Permutation invariant polynomial neural network based diabatic ansatz for the (E plus A) x (e plus a) Jahn-Teller and Pseudo-Jahn-Teller systems

In this work, the permutation invariant polynomial neural network (PIP-NN) approach is employed to construct a quasi-diabatic Hamiltonian for system with non-Abelian symmetries. It provides a flexible and compact NN-based diabatic ansatz from the related approach of Williams, Eisfeld, and co-workers. The example of H-3(+) is studied, which is an (E + A) x (e + a) Jahn-Teller and Pseudo-Jahn-Teller system. The PIP-NN diabatic ansatz is based on the symmetric polynomial expansion of Viel and Eisfeld, the coefficients of which are expressed with neural network functions that take permutation-invariant polynomials as input. This PIP-NN-based diabatic ansatz not only preserves the correct symmetry but also provides functional flexibility to accurately reproduce ab initio electronic structure data, thus resulting in excellent fits. The adiabatic energies, energy gradients, and derivative couplings are well reproduced. A good description of the local topology of the conical intersection seam is also achieved. Therefore, this diabatic ansatz completes the PIP-NN based representation of DPEM with correct symmetries and will enable us to diabatize even more complicated systems with complex symmetries.

Automated summary

In this work, the PIP-NN approach is used to construct a quasi-diabatic Hamiltonian for systems with non-Abelian symmetries, providing a flexible and accurate method for studying complex systems. The PIP-NN diabatic ansatz not only preserves correct symmetry, but also accurately reproduces electronic structure data, demonstrating excellent fits and reproducing adiabatic energies, energy gradients, and derivative couplings effectively.