A new permutation-symmetry-adapted machine learning diabatization procedure and its application in MgH₂ system

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Machine Learning in Chemistry

Background:

• Accurate potential energy surfaces are essential for understanding chemical dynamics.
• Diabatization methods are crucial for describing non-adiabatic processes, especially near conical intersections.
• Existing methods often struggle with global accuracy and computational efficiency.

Purpose of the Study:

• To develop a novel machine learning approach for constructing global diabatic potential energy matrices (DPEMs).
• To apply this method to the MgH2 system, generating the first global DPEMs.
• To validate the accuracy of the generated DPEMs through spectroscopic calculations.

Main Methods:

• Introduced the diabatization by equivariant neural network (DENN), a permutation-symmetry-adapted machine learning procedure.
• Simultaneously modeled permutation symmetric and anti-symmetric elements of DPEMs using equivariant neural networks.
• Incorporated non-zero diabatic coupling within a deep neural network framework for enhanced accuracy near degeneracies.

Main Results:

• Successfully constructed global DPEMs for the 1¹A' and 2¹A' states of MgH2.
• Achieved low root-mean-square errors (RMSEs) for diagonal (5.824, 5.307 meV) and off-diagonal (5.796 meV) elements near conical intersections.
• Spectroscopic calculations showed excellent agreement with experimental and theoretical data, with frequency differences within 1.38 cm⁻¹.

Conclusions:

• The DENN method provides accurate and efficient global DPEMs for molecular systems.
• The generated MgH2 DPEMs represent a significant advancement for theoretical studies of this system.
• These global DPEMs will facilitate future quantum mechanics dynamic simulations of MgH2.