The effect of electron spin-rotational (SR) interaction in species with an effective-spin S-eff=1/2 is treated for molecular rotations representing an adiabatic perturbation to the electronic system. Based on the adiabatic rotation of effective spin (ARES) concept as well as an the transformation of the Hamiltonian to the rotating molecular frame a useful expression is obtained for the effective spin-Hamiltonian of SR interaction whereby the. spin-rotational tenser is represented in terms of,a tenser gamma(($) over cap) (relating L + S to S-eff) instead of the gamma tenser (related to L + g(e)S). This relation is valid for rotating systems with arbitrary strength of spin-orbit coupling (SOC). An example is provided to demonstrate the dependence of the gamma tensor on the SOC parameter. It is shown that only in the case of weak SOC, the traditional representation of the SR Hamiltonian, is equivalent to the more general ARES Hamiltonian. Furthermore, a direct relation between the ARES and the geometrical (topological phase) approach to the problem is pointed out. The ARES spin-Hamiltonian can be represented in terms of a U(2) non-Abelian gauge potential.