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 1(1)A' and 2(1)A' 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 (H-11 and H-22) and the off-diagonal element (H-12) 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 1(1)A' 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. Published under an exclusive license by AIP Publishing.

Automated summary

This work introduced a new permutation-symmetry-adapted machine learning diabatization procedure called DENN, which constructed global DPEMs for 1(1)A' and 2(1)A' states of MgH2 system with improved accuracy in the near degenerate region. Spectroscopic calculations confirmed good agreement between calculated results and experiments.