. & Radom, L. Harmonic vibrational frequencies: scaling factors, J. Phys. Chem. (1996).
  2. Barone, V. Anharmonic vibrational properties by a fully automated second-order perturbative approach (VPT2), J. Chem. Phys. (2005).
  3. Bannwarth, C., Ehlert, S. & Grimme, S. GFN2-xTB, J. Chem. Theory Comput. (2019).
  4. NIST Computational Chemistry Comparison and Benchmark Database (CCCBDB) — scaling-factor tables.