  First-principles density functional theory calculations have been performed
to understand the electronic structure and orbital polarization of LaNiO$_3$
with a reduced coordination and under strain. From the slab calculation to
simulate [001] surface, it is found that $d_{3z^2-r^2}$ orbital occupation is
significantly enhanced relative to $d_{x^2-y^2}$ occupation owing to the
reduced coordination along the perpendicular direction to the sample plane.
Furthermore, the sign of the orbital polarization does not change under
external strain. The results are discussed in comparison to the bulk and
heterostructure cases, which sheds new light on the understanding of the
available experimental data.
