We calculate the electron emission from nanostructures under an applied electric field using the ab initio pseudopotential method. The transition rates of the electrons are calculated by integrating the time-dependent Schrodinger equation for the states initially inside the emitter. A localized basis set is used for obtaining the eigenstates before emission and the potential that drives the field emission. The calculated electron-tunneling graph is quite linear in the short-time region, giving the transition rate within the simulation time. We have applied this new method to the field emission of carbon nanotubes as a test. Then we calculate the electronic structure of the fullerenes encapsulated inside the carbon nanotubes. the so-called carbon "nanopeapods". The fullerenes may or may not contain metallic atoms such as gadolinium or potassium, There is an interesting effect of strain when the diameter of the carbon nanotube is smaller than that of the inserted fullerene plus twice the van der Waals distance. (C) 2002 Published by Elsevier Science B.V.