The global potential energy surfaces of the [H,C,N,O](+) system both in doublet and quarter states have been rather exhaustively studied with the B3LYP density functional method, with special attention to cover nearly all intermediate and transition states. Ionization potentials, energies of reactions, and proton affinities of fragments are calculated and compared with experiments to assess the reliability, In the doublet state, all six chain isomers and three cyclic structures exist, and rearrangements among them take place over high barriers mainly via the 1,3-H shift and chain-cycle transformation. Pathways for fragmentations of the isocyanic acid cation HNCO+ and fulminic acid cation HCNO+ have been identified and compared with the experiments. In the quartet state, there exist ion-molecule complexes between fragments as well as trans and cis forms of chain isomers and cyclic and open branched isomers, and the potential surfaces for interconversion and fragmentation are much more complicated. The potential energy profiles for the reaction of O+(S-4)+HCN have been examined and pathways for production of experimentally observed HCN+, NO+, HCO+, and HOC+ have been identified to go through long-lived chain intermediates HCNO+ and HOCN+ and open branched intermediate NCHO+, while production of CO+ is more complicated. The crossing seam minimum with the doublet has been found right at the quartet intermediate HCNO+, and intersystem crossing and production of the stable doublet fulminic acid cation HCNO+ is likely to be an efficient process.