In spectroscopy it is common to describe excited-states as ionic or covalent.
I understand the concept on a toy model e.g. $\ce{H2}$ with a minimal basis set
\begin{align} \Phi_0 &= [\chi_A(1) + \chi_B(1)][\chi_A(2) + \chi_B(2)]\tag{1} \\ &= \underbrace{\chi_A(1)\chi_A(2) + \chi_B(1)\chi_B(2)}_{\mathrm{Ionic \ Part}} + \underbrace{\chi_A(1)\chi_B(2) + \chi_B(1)\chi_A(2)}_{\mathrm{Covalent \ Part}}\tag{2} \end{align} $\chi$ are the AOs, $A,B$ are the atom labels, and $1,2$ are the electron labels.
However, how can I determine ionic/covalent for more complex molecules using computations?
For example, I am doing complete-active space self-consistent field calculations and I have the CI coefficients $c_i$ for the different determinants e.g. here are the $c_i$ coefficients for the first excited-state
0.70266226570264 X54 A55 B56 0.70266226570264 X54 B55 A56 0.07890494054450 A54 B55 X56 0.07890494054450 B54 A55 X56
$A$ refers to an $\alpha$ electron, B a $\beta$ electron, and X doubly occupied orbital.
I've determined using symmetry that the first excited-state is of $B_u$ symmetry (orbital 55=$b_g$, orbital 56=$a_u$, $b_g\times a_u=B_u$).
