Reactions of fullerene C60 with atomic fluorine are studied by the unrestricted broken spin symmetry Hartree-Fock (UBS HF) approach implemented in semiempirical codes based on the AMI technique. The calculations are focused on a successive addition of a fluorine atom to the fullerene cage following the indication of the highest chemical susceptibility of the cage atom, which is calculated at each step. The proposed computational synthesis is based on the effectively-unpaired-electron concept of the chemical susceptibility of fullerene atoms. The obtained results are analyzed from the standpoints of energy, symmetry, and the composition abundance. A good fitting of the data to experimental findings proves a creative role of the suggested synthetic methodology