We use a fast Fourier transform block Lanczos diagonalization algorithm to study the electronic states of excess electrons in fluid alkanes (methane, ethane, and propane) and in a molecular model of amorphous polyethylene (PE) relevant to studies of space charge in insulating polymers. We obtain a new pseudopotential for electron-PE interactions by fitting to the electronic properties of fluid alkanes and use this to obtain new results for electron transport in amorphous PE. From our simulations, while the electronic states in fluid methane are extended throughout the whole sample, in amorphous PE there is a transition between localized and delocalized states slightly above the vacuum level (similar to+0.06 eV). The localized states in our amorphous PE model extend to -0.33 eV below this level. Using the Kubo-Greenwood equation we compute the zero-field electron mobility in pure amorphous PE to be muapproximate to2x10(-3) cm(2)/V s. Our results highlight the importance of electron transport through extended states in amorphous regions to an understanding of electron transport in PE. (C) 2003 American Institute of Physics.