Enabling a Unified Description of Both Internal Conversion and Intersystem Crossing in Formaldehyde: A Global Coupled Quasi-Diabatic Hamiltonian for Its S0, S1, and T1 States

In our recent work, a diabatic Hamiltonian that couples the S0 and S1 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 S0 and S1, the spin-orbit couplings between singlet states (S0, S1) and triplet state T1 are also determined in the same diabatic representation. The diabatized spin-orbit couplings are then fit with a symmetrized neural-network functional form. The ab initio spin-orbit couplings are well reproduced in large configuration space. Together with the neural-network-based potential energy surface for T1, the full quasi-diabatic Hamiltonian for the S0, S1, and T1 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.