We report recent development of relativistic exact two-component (X2C) Hamiltonians for accurate treatments of spin-orbit coupling. We discuss formulation and efficient implementation of atomic mean-field spin-orbit approaches within X2C for both perturbative and non-perturbative treatments of spin-orbit coupling. Combining the relativistic electronic-structure methods and multistate vibronic Hamiltonian, we develop a generally applicable computational approach to determine vibronic branching ratios in polyatomic molecules to the 10<sup>-5</sup> level, including for nominally symmetry-forbidden transitions. This approach is demonstrated for metal-containing molecules, showing approximately two orders of magnitude improved sensitivity compared with the previous state of the art. This enables probing subtle molecular physics and will benefit the field of quantum computation through an informed choice of best molecules.

Relativistic molecular quantum mechanics and application to laser cooling of polyatomic molecules

ACS Spring 2022

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