  We investigate the electronic state and structure transition of BaNi2As2,
which shows a similar superconducting phase diagram as Fe-based
superconductors. We construct the ten-orbital tight-binding model for BaNi2As2
by using the maximally localized Wannier function method. The Coulomb and
quadrupole-quadrupole interactions are treated within the random-phase
approximation. We obtain the strong developments of charge quadrupole
susceptibilities driven by the in-plane and out-of-plane oscillations of Ni
ions. The largest susceptibility is either O_{X^2-Y^2}-quadrupole
susceptibility at q = (pi, 0, pi) or O_{XZ(YZ)}-quadrupole susceptibility at q
= (pi, pi, pi), depending on the level splitting between d_{X^2-Y^2} and
d_{XZ(YZ)}. These antiferro-quadrupole fluctuations would then be the origin of
the strong coupling superconductivity in Ni-based superconductors. Also, we
propose that the antiferro-quadrupole O_{X^2-Y^2} order with q = (pi, 0, pi) is
the origin of the zigzag chain structure reported in experiments. We identify
similarities and differences between Ni- and Fe-based superconductors.
