Molecular Dynamics Physics
Dan Schroeder describes the physics of the Lennard-Jones molecular dynamics model as follows:
- The force between the molecules is calculated from the Lennard-Jones formula (truncated at a distance
of 3 molecular diameters). This is a reasonably accurate model of the interactions between noble gas
atoms.
- The model uses a natural system of units, with the molecular diameter, the molecular mass, the
depth of the Lennard-Jones potential, and Boltzmann's constant all set equal to 1. For argon (for
example), the unit of distance is 3.4 angstroms, the unit of mass is 40 atomic mass units, and the unit of
energy is 0.01 electron-volts; the corresponding unit of time is then 2.2 picoseconds, the unit of
velocity is 160 meters per second, and the unit of temperature is 120 kelvin.
- The motion of the molecules is governed by Newton's laws, approximated using the Verlet algorithm with
the indicated time step. For sufficiently small time steps dt, the system's total energy should be
approximately conserved.
- The walls exert a linear (spring) force on the molecules, with a spring constant of 50 in natural
units.
- There's also an optional uniform downward force, controlled by the the gravity parameter. The
magnitude of this force, however, is not meant to be realistic. Earth's gravitational constant is utterly
negligible in the units used here (a little over 10-13 for argon).
- That's all the physics! Everything else you see is a consequence of these basic laws (applied
repeatedly as the molecules move), plus the initial placement of the molecules. The simulation code knows
nothing about phase transformations or crystal structure or irreversibility.
References:
The Molecular Dynamics model is based on a Java applet written by Dan Schroeder, Physics Department, Weber
State University. See: <http://physics.weber.edu/schroeder/software/>