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Extra resources for Advances in Chemical Physics: Intermolecular Forces, Volume 12

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In order for the second-order term in Eq. (82) to lead to the same asymptotic form for large separations, it is necessary that This relation is particularly simple when a and b do not have permanent dipole moments in their initial states. Our derivations are quite different from the ones used by Margenau"' and by Dalgarno and Lynn,'I6 but the final results are the same. Dalgarno and Lynn used this technique to obtain good results for the energy of interaction of two ground-state hydrogen atoms at intermediate separations ( R > 4a0).

AJ) Coupling. For interatomic separations for which the electrostatic interaction energy is greater than the atomic fine structure splittings, the (S,,L,,Msa,MLn)coupling scheme" is applicable for the atomic states and the spin-orbit coupling is neglected. The molecular states of the interacting atoms can usually be characterized by the quantum numbers A and S, respectively, for the absolute value of the projection of the total orbital angular momentum along R and for the total spin of the system.

G1 The term C,(dis) R - 8 results from the dipole-quadrupole perturbation, V,. The term Clo(dis) R-" is the result of contributions from both the quadrupole-quadrupole and the dipole-octopole interactions. The importance of the dipole-octopole contribution to the R-" interaction energy should be e m p h a s i ~ e d ' ~ " * ~ ~ * ~ ~ and, in the case of two hydrogen atoms, can be seen in Table IV. 1A,( Wq4 j)) -c c l [(a,IMi)Ui)) + ( 6 , - bq,)]Rk+' v k r#qu#q' aq) where v k and Vl are different operators.

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