Dispersion interaction

In chemistry and physics, the gradient of the dispersion interaction is one of the components of the intermolecular force. The dispersion interaction acts  between any two molecules or atoms ("monomers") and is always attractive, that is, the corresponding force pulls the monomers together. The dispersion force is the only attractive force acting between noble gas atoms and is the cause that noble gases can undergo phase transitions, that is, can become stable liquids and crystals. Also for non-polar molecules such as methane, benzene, and other hydrocarbons, the dispersion interaction gives one of the most important attractive forces between the molecules. It explains, for instance, why benzene under normal temperature and pressure is a liquid.

In 1930 R. Eisenschitz and F. London gave the first complete explanation of intermolecular forces, sometimes also referred to as van der Waals forces. They distinguished different effects and among them the effect that is now known as dispersion interaction. The corresponding dispersion force (minus the gradient of the potential, sometimes referred to as London force) falls of as R&minus;7, where R is the distance between the monomers. Eisenschitz and London point out that so-called  "oscillator strengths" f are an important ingredient of their theoretical description. These f-values entered  previously  the classical theory of the dispersion of light formulated by Lorentz and Drude. The same f-values are also needed in  the "old" (Planck-Bohr-Sommerfeld) quantum theory  of  dispersion given by Kramers and Heisenberg

Because of the similarity between the theories, London baptized the molecular attraction, described by the oscillator strengths f, the dispersion effect.

Because the Eisenschitz-London work is very complete and accordingly not easy, London gave in the same year a less mathematical description of the dispersion force in which he modeled each monomer of a dimer as a three-dimensional isotropic harmonic oscillator. The oscillators consist of a particle of mass m and charge e and the two oscillating particles interact through a Coulomb force. By an approximate quantum mechanical treatment London derived the following form of the interaction potential of the oscillators in their ground (lowest energy) state:

E = -\tfrac{3}{4} h\nu_0 \frac{\alpha^2}{R^6}, $$ an expression which is similar (quadratic in &alpha;, depending on R&minus;6) to the dispersion formula he derived together with Eisenschitz. The derivative of &minus;E with respect to R is proportional to &minus;R&minus;7 and is the attractive force associated with this potential. London stresses that his formula is due to the zero point motion of the free oscillators. The zero point motion is a typical quantum mechanical phenomenon related to Heisenberg's uncertainty principle. Without zero point motion, London's model does not give an attraction between ground state oscillators.

In the section London forces of the article intermolecular forces the Eisenschitz-London theory, derived by perturbation theory and based on  oscillator strengths, is discussed. In this article the simple London model of two interacting oscillating dipoles will be worked out in some detail.

(To be continued)