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Extra info for Advances in Chemical Physics: Intermolecular Forces, Volume 12
Note that the Q;" defined by Eq. (50) are equal to [(I - I m I ) ! Ill2 times the Q;" defined in reference 1, p. 840. This change of definition is required in order to make the Q;"conform to irreducible tensorial notation. As discussed in reference 1, the coefficients V,, represent the instantaneous interaction of the various electrostatic multipoles of atoms a and 6 : V , is the chargesharge interaction, V2 the charge-dipole interaction, V3 the sum of the dipoledipole and charge-quadrupole interactions, etc.
The zeroth-order energy is e0 = E,,, = a4 + b,. (52) corresponding to the energy of the isolated atoms a and b, while the interaction energy is given by Eab = EO - &O + EL2’ + EL3’ + = EL1) ”’ (53) with V = Ve in Eqs. (40)-(45). There are three types of interactions : nonresonant, resonant, and almost degenerate which are considered in subsections 3, 4, and 5, respectively. The special feature of resonance interactions is that the initial state qq’ is degenerate and at least part of the degeneracy is broken up in the first order of perturbation.
J,,J,) Coupling. For values of R for which the electrostatic interaction energy is less than the atomic fine structure splitting the (S,,L,,J,, MJa)coupling scheme" is most suitable for the atomic states and the zeroth-order Hamiltonian is taken to be HA = H o + H,,(a) + H,,(b). The molecular states are now characterized by the quantum number R for the absolute value of the total angular momentum along R. This coupling scheme is often referred to as Hund's case c c o ~ p l i n g . ~ ~ * ~ ~ c.