Although an isolation of elusive tricyanomethane HC(CN)(3) was recently reported, the.existence of other HC4N3 species has yet to be confirmed. In this work, the relative stabilities, spectroscopic features, and rearrangements of tricyanomethane and its four isomers are examined using single-(CCSD(T), CCSD(T)-F-12) and multireference (MCSCF, MRPT2) methods. Tricyanomethane and dicyanoketenimine (NC)2CCNH, which are found to be the two most stable HC4N3 isomers lying within 9 kcal/mol, can be discriminated by their spectroscopic parameters. The predicted stepwise interconversion path relating HC(CN)(3) and (NC)(2)CCNH features the HC4N3 species comprising the C-C N ring moiety, with the largest barrier being associated with the initial H migration to one of the CN carbons. Adding a water molecule reduces the H migration barrier strongly and makes it possible to interconvert tricyanomethane to dicyanoketenimine in a "concerted" way.