In symmetry-adapted perturbation theory, the interaction energy of a non-covalently bound pair of molecules (it could be done to arbitrary order but is usually just pairs) is built up from a perturbative expansion of the interaction potential between two monomers.
The first-order perturbation drops out a term which we call induction. This has components associated with the induction on monomer B by monomer A and vice versa. The second-order perturbation drops out a term which we call dispersion (this is what people usually refer to when they say van der Waal's force (although that's not technically correct...)).
My question is, can that second-order perturbation term--dispersion-- have a non-zero contribution to the total energy while the first-order induction terms do not contribute?
When I imagine this situation physically, it doesn't make much sense because it means that the presence of monomer A near monomer B does not perturb the eigenstates of monomer B (beyond electrostatics, exchange, etc.) and vice versa, but somehow there is a mutual dispersion effect.
So basically what I'm asking is if it is mathematically possible to have a non-zero dispersion term while simultaneously having zero contributions from the first-order induction terms in the interaction potential expansion?
Also, if it is not possible, it seems as if we ought to be able to write the dispersion energy in terms of the induction energies, but clearly we can't because dispersion is a second-order perturbation. If the effects are related, however, can we approximate dispersion using induction? I imagine this to be similar to how in Moller-Plesset perturbation theory you can approximate the fourth-order perturbation using the second-order perturbation.
I don't know too much about the details of what I'm asking about, so if I've said something quite stupid please let me know.