Recently, many interesting materials made from carbon atoms have been discovered such as carbon nanotubes, fullerenes, and graphenes. In this article, we studied electronic structures and molecular structures of polyynes with sp2 carbons on both ends. Polyynes calculated were H2CCnCH2 with various number of n. These molecules have two π systems which are perpendicular to each other and these π systems have their tendency to make double bond nature by Peierls instability but for different alternating bonds. In other words, these two π systems are competing to form the double bond formations. The calculations were performed at Hartree–Fock level geometry optimization with 6-31G, 6-311G, and 6-31G** basis sets. For CH2(C)2mCH2, we have found that there are two metastable structures, one of which is the bond-alternating structure and another is nearly equi-bond structure. The former has small highest occupied molecular orbital (HOMO)–lowest unoccupied molecular orbital (LUMO) gap while the latter has relatively large gap although it is smaller in comparison with the value of polyyne with sp carbon atoms on both ends: H(C)2mH. The small highest occupied molecular orbital (HOMO)–lowest unoccupied molecular orbital (LUMO) gap in bond-alternating structure is due to the fact that HOMO and MO's near to HOMO have relatively localized electronic distribution in both end regions, and thus, the weak interaction between the both regions leads to the small HOMO–LUMO gap. The stability is larger for the former especially in long polyynes. For CH2(C)2m+1CH2, we have found only one stable structure, that is, equi-bond structure. This type of polyyne oligomers has two terminal CH2 groups which are perpendicular with each other. It is found that the longer the length of oligomer is, the smaller the HOMO–LUMO gap is as is usually expected. By summarizing these results, we proposed a design for a single-chain electronically conductive polymers. © 2012 Wiley Periodicals, Inc.