  We use density functional theory (DFT) calculations to study the lattice
vibrations and electronic properties of the correlated metal LaNiO$_3$. To
characterize the rhombohedral to cubic structural phase transition of
perovskite LaNiO$_3$, we examine the evolution of the Raman-active phonon modes
with temperature. We find that the $A_{1g}$ Raman mode, whose frequency is
sensitive to the electronic band structure, is a useful signature to
characterize the octahedral rotations in rhombohedral LaNiO$_3$. We also study
the importance of electron--electron correlation effects on the atomic
structure with two approaches which go beyond the conventional band theory
(local spin density approximation): the local spin density+Hubbard $U$ method
(LSDA$+U$) and hybrid exchange-correlation density functionals which include
portions of exact Fock-exchange. We find the conventional LSDA accurately
reproduces the delocalized nature of the valence states in LaNiO$_3$ and gives
the best structural and vibrational agreement to the available experimental
data. Based on our calculations, we show that the electronic screening effect
from the delocalized Ni 3$d$ and O-2$p$ states mitigate the electronic
correlations of the $d^7$ Ni cations, making LaNiO$_3$ a weakly correlated
metal.
