We present a theory of radical-molecule abstraction reactions based on the crossing of reactant ground and ionic states at the transition state. By calculating the evolution of ground- and ionic-state energies as the reactants approach each other, we are able to specify the boundary conditions for an avoided curve crossing problem as the atom is transfered. The lower the ionic-state energy, the lower in energy the transition state will be. This drives strong correlations between barrier heights and the difference of ionic- and ground-state energies. This theory successfully explains the evolution of barrier heights in a series of reactions involving alkanes and several radicals (OH, O, H, F, Cl, Br), in which barriers range from 0 to 10 kcal/mol. A perturbation treatment of the ionic- and ground-state energies improves the performance of the theory. We compare predicted curve-crossing heights with observed barriers for both our theory and for the covalent (singlet-triplet) curve-crossing theory. We also compare observed barriers with reaction enthalpy. Only the ionic curve-crossing theory can simultaneously explain both radical and molecule reactivity.