Range Contributions to the Intermolecular Energy

The electrostatic energy is the first-order term in long-range perturbation theory and is usually the interaction that persists over the longest range. The Coulombic interaction between the undistorted molecular charge distributions 

Second-order perturbation theory provides expressions for the polarization or induction energy. This is the attractive energy term arising from the distortions of the charge density of each molecule due to the field arising from the other (undistorted) molecule  

This term represents the additional energy from the changes in the charge density of A (a molecule whose excited state wavefunctions are of energy E ) 

There are no electrostatic or induction forces between spherical molecules, such as argon, and yet there is clearly a long-range attractive force that causes the liquefaction of argon at low temperatures. This is the dispersion energy, the universal long-range force, which appears at second-order perturbation theory as  

The dispersion forces arise from a purely quantum mechanical effect, and thus are difficult to envisage. The sum over all the excited states of both A and B shows that the dispersion arises from correlated distortions in the two molecular charge densities. Application of the central multipole expansion produces the usual series. 

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