While the working expressions for calculating the matrix elements of the BP Hamiltonian between the pairs of non-relativistic states have been throughly described in previous works, one important aspect of the theory has not yet been fully developed. To construct experimentally relevant quantities, such as rates of ISC crossing, oscillator strengths, or magnetic anisotropies, one needs SOCs computed for all multiplet components. For example, the expression for the SOC constant (SOCC), the quantity that enters the Fermi golden rule expression of the ISC rate, is given by the following expression :