London Dispersion Interaction

[Sheik Sahadat]

Hello,
Can someone please explain what E is proportional to (a1)(a2)/r^6 means? I think that E is the LDF interaction, showing that it's proportional to something. But I'm not too sure what all of the elements are representing or even what this means. I just remember it showing up on the midterm.
Thank you

[Joseph Dekel 1F]

The formula E∝(a1∗a2)/r6 describes the London Dispersion Forces (LDF), a type of intermolecular force. Here, E is the energy of the LDF interaction, a1 and a2 represent the polarizabilities of two interacting particles (which measure how easily their electron clouds are distorted), and r is the distance between the particles. The equation shows that LDF energy is directly proportional to the product of the polarizabilities of the particles and inversely proportional to the sixth power of their separation distance.

Essentially what this means is that LDF is stronger between more polarizable molecules and decreases rapidly with increasing distance.

Hope this helps!