  We report a detailed electronic structure calculation for Vanadium (V) using
DFT, DFT+$U$, $G_0W_0$, $GW_0$ and DFT+DMFT methods. The calculated values of
$W$, $U$ and $J$ by cRPA method are $\sim$1.1, $\sim$3.4 and $\sim$0.52 eV,
respectively. The comparison between calculated spectra (CS) and experimental
spectra (ES) suggests that $W$ ($U$) is more accurate for DFT+$U$ (DFT+DMFT)
method. The CS, obtained by these methods, give fairly good agreement with ES
for peaks' positions except $GW_0$. The shallowness of the dips lying $\sim$
-1.5 eV and $\sim$1.0 eV in ES are properly explained by DFT+DMFT method only,
due to the presence of incoherent $t_{2g}$ states. This work suggests that for
the proper explanation of ES, sophisticated many-body theory is needed even for
the simple metal.
