LJPotential2D

2D Lennard-Jones Potential

Syntax

Text Only
1 2 3 4	`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.,

\[ V_{LJ}=4\alpha\left(\left(\dfrac{\sigma}{r}\right)^{12}-\left(\dfrac{\sigma}{r}\right)^{6}\right), \]

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

\[ F_{LJ}=-\dfrac{\partial{}V_{LJ}}{\partial{}r} =\dfrac{24\alpha}{r}\left(\left(\dfrac{\sigma}{r}\right)^{6}-2\left(\dfrac{\sigma}{r}\right)^{12}\right). \]