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

This work introduces a new permutation-symmetry-adapted machine learning diabatization procedure, termed the diabatization by equivariant neural network (DENN). In this approach, the permutation symmetric and anti-symmetric elements in diabatic potential energy metrics (DPEMs) were simultaneously simulated by the equivariant neural network. The diabatization by deep neural network scheme was adopted for machine learning diabatization, and non-zero diabatic coupling was included to increase accuracy in the near degenerate region. Based on DENN, the global DPEMs for 1¹A' and 2¹A' states of MgH₂ have been constructed. To the best of our knowledge, these are the first global DPEMs for the MgH₂ system. The root-mean-square-errors (RMSEs) for diagonal elements (H₁₁ and H₂₂) and the off-diagonal element (H₁₂) around the conical intersection region were 5.824, 5.307, and 5.796 meV, respectively. The RMSEs of global adiabatic energies for two adiabatic states were 4.613 and 12.755 meV, respectively. The spectroscopic calculations of the 1¹A' state in the linear HMgH region are in good agreement with the experiment and previous theoretical results. The differences between calculated frequencies and corresponding experiment values are 1.38 and 1.08 cm^-1 for anti-symmetric stretching fundamental vibrational frequency and first overtone. The global DPEMs obtained in this work should be useful for further quantum mechanics dynamic simulations on the MgH₂ system.