Dispersion energy in the multipole representation

After inserting V in the multipole representation (p. 701) into the expression for the dispersion energy we obtain 

The square in the formula pertains to all terms. The other terms, not shown in the formula, have the powers of higher than R.  

if we squared the total expression, the most important term would be the dipole-dipole contribution with the asymptotic R distance dependence. 

As we can see from formula (13.12), its calculation requires double electronic excitations (one on the first, the other one on the second interacting molecules), and these already belong to the correlation effect (cf. Chapter 10, p. 558). 

The dispersion uiieiaetioii is a pure euirelatiuii effeei and therefore the methods used in a supermolecular approach, that do not take into account the electronic correlation (as for example the Hartree-Fock method) are unable to produce any non-zero dispersion contribution. 

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Electrostatic Energy in the Multipole Representation Plus the Pmetiation Enagy Induction Energy in the Multipole Representation Dispersion Energy in the Multipole Representation Dispersion Energy Model-Calculation on Fingers... 

Dispersion energy in the multipole representation Symmetry-Adapted Perturbation Theories (SAPT) ( U )... 

The macroscopic approach to the dispersion energy is based on the interactit n of the multipoles of particles 1 and 2, i.e., we have to find exact representations of these multipoles. This is possible in the case of planar, cylindrical, and spherical symmetry. Let us now consider the attraction between two cylinders 1 and 2. 

If the charge distribution is described by a set of distributed multipoles, as described in Section 4.2.3, the coulombic contributions to the intermolecular potential energy are calculated as multipole-multipole terms. The main disadvantage of even a rigorous distributed multipole model is that such a representation is still very localized, so that coulombic energies miss a large part of the penetration contribution. For use in a complete representation of intermolecular interactions, the dispersion, polarization, and repulsion terms must be evaluated separately by some semi-empirical or fiilly empirical method, for example the approximate atom-atom formulations of equations 4.38. 39. This approach has been extensively exploited by S. L. Price and coworkers over the years, in applications to molecular crystals [48]. 

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