Computes forces for the 12-6 Lennard Jones (LJ) potential. More...

#include "ljForce.h"
#include <stdlib.h>
#include <assert.h>
#include <string.h>
#include "constants.h"
#include "mytype.h"
#include "parallel.h"
#include "linkCells.h"
#include "memUtils.h"
#include "CoMDTypes.h"

Include dependency graph for ljForce.c:

Go to the source code of this file.

Data Structures
struct	LjPotentialSt
	Derived struct for a Lennard Jones potential. More...

Macros
#define	POT_SHIFT 1.0

Typedefs
typedef struct LjPotentialSt	LjPotential
	Derived struct for a Lennard Jones potential. More...

Functions
static int	ljForce (SimFlat *s)

static void	ljPrint (FILE file, BasePotential pot)

void	ljDestroy (BasePotential **inppot)

BasePotential *	initLjPot (void)
	Initialize an Lennard Jones potential for Copper. More...

Detailed Description

Computes forces for the 12-6 Lennard Jones (LJ) potential.

The Lennard-Jones model is not a good representation for the bonding in copper, its use has been limited to constant volume simulations where the embedding energy contribution to the cohesive energy is not included in the two-body potential

The parameters here are taken from Wolf and Phillpot and fit to the room temperature lattice constant and the bulk melt temperature Ref: D. Wolf and S.Yip eds. Materials Interfaces (Chapman & Hall 1992) Page 230.

Notes on LJ:

http://en.wikipedia.org/wiki/Lennard_Jones_potential

The total inter-atomic potential energy in the LJ model is:

$E_{tot} = \sum_{ij} U_{LJ}(r_{ij})$

$U_{LJ}(r_{ij}) = 4 \epsilon \left\{ \left(\frac{\sigma}{r_{ij}}\right)^{12} - \left(\frac{\sigma}{r_{ij}}\right)^6 \right\}$

where $\epsilon$ and $\sigma$ are the material parameters in the potential.

$\epsilon$ = well depth
$\sigma$ = hard sphere diameter

To limit the interation range, the LJ potential is typically truncated to zero at some cutoff distance. A common choice for the cutoff distance is 2.5 * $\sigma$ . This implementation can optionally shift the potential slightly upward so the value of the potential is zero at the cuotff distance. This shift has no effect on the particle dynamics.

The force on atom i is given by

$F_i = -\nabla_i \sum_{jk} U_{LJ}(r_{jk})$

where the subsrcipt i on the gradient operator indicates that the derivatives are taken with respect to the coordinates of atom i. Liberal use of the chain rule leads to the expression

$\begin{eqnarray*} F_i &=& - \sum_j U'_{LJ}(r_{ij})\hat{r}_{ij}\\ &=& \sum_j 24 \frac{\epsilon}{r_{ij}} \left\{ 2 \left(\frac{\sigma}{r_{ij}}\right)^{12} - \left(\frac{\sigma}{r_{ij}}\right)^6 \right\} \hat{r}_{ij} \end{eqnarray*}$