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It is clear that we can expand a cationic state of a molecule in terms of configuration interaction (up to double excitation). It means: $$|I \rangle = \sum_j c^{(I)}_j a_j|\phi_0 \rangle \ + \ \sum_{r,k<l} c^{(I)}_{rkl} a_r{\dagger} \ a_k \ a_l|\phi_0 \rangle \ + \ ... $$

where C are coefficients, $a_i(a^{\dagger})$ is annihilation (creation) operator, and $|\phi_0 \rangle$ is HF Ground state of nuetral molecule.

I would like to know how can I construct spin-free $c^{(I)}_{rkl}$, which is the coefficient of 2h1p configuration? Particularly, I interested in this procedure when cationic state and accordingly 2h1p configuration is doublet.

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