The local electron affinity (EA(L)) and the local ionization energy (IE(L)) are successfully used for predicting properties of closed-shell species for drug design and for nanoelectronics. Here the respective unrestricted Hartree-Fock variants of EA(L) and IE(L), i.e., the unrestricted local electron affinity (UHF-EA(L)) and ionization energy (UHF-IE(L)), have been shown to be useful for predicting properties of open-shell species. UHF-EA(L) and UHF-IE(L) have been applied for explaining unique electronic properties of an exemplary nanomaterial carbon peapod. It is also demonstrated that UHF-EA(L) is useful for predicting and better understanding reactivity of radicals related to alkanes activation.