Permutation invariant polynomial neural network approach to fitting potential energy surfaces. II. Four-atom systems

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Machine Learning

Background:

• Accurate potential energy surfaces (PESs) are crucial for understanding chemical reactions.
• Traditional methods for fitting PESs can be computationally intensive and complex.
• Incorporating molecular symmetries is essential for robust PES fitting.

Purpose of the Study:

• To introduce a general, simple, and rigorous method for fitting permutation invariant PESs using neural networks (NNs).
• To demonstrate the effectiveness of the permutation invariant polynomial neural network (PIP-NN) method for reactive systems.

Main Methods:

• Developed a PIP-NN method that enforces permutation symmetry using symmetry functions based on permutation invariant polynomials (PIPs).
• Determined that for systems with more than three atoms, the number of symmetry functions must exceed internal coordinates to capture primary and secondary invariant polynomials.
• Applied the PIP-NN method to three-atom triatomic reactive systems.

Main Results:

• Successfully generated full-dimensional global PESs for triatomic reactive systems.
• Achieved average errors on the order of meV, demonstrating high accuracy.
• The fitted PESs were utilized in full-dimensional quantum dynamical calculations.

Conclusions:

• The PIP-NN method provides an effective and generalizable approach for constructing accurate, symmetry-adapted PESs.
• This method facilitates high-fidelity quantum dynamical simulations of chemical processes.
• The PIP-NN approach represents a significant advancement in computational chemistry for molecular dynamics.