LJPotential2D

2D Lennard-Jones Potential

Syntax

constraint LJPotential2D (1) [2] [3]
# (1) int, unique constraint tag
# [2] double, spacing, default: 1.0
# [3] double, alpha, default: 1.0

Theory

This constraint implements the Lennard-Jones potential for 2D systems, viz.,

$$V_{LJ}=4\alpha ({\left({\displaystyle \frac{\sigma }{r}}\right)}^{12}-{\left({\displaystyle \frac{\sigma }{r}}\right)}^6),$$

where $r$ is the distance between two particles, $\sigma$ is the size of particle, which is taken as one tenth of spacing [2].

The force is computed as

$$F_{LJ}=-{\displaystyle \frac{\partial V_{LJ}}{\partial r}}={\displaystyle \frac{24\alpha }{r}}({\left({\displaystyle \frac{\sigma }{r}}\right)}^6-2{\left({\displaystyle \frac{\sigma }{r}}\right)}^{12}).$$