A formula is derived for the R-atom valence in the valence bond structure X center dot R:Y, with one overlapping atomic orbital per atomic center. Using this formula, the results of STO-6G valence bond calculations for linear H-3, HFH, FHF, and F-3 transition states show that for each molecule, the R-atom exhibits increased-valence or electronic hypervalence, that is, its valence exceeds that for the Lewis structure X RN, with no one-electron bond Consideration is also given to (a) valence bond formulations for the conversion of the excited states of the reactants into the excited states of the products for the X-center dot + R:Y -> X:R + Y-center dot and X:(-) + R:Y -> X:R + Y:(-) reactions and the state correlation diagram for X-center dot + R:Y -> X:R + Y-center dot, (b) Kekule and Dewar increased-valence structures for D-6h, symmetry systems, and (c) the three-center molecular orbital interaction of the X-center dot electron with the antibonding molecular orbital of R:Y, to form the one-electron X R bond of X center dot R:Y