Permutation invariant polynomial neural network based diabatic ansatz for the (E + A) × (e + a) Jahn-Teller and...

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Theoretical Chemistry

Background:

• Constructing accurate diabatic Hamiltonians is crucial for understanding molecular systems with complex electronic structures.
• Systems exhibiting non-Abelian symmetries, such as Jahn-Teller and Pseudo-Jahn-Teller effects, pose significant challenges for traditional methods.
• Existing methods may lack the flexibility to capture the intricate details of conical intersections.

Purpose of the Study:

• To develop a novel, symmetry-adapted neural network-based diabatic ansatz for constructing quasi-diabatic Hamiltonians.
• To apply this approach to the H3+ molecular ion, a well-known system with (E + A) × (e + a) Jahn-Teller and Pseudo-Jahn-Teller interactions.
• To demonstrate the capability of the permutation invariant polynomial neural network (PIP-NN) approach in accurately representing complex potential energy surfaces.

Main Methods:

• Employing the permutation invariant polynomial neural network (PIP-NN) approach to build a quasi-diabatic Hamiltonian.
• Utilizing symmetric polynomial expansions with neural network functions taking permutation-invariant polynomials as input.
• Applying the method to the H3+ system to model its electronic structure.

Main Results:

• The PIP-NN diabatic ansatz successfully preserves the correct non-Abelian symmetries of the system.
• The approach provides functional flexibility, accurately reproducing ab initio electronic structure data, including adiabatic energies, energy gradients, and derivative couplings.
• An excellent description of the local topology of the conical intersection seam was achieved for H3+.

Conclusions:

• The PIP-NN based diabatic ansatz offers a powerful and flexible tool for constructing symmetry-adapted quasi-diabatic Hamiltonians.
• This method enables accurate reproduction of complex electronic structure data and conical intersection topologies.
• The developed ansatz is a significant step towards diabatizing more complicated molecular systems with intricate symmetries.