## Details on LJ $V = 4\epsilon \left[ \left( \frac{\sigma}{r_{ij}} \right)^{12}-\left( \frac{\sigma}{r_{ij}} \right)^6 \right]$ ![[Drawing 2023-09-24 19.33.43.excalidraw.svg]] ^3e2485 Van der Waals interaction is from induced dipole-dipole interaction, This also known as “dispersive interaction”. The origin is thought to be from instantaneous position of electrons, which created the finite dipole moment and generate electric fields. Such dipole moment gets $\sim \frac{1}{r^3}$, so the overall attraction for a pair is $\sim \frac{1}{r^6}$. - This dispersive interaction is long range, compare with $\frac{1}{r^{12}}$, may be effective from 10 to 0.2 nm. - The interaction may be repulsive or attractive, and in general do not follow simple power law. - Such interaction not only bring molecules together, but also tend to align/orient them, though this effect is weak. >[!Note] >Align/orient since it's a dipole. - Such interaction is *non-additive*. i.e., The dispersive force between two particles are affected by other particle nearby. This means the non-additive of an interaction. The original repulsive part is Pauli principle (i.e., Pauli repulsion), which is quantum explained. This can be understood as the overlap of orbital at a short distance. >[!Note] > Pauli principle: No two electrons with the same quantum number can exist in the same orbital or quantum state. >[!Info] >See more on LJ: https://en.wikipedia.org/wiki/Lennard-Jones_potential