Complication if perturbation is done without multipole expansion first

[MarieDeseyn]

A first conceptual problem is that the term Q^0V^0 is brought into H_0, this term has energies of the order of eV and is not so negligable with respect to the other terms in H_0, if we would not do that the perturbation will not converge rapidly and we would need to calculate higher order perturbation terms.
Moreover if we don’t use multipole expansion we need to calculate Q x V which is a complicated calculation.
Moreover if we look at the charge-charge interaction all odd terms vanish and we can truncate after the quadrupole term, which is not possible if we do not do the multipole expansion.
Probably also the overlap corrections will be more difficult to calculate

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