While a nearest-neighbor-only Su-Schrieffer-Heeger model cannot distin
guish cis- from trans-polyacetylene, a simple extension which includes
a third-neighbor interaction can. This extended model gives a nondege
nerate cis structure with a larger band gap and a smaller cohesive ene
rgy than trans, and yields the correct order of the total energies of
the trans, cis-transoid, and trans-cisoid structures. It also produces
bound bipolarons or excitons on doubly charged cis chains. All confor
mational excitations in both isomers are found to be repelled from the
chain ends.