The symbolisms used by Shaik and Hiberty (2003, Helvet. Chim Acta, 86, 1063) to provide valence-bond (VB) structures for the Pauling three-electron bond (or three-electron two atomic orbital bond) and the ground-state of O₂, are compared with those provided by Green and Linnett (1960, J. Chem. Soc. 4949). The incorporation of the Green-Linnett VB structure for O₂ into the VB structures for numerous diamagnetic as well as paramagnetic tri- and polyatomic molecules, to generate increased-valence structures, is re-described. Illustrative examples include molecular systems of the types R-O₂ and R-O₂-R, with for either or both species, R = F, NO, Co^II(S = 1/2), O(S = 1), Fe^II(S = 1), O₂(S = 1), and Cu^I(S = 1). The use of increased-valence structures to provide VB formulations of S_N2 reactions is also redescribed. The origin of the existence of a triplet-spin (S = 1) ground-state for O₂ is re-examined, with attention given to two-electron delocalisation (exchange) resonance which is associated with reduced electron-electron repulsion.

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