Molecular Hessian matrices from a machine learning random forest regression algorithm

Area of Science:

• Computational chemistry
• Machine learning in quantum chemistry

Background:

• Calculating molecular Hessians is computationally intensive.
• Accurate Hessians are crucial for understanding molecular vibrations and energies.

Purpose of the Study:

• To develop a fast and accurate machine learning model for molecular Hessian estimation.
• To enable efficient prediction of vibrational frequencies, normal modes, and zero-point energies.

Main Methods:

• A random forest-based machine learning model was employed.
• The model learns second derivatives of energy with respect to internal coordinates.
• Rotational and translational invariance is ensured through coordinate representation.

Main Results:

• The model provides fast and accurate Hessian estimates.
• It was trained on QM7 data and validated on QM9 molecules.
• Reasonable predictions of vibrational frequencies, normal modes, and ZPEs were achieved.

Conclusions:

• Machine learning offers an efficient alternative for Hessian calculations.
• The developed model shows promise for larger molecular systems.
• This method can accelerate computational chemistry workflows.