A general method for the development of diabatic spin-orbit models for multi-electron systems

Spin-orbit (SO) coupling can have significant effects on the quantum dynamics of molecular systems, but it is still difficult to account for accurately. One promising way to do this is to devise a diabatic SO model combined with the molecular potential energy. Few such models have been developed utilizing spatial and time-reversal symmetry. These models are tedious to derive and are specific for the molecular symmetry and included spin states. Here, we present a relatively simple approach to construct such models for various spin states with S not equal 1/2 from a basic one-electron SO case with S = 1/2. The multi-electron fine structure states are expressed in terms of Slater determinants of single-electron spin functions (spinors). The properties of all single-electron matrix elements over the SO operator are derived and expressed as Taylor expansions in terms of symmetry-adapted nuclear coordinates. The SO matrix elements for the multi-electron case are then obtained from these single-electron matrix elements using the Slater-Condon rules. This yields the full SO matrix and symmetry properties of the multi-electron matrix elements in a straightforward way. The matrix elements are expressed as symmetry-adapted polynomials up to arbitrary order. This approach is demonstrated first for an abstract model of two electrons in a set of p orbitals in a C-3v symmetric environment and then applied to set up a diabatic model for the photodissociation of methyl iodide (CH3I). The high accuracy of this new approach is demonstrated in comparison to an available analytic SO model for CH3I.