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=$a_u$, $b_g\times a_u=B_u$).

  • $\begingroup$ In Eqs. 1-2 the molecular wavefunction seems to be written as a linear combination of atomic orbitals, with every coefficient = 1? $\endgroup$ – Nike Dattani Apr 25 at 2:54

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