Induction, dispersion multipole interactions, penetration effects

2 Induction, Dispersion Multipole Interactions, Penetration Effects 

The second order interaction energy, according to Rayleigh hrddinger perturbation theory is given by  

Hi er order terms can be defined as well, but what little experience is availabk has taught us that they are generally smaller by at least an order of magnitude. Still, they can be important if we look at specific effects such as the non-pairwise additive components to the interaction oiergy in Van der Waals trimers or multimers (cf. the last part of this section). In the second order sununation over excited states (18) we can separate three different contrilmtions  

It is easy to see that the first term corre nds with the classical polarization (or induction) energy of molecule B in the electric field of the electronic charge distribution plus the nuclei of A, the second term with the induction energy of molecule A in the field of q plus the nuclei of B, while the third term, the dispersion energy, has no classical equii ent. 

for the short range, the second order energy contributions, (18), (19), calculated with the exact operator (11) start to deviate from the R power series expansions, (20) and (21), and we can define the penetration effects  

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