A density functional theory (DFT) study was carried out to investigate possible reactions of dibenzofuran (DF) and dibenzo-p-dioxin (DD) in a reducing environment. Reaction energies, barrier heights, and molecular parameters for reactants, intermediates, products, and transition states have been generated for a wide range of possible reactions. It was found that C-O beta-scission in DF incurs a very large energy barrier (107 kcal/mol at 0 K), which is just 3 kcal/mol less than the direct H fission from C-H in DF to form dibenzofuranyl radicals. It was found that DF allows direct H addition to C1-C4 and C6-C9 as well as addition of two H atoms from a hydrogen molecule at sites 1 and 9 of DF. A bimolecular reaction of DF with H or H-2 is found to have a significantly lower barrier than unimolecular decomposition through C-O beta-scission. An explanation for the predominance of polychlorinated dibenzofurans (PCDF) over polychlorinated dibenzo-p-dioxins (PCDD) in municipal waste pyrolysis is presented in the view of the facile conversion of DD into DF through ipso-addition at the four C sites of the two C-O-C central bonds in DD.