Butadiyne (diacetylene, HC4H) is produced during combustions, and has been quantified in different flames as well as a biomass burning emission. Its reaction with the hydroxyl radical, HO((2)Pi(3/2)), under combustion conditions, was investigated in a thorough RRKM study by J. P. Senosiain, S. J. Klippenstein, and J. A. Miller (Proc. Combust. Inst. 2007, 31, 185-192). The present density functional theory (DFT) study focuses on the mechanism of further oxidation by O-2((3)Sigma(-)(g)). The DFT(M06-2X)/cc-pVTZ reaction energy hypersurface for the system C4H2/HO center dot/O-2 is studied to define a variety of reaction pathways, and the relevant thermochemistry for temperatures ranging from 200 to 2500 K is assessed, thus encompassing combustive, postcombustive, and tropospheric conditions. Energies are then recomputed at the coupled cluster level [CCSD(T)/cc-pVTZ], and combined with the DFT thermochemistry. Finally, the role of the different reaction channels is assessed by RRKM-ME simulations in the same temperature range for P = 1 atm, to comprise the situation of emission in the troposphere and those pertaining to different flames. This shows that, when considering HO addition to the triple bond, dioxygen takes part in C4H2 oxidation with higher efficiency at lower temperatures, whereas, as T rises, the O-2 adducts are inclined to redissociate: for instance, a 50% redissociation is estimated at T=1800 K. For 200 < T < 1100 K, two polycarbonyl products (CHO.CO.C CH and CHO.CO.CH=C=O) and two fragmentation products (HCOOH plus OC center dot-C CH) are the main species predicted as products from the addition channel (fragmentation is entropy-favored by higher T values). However, at higher temperatures, an initial H abstraction by HO can give the butadiynyl radical (HC4 center dot) as the starting point for subsequent dioxygen intervention. Then, new pathways opened by O-2 addition become accessible and bring about fragmentations mainly to HC3 center dot + CO2 and also to (HC3O)-O-center dot + CO.