The reaction between the simplest nitro compound HNO2 (hydrogen nitryl) and acetylene HCCH - formally proceeding via 1,3-dipolar cycloaddition - has been studied by means of the B3LYP, MPW1K and MP2 methods. The energy barrier of 20.74 divided by 32.91 kcal/mol is similar to Delta E-a of the NNO + HCCH process but is essentially larger than computed for the reactions of HCCH with fulminic acid (HCNO) and NNCH2. Whole process is exothermic with the reaction energy: -10.87 divided by -17.94 kcal/mol. An evolution of the chemical bonding has been analyzed by means of the Bonding Evolution Theory (BET) at the B3LYP/6-31+G(d) and B3LYP/cc-pVTZ levels. Two approximations of the reaction path have been considered, namely: the IRC and pseudo-reaction paths. The reaction requires five steps and seven catastrophes of the fold and cusp type. A different effect of first fold catastrophe has been noticed. At the B3LYP/6-31+G(d) level one of two nonbonding V-i=1,V-2(N) attractors is annihilated (F), meanwhile at B3LYP/cc-pVTZ new V(N) attractor is created (F+). The chemical bonds are not formed/broken in TS. (C) 2010 Wiley Periodicals, Inc. Int J Quantum Chem 111: 23782389, 2011