** Next:** 6.3.3 Beyond Basic Molecular
**Up:** 6.3 Molecular Dynamics Simulation
** Previous:** 6.3.1 Hard Spheres /

##

6.3.2 Continuous Potentials

For continously varying pair potentials we have for a particle
at any time

Considering the Lennard-Jones interaction, we find for the pair
force

where
.
The above-mentioned *nearest image convention* (NIC) is used in the
evaluation of the force acting on a particle.

Having determined this total force, the equation of motion
for particle may be numerically integrated.
A widely used technique is Verlet's algorithm

(with
).

__PROJECT MD (LENNARD-JONES):__
Augment the subroutine module ENERGY such that it computes, for each
Lennard-Jones particle in the system, the total force exerted on it
by all other particles :
, with
as given above; remember to apply the
*nearest image convention*.
Write a subroutine MOVE to integrate the equations of motion by a suitable
algorithm such as Verlet's. Having advanced each particle for one
time step, do not forget to apply *periodic boundary conditions*
to retain them all in the simulation box.

Write a main routine that puts the subroutines STARTCONF, ENERGY and
MOVE to work. Test your first MD code by monitoring the mechanically
conserved quantities.

Do a number of MD steps - say, - - and average the
quantity
to estimate the actual temperature.
To adjust the temperature to a desired value, scale all
velocity components of all particles in a suitable way. Repeat
this procedure up to 10 times. After - steps the
fluid will normally be well randomized in space, and the temperature
will be steady - though fluctuating slightly.

** Next:** 6.3.3 Beyond Basic Molecular
**Up:** 6.3 Molecular Dynamics Simulation
** Previous:** 6.3.1 Hard Spheres /
* Franz J. Vesely Oct 2005*

See also: "Computational Physics - An Introduction," Kluwer-Plenum 2001