Physical origins of van der Waals interactions

A polar molecule such as HC1 possesses a permanent dipole moment // by virtue of the non-uniform electric charge distribution within the neutral molecule. The electrostatic energy between two interacting dipoles //1 and 112 is strongly dependent on their relative orientation. If all relative orientations are equally probable and each orientation carries the Boltzmann weighting factor e-cW r, the following expression is obtained  

This expression shows that the attractive electrostatic interaction, commonly known as the Keesom energy, is inversely proportional to the sixth power 

Some non-polar molecules such as CO2 possess an electric quadrupole moment Q which can contribute to the electrostatic energy in a similar manner. The results for dipole-quadrupole and quadrupole-quadrupole interactions are 

When a polar molecule and a non-polar molecule approach each other, the electric field of the polar molecule distorts the electron charge distribution of the non-polar molecule and produces an induced dipole moment within it. The interaction of the permanent and induced dipoles then results in an attractive force. This induction contribution to the electrostatic energy is always present when two polar molecules interact with each other. 

The average induction energy (called Debye energy) between a polar molecule with dipole moment // and a non-polar molecule with polarizability a is 

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