Communication: Fitting potential energy surfaces with fundamental invariant neural network

Area of Science:

• Computational chemistry
• Quantum mechanics
• Machine learning

Background:

• Constructing accurate potential energy surfaces (PES) is crucial for molecular simulations.
• Existing methods can be computationally expensive, especially for systems with identical atoms.

Purpose of the Study:

• To develop a more flexible and efficient neural network (NN) method for PES construction.
• To utilize fundamental invariants (FIs) as input for NNs to handle permutation symmetry.

Main Methods:

• Proposed the fundamental invariant neural network (FI-NN) method.
• FIs were used as input vectors for the NN, leveraging their ability to generate permutation invariant polynomial rings.
• Provided FIs for molecular systems up to five atoms.

Main Results:

• FI-NN demonstrated the ability to approximate functions to arbitrary accuracy.
• Successfully constructed PES for OH3 and CH4 systems.
• The accuracy of FI-NN was validated through quantum dynamic scattering and bound state calculations.

Conclusions:

• FI-NN offers an efficient approach for constructing PES, particularly for polyatomic systems with identical atoms.
• The method minimizes input size, reducing potential energy evaluation time.
• FI-NN provides a flexible and accurate tool for computational chemistry research.