[en] The complex band structure of an isolated polyethylene chain is calculated within density functional theory (DFT). A plane wave basis and ultrasoft pseudopotentials are used. The results are compared with those obtained via a local basis set. We obtain a gap between the highest occupied molecular orbital (HOMO) and the antibonding unoccupied molecular orbitals of 9.3 eV and a non-resonant tunnelling β parameter of 0.9 per monomer, in reasonable agreement with experiment and with results obtained via local basis. Polyethylene is a negative electron affinity material and the actual gap should be the energy of the HOMO with respect to the vacuum level (in DFT approximation only about 5.14 eV). The Bloch states at imaginary k are mainly free-electron-like parabolic bands which are missing in the local basis. We present also the complex bands of bulk polyethylene in order to estimate the effects of the chain-chain interactions on the complex band structure. The relevance of these results for the tunnelling conduction of n-alkane chains is discussed