The apex region of a capped (5,5) carbon nanotube (CNT) has been modelled with the DFT package ONETEP, using boundary conditions provided by a classical calculation with a conducting surface in place of the CNT. Results from the DFT solution include the Fermi level and the physical distribution and energies of individual orbitals for the CNT tip. Application of an external electric field changes the orbital number of the highest occupied molecular orbital (HOMO) and consequently changes its distribution on the CNT