Molecular Vibration Analysis Skill

Goal

Calculate the vibrational frequencies ($\nu$), normal modes, and zero-point energy (ZPE) of non-periodic (finite) systems — molecules, clusters, and adsorbates — within the harmonic approximation using Machine Learning Interatomic Potentials (MLIPs).

[!IMPORTANT] This skill is for molecules and finite systems only. For periodic crystals, use the phonon skill instead.

Background

In the harmonic approximation, the potential energy surface near a local minimum is approximated as $V \approx V_0 + \frac{1}{2} \sum_{ij} H_{ij} \Delta r_i \Delta r_j$, where $H_{ij} = \frac{\partial^2 V}{\partial r_i \partial r_j}$ is the Hessian (force constant) matrix. Diagonalizing the mass-weighted Hessian yields $3N$ eigenvalues: for a nonlinear molecule, $3N-6$ are real vibrational modes (and $3N-5$ for linear molecules), while the remaining eigenvalues correspond to translational and rotational degrees of freedom (near zero).

1. Prerequisites

• An MLIP wrapper must be available (MACEWrapper, MatGLWrapper, or FAIRCHEMWrapper).
• ASE must be installed in the relevant conda environment.
• The input structure must be a molecule or cluster (non-periodic). Periodic systems should use mat-phonon.

2. Choosing a Foundation Potential

[!IMPORTANT]

• Use OMAT or MatPES trained models (e.g., MACE-OMAT-0-small). These are optimized for forces and give reliable Hessians.
• The harmonic approximation requires a well-converged equilibrium geometry. Always relax with tight force tolerance (fmax ≤ 0.001 eV/Å) before computing vibrations.

Refer to the foundation-potentials skill for details.

3. Calculation Workflow

Step 1: Prepare a molecule

Use ASE's built-in molecule database or provide a structure file:

# Built-in molecules: H2O, CO2, CH4, NH3, CH3OH, C2H6, etc.
# Or provide a .xyz / .cif / POSCAR file

Step 2: Run vibration analysis

# Env: mace-agent
python .agents/skills/chem-vibration/scripts/calculate_vibrations.py \
    --molecule H2O \
    --model_type mace \
    --model_name MACE-OMAT-0-small \
    --output_dir research/my_folder/vibrations

With a structure file instead:

# Env: mace-agent
python .agents/skills/chem-vibration/scripts/calculate_vibrations.py \
    --structure path/to/molecule.xyz \
    --model_type mace \
    --model_name MACE-OMAT-0-small \
    --no_relax \
    --output_dir research/my_folder/vibrations

Key Parameters:

• --molecule: ASE built-in molecule name (e.g., H2O, CO2, CH4)
• --structure: Path to structure file (alternative to --molecule)
• --delta: Finite-difference displacement in Å (default: 0.01)
• --nfree: Number of displacements per degree of freedom, 2 or 4 (default: 2)
• --relax / --no_relax: Whether to relax before vibration analysis (default: relax)
• --fmax: Force convergence for relaxation (default: 0.001 eV/Å)

4. Output Files

• vibration_results.json: Summary including:
  • frequencies_cm1: All frequencies in cm⁻¹
  • frequencies_meV: All frequencies in meV
  • real_modes: Indices and frequencies of real vibrational modes
  • imaginary_modes: Indices and frequencies of imaginary modes (should be near zero)
  • zero_point_energy_eV: Zero-point energy in eV
  • n_atoms, formula, is_linear
• vib.N.traj: Trajectory files for each vibrational mode (for visualization)

5. Examples

See examples/H2O/ for a water molecule vibration analysis.

# Env: mace-agent
python .agents/skills/chem-vibration/scripts/calculate_vibrations.py \
    --molecule H2O \
    --model_type mace \
    --model_name MACE-OMAT-0-small \
    --output_dir .agents/skills/chem-vibration/examples/H2O

Expected H2O vibrational modes (experimental reference):

Mode	Type	Experimental (cm⁻¹)
Bending	ν₂	~1595
Symmetric stretch	ν₁	~3657
Asymmetric stretch	ν₃	~3756

6. Constraints

• Molecule/cluster only: This skill applies the harmonic approximation to finite systems. For periodic crystals, use mat-phonon.
• Equilibrium required: The structure MUST be at a local minimum (forces ≈ 0). Large residual forces invalidate the harmonic approximation.
• Harmonic approximation: Only valid near equilibrium. Accuracy degrades for large-amplitude motions and near dissociation.
• Environments: Scripts require conda environments with MLIP packages:
  • mace-agent for MACE models
  • matgl-agent for MatGL/CHGNet models
  • fairchem-agent for FairChem/UMA models

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Author: Bowen Deng Contact: GitHub @learningmatter-mit