SciCode / 51.1 / Based on lennard jones potential with potential well depth epislon that reaches…

Background
The Lennard-Jones potential models soft repulsive and attractive (van der Waals) interactions. Hence, the Lennard-Jones potential describes electronically neutral atoms or molecules. The commonly used expression for the Lennard-Jones potential is:

V_(LJ)(r)=4ε[((σ)/(r))¹²−((σ)/(r))⁶]

where r is the distance between two interacting particles, epsilon is the depth of the potential well (usually referred to as 'dispersion energy'), and sigma is the distance at which the particle-particle potential energy V is zero (often referred to as 'size of the particle').

To get force, we just use the negative gradiant of Lennard-Jones potential (by definition):

(F)→=−(∂U)/(∂(r)→)=−((∂U)/(∂x);(∂U)/(∂y);(∂U)/(∂z))

Background
The Lennard-Jones potential models soft repulsive and attractive (van der Waals) interactions. Hence, the Lennard-Jones potential describes electronically neutral atoms or molecules. The commonly used expression for the Lennard-Jones potential is:

$V_{\mathrm{LJ}}(r)=4 \varepsilon\left[\left(\frac{\sigma}{r}\right)^{12}-\left(\frac{\sigma}{r}\right)^6\right]$

where r is the distance between two interacting particles, epsilon is the depth of the potential well (usually referred to as 'dispersion energy'), and sigma is the distance at which the particle-particle potential energy V is zero (often referred to as 'size of the particle').

To get force, we just use the negative gradiant of Lennard-Jones potential (by definition):

$\vec{F}=-\frac{\partial U}{\partial \vec{r}}=-\left(\frac{\partial U}{\partial x} ; \frac{\partial U}{\partial y} ; \frac{\partial U}{\partial z}\right)$