  Electric field gradients (EFG's) were calculated for the $CeIn_3$ compound at
both $^{115}In$ and $^{140}Ce$ sites. The calculations were performed within
the density functional theory (DFT) using the augmented plane waves plus local
orbital (APW+lo) method employing the so-called LDA+U scheme. The $CeIn_3$
compound were treated as nonmagnetic, ferromagnetic, and antiferromagnetic
cases. Our result shows that the calculated EFG's are dominated at the
$^{140}Ce$ site by the Ce-4f states. An approximately linear relation is
intuited between the main component of the EFG's and total density of states
(DOS) at Fermi level. The EFG's from our LDA+U calculations are in better
agreement with experiment than previous EFG results, where appropriate
correlations had not been taken into account among 4f-electrons. Our result
indicates that correlations among 4f-electrons play an important role in this
compound and must be taken into account.
