Perturbation theory multipole contributions

Equation (1-239) relates the interaction-induced part of the dipole moment of the complex AB to the distortion of the electron density associated with the electrostatic, exchange, induction, and dispersion interactions between the monomers. The polarization contributions to the dipole moment through the second-order of perturbation theory (A/a, A/a, and A/a ) have an appealing, partly classical, partly quantum, physical interpretation. The first-order multipole-expanded polarization contribution (F) is due to the interactions of permanent multipole moments on A with moments induced on B by the external field F, and vice versa. The terms... 

Recent calculations by Bems et al. show that also for the He—H2 system the dispersion contribution is small. At long range it is completely dominated by induction, at short range by overlap effects. The calculations of Bems et al. have been performed by the VB approach mentioned above No perturbation theory or multipole expan-... 

It is possible to apply the multipole expansion and perturbation theory in order to derive long range expressions for T (R), thus relating this quantity to monomer properties. A simple example of such a procedure can be found in the appendix of ref. , where the induction contribution to the dipole moment (J = 1) of an arbitrary Van der Waals dimer has been evaluated. 

The propensity rules for collision-induced transitions between electronic states and among the fine-structure components of non-1E+ states depend on the identity of the leading term in the multipole expansion of the molecule/collision-partner interaction potential. Alexander (1982a) has considered the dipole-dipole term, which included both permanent and transition dipole contributions. In the limit that first-order perturbation theory applies (not the usual circumstance for thermal molecular collisions), the following collisional propensity rules for the permanent dipole term can be enumerated from the selection rules for both perturbations and pure rotational transitions... 

The second-order induction effects pertain to polarization by the charge distributions corresponding to the isolated molecules. However, the induced multipoles introduce a change in the electric field and in this way contribute to further changes in charge distribution. These effects already belong to the third and higher orders of perturbation theory. 

The book contains basic facts about the field of intermolecular interactions given in the language of perturbation theory, as well as the multipole expansion (including a lot of usefiil formulas for the electrostatic, induction, and dispersion contributions). This very well written book presents many important problems in a clear and comprehensive way. 

---