  Recent studies reveal a pressure induced transition from a paramagnetic
tetragonal phase (T) to a collapsed tetragonal phase (CT) in $CaFe_2As_2$,
which was found to be superconducting with non-hydrostatic pressure at low
temperature. We have investigated the effects of electron correlation and local
fluctuating moment in both tetragonal and collapsed tetragonal phases of the
paramagnetic $CaFe_2As_2$ using self consistent DFT+DMFT with continuous time
quantum Monte Carlo as the impurity solver. From the computed optical
conductivity, we find a gain in the optical kinetic energy due to the loss in
Hund's rule coupling energy in the CT. We find that the transition from T to CT
turns $CaFe_2As_2$ from a bad metal into a good metal. Computed mass
enhancement and local moments also show significant decrease in the CT, which
confirms the suppression of the electron correlation in the CT phase of
$CaFe_2As_2$.
