## Expression for potential terms There are multiple models to characterize the potential, like - hard sphere (only collision), $ \begin{equation} V=\begin{cases} \infty, & r\leq \sigma\\ 0, & r>\sigma \end{cases} \end{equation}$ ^8a6900 - soft sphere, $V=\epsilon \left( \frac{\sigma}{r} \right)^\nu$ ![[Drawing 2023-09-24 18.53.34.excalidraw.svg]] >[!Note] >Here $\sigma$ can be considered as the sphere radius. - Harmonic, $V = a_0 + \frac{1}{2} k (r_i-r_0)^2$ - [[Details on LJ|Lennard-Jones potential, LJ]], $V = 4\epsilon \left[ \left( \frac{\sigma}{r_{ij}} \right)^{12}-\left( \frac{\sigma}{r_{ij}} \right)^6 \right]$, which we'll discuss later. >[!Note] >In LJ, $\epsilon$ is called dispersion energy. People use different models for different bonds/interactions.