Abstract In this paper, we report the design of models for interstellar molecules HC n N ( n = 1–17) by means of the B3LYP density functional method. We performed geometry optimization and calculation on vibrational frequency. We find that the ground-state (G-S) isomers of HC n N ( n = 1–17) are with the N atom located at one end and the H atom at the other end of a C n chain; they are all linear except for HC 2N which is bent. When n is odd, the C n chain is polyacetylene-like whereas when n is even, the C n chain displays a structure that is cumulenic-like in the middle of the C n chain. It is found that the G-S isomers of odd- n HC n N ( n = 1–17) are more stable than those of even- n ones. The finding is in accord with the relative intensities of HC n N recorded in laboratory investigations, and in consistent with the results of objects observed in interstellar media. We provide explanations for such a trend of even/odd alternation based on concepts of the highest vibrational frequency, bonding character, electronic configuration, incremental binding energy, nucleus-independent chemical shift, and dissociation channels.