Evaluation of Spin-Orbit Integrals

The no-pair spin-orbit Hamiltonian [105] differs from the corresponding BP terms [103] by momentum dependent factors of the type Ai/(Ej + me2) or (AjAj)/ (Ej+ mec2), where E, and A,- or A - have been defined in [106] and [107], respectively. There are essentially two ways of taking these factors into account. 

Within the ZDO approximation only one-center contributions are considered and all neglected terms are lumped into the empirical spin-orbit coupling parameters (iy.. Then, 

As the bonded functions of both states are built from the same set of real MOs (. , Z,°. = 0, and thus is nonzero only if the bonded functions /) and J) diner exactly in one MO, i.e. if i = a andy =A. 

In order to evaluate the Cartesian components of the SOC vector, the principal magnetic axes have to be determined by considering the spin-spin dipolar coupling [23] 

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