Enabling a Unified Description of Both Internal Conversion and Intersystem Crossing in Formaldehyde: A Global Coupled Quasi-Diabatic Hamiltonian for Its S, S, and T States.

In our recent work, a diabatic Hamiltonian that couples the S and S states of formaldehyde was constructed using a robust fitting-and-diabatizing procedure with artificial neural networks, which is capable of representing adiabatic energies, energy gradients, and derivative couplings over a wide range of geometries including seams of conical intersection. In this work, based on the diabatization of S and S, the spin-orbit couplings between singlet states (S, S) and triplet state T are also determined in the same diabatic representation. The diabatized spin-orbit couplings are then fit with a symmetrized neural-network functional form. The spin-orbit couplings are well reproduced in large configuration space. Together with the neural-network-based potential energy surface for T, the full quasi-diabatic Hamiltonian for the S, S, and T states is completed, enabling a unified description of both internal conversion and intersystem crossing in formaldehyde. The vibrational levels on the three adiabatic states are found to be in good agreement with known experimental band origins.