  We study the charge and spin density distributions of excitonic insulator
(EI) states in the tight-binding approximation. We first discuss the charge and
spin densities of the EI states when the valence and conduction bands are
composed of orthogonal orbitals in a single atom. We show that the anisotropic
charge or spin density distribution occurs in a unit cell (or atom) and a
higher rank electric or magnetic multipole moment becomes finite, indicating
that the EI state corresponds to the multipole order. A full description of the
multipole moments for the $s$, $p$, and $d$ orbitals is then given in general.
We find that, in contrast to the conventional density-wave states, the
modulation of the total charge or net magnetization does not appear in this
case. However, when the conduction and valence bands include the component of
the same orbital, the modulation of the total charge or net magnetization
appears, as in the conventional density-wave state. We also discuss the
electron density distribution in the EI state when the valence and conduction
bands are composed of orbitals located in different atoms. We show that the
excitonic ordering in this case corresponds to the bond order formation. Based
on the results thus obtained we discuss the EI states of real materials
recently reported.
