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Recently, G-quadruplexes (Gq) formed in B-DNA as secondary structures are found to be important therapeutic targets and material for developing nanodevices. Gq are guanine-rich and thus susceptible to oxidative damage by producing short-lived intermediate radicals via proton-transfer reactions. Understanding the mechanisms of radical formation in Gq is of fundamental interest to understand the early stages of DNA damage. Herein, we used density functional theory including aqueous phase (ωB97XD-PCM/6-31++G**) and considered single layer of Gq [G-quartets (G4): association of four guanines in a cyclic Hoogsteen hydrogen-bonded arrangement (Scheme 1)] to unravel the mechanisms of formation of intermediates by calculating the relative Gibbs free energies and spin density distributions of one-electron-oxidized G4 and its various proton-transfer states: G^•+, G(N₁–H)^•, G(N₂–H′)^•, G(N₂–H″)^•, G(N₁ …