  The electronic properties of squashed arm-chair carbon nanotubes are modeled
using constraint free density functional tight binding molecular dynamics
simulations. Independent from CNT diameter, squashing path can be divided into
{\it three} regimes. In the first regime, the nanotube deforms with negligible
force. In the second one, there is significantly more resistance to squashing
with the force being $\sim 40-100$ nN/per CNT unit cell. In the last regime,
the CNT looses its hexagonal structure resulting in force drop-off followed by
substantial force enhancement upon squashing. We compute the change in band-gap
as a function of squashing and our main results are: (i) A band-gap initially
opens due to interaction between atoms at the top and bottom sides of CNT. The
$\pi-$orbital approximation is successful in modeling the band-gap opening at
this stage. (ii) In the second regime of squashing, large $\pi-\sigma$
interaction at the edges becomes important, which can lead to band-gap
oscillation. (iii) Contrary to a common perception, nanotubes with broken
mirror symmetry can have {\it zero} band-gap. (iv) All armchair nanotubes
become metallic in the third regime of squashing. Finally, we discuss both
differences and similarities obtained from the tight binding and density
functional approaches.
