  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 orbilar
(HOMO) and the antibonding unoccupied molecular orbitals of 9.3 eV and a
non-resonant tunneling $\beta$ 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 the 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.
