The interaction between segregated alloying elements (Al, Li, Sn, Y, and Ca) and three crack systems is investigated in magnesium simple crystal under mode I loading condition. Using molecular statics in the framework of the (modified) embedded-atoms method, the effect of segregated alloying elements on both the fracture behavior and the intrinsic fracture toughness were identified, and analyzed quantitatively in the framework of the Rice's theory for dislocation emission at a crack tip (Rice, 1992. J. Mech. Phys. Solids 40 239-271). In addition, the variations of the critical stress intensity factor as a function of the misfit strain between the alloying element and magnesium are discussed. The results revealed the existence of a transition from cleavage to dislocation emission at a crack tip. Such transition from cleavage to dislocation emission at the crack tip depends on (i) the orientation of the crack system, and (ii) the nature of the alloying element segregated at the crack tip. Furthermore, when analyzed as a function of the misfit strain between the alloying element and magnesium, our data suggest a direct relation between the fracture toughness and the misfit strain, independently of crack orientation. While alloying element with compressive misfit strain enhances the intrinsic fracture toughness of magnesium single crystal, alloying element with tensile misfit strain worsens the intrinsic fracture toughness of magnesium single crystal.