  Recent nuclear magnetic resonance measurements on isotope engineered double
walled carbon nanotubes (DWCNTs) surprisingly suggest a uniformly metallic
character of all nanotubes, which can only be explained by the interaction
between the layers. Here we study the inter-shell interaction in DWCNTs by
density functional theory and inter-molecular H\"uckel model. We find charge
transfer between the layers using both methods. We show that not only does the
charge transfer appear already at the fundamental level of the inter-molecular
H\"uckel model, but also that the spatial distribution of the change in the
electron density is well described already at this level of theory. We find
that the charge transfer between the walls is on the order of 0.001 e/atom and
that the inner tube is always negatively charged. We also observe orbital
mixing between the states of the layers. We find that these two effects
combined can in some cases lead to a semiconductor--to--metal transition of the
double walled tube, but not necessarily in all cases.
