  In this work, we present a systematic study of the occupied and unoccupied
electronic states of LaCoO$_{3}$ compound using DFT, DFT+$\textit{U}$ and
DFT+embedded DMFT methods. The value of $\textit{U}$ used here is evaluated by
using constrained DFT method and found to be $ \backsim $ 6.9 eV. It is found
that DFT result has limitations with energy positions of PDOS peaks due to its
inability of creating a hard gap although the DOS distribution appears to be
fine with experimental attributes. The calculated value of $\textit{U}$ is not
an appropriate value for carrying out DFT+$\textit{U}$ calculations as it has
created an insulating gap of $ \backsim $ 1.8 eV with limitations in
redistribution of DOS which is inconsistent with experimental spectral
behaviour for the occupied states mainly. However, this value of $\textit{U}$
is found to be an appropriate one for DFT+embedded DMFT method which creates a
gap of $\backsim $ 1.1 eV. The calculated PDOS of Co 3$\textit{d}$, La
5$\textit{d}$, La 4$\textit{f}$ and O 2$\textit{p}$ states are giving a
remarkably good explanation for the occupied and unoccupied states of the
experimental spectra in the energy range $\backsim $ -9.0 eV to $\backsim $
12.0 eV.
