From jkl@ccl.net Thu Mar 12 14:35:07 1992
To: chemistry@ccl.net
Subject: Time step in MD
Date: Thu, 12 Mar 92 14:35:01 EST
From: jkl@ccl.net
Status: R

The discussion on the cutoff distances and time steps is very stimulating.
However, I do not understand something here. 
The time step chosen in Molecular Dynamics is for me a purely mathematical
parameter affecting the precision of integration, but not the physics of the
simulated system. If we had computers with infinite precision and infinite
speed, we should use the small integration step (e.g., 1.0E-20 s). But
our machines have final floating point precision and we cannot go too small
or the truncation errors will add up substantially. Also the machines of
today are slow, and we would not get results in our lifetime.
On the other hand, choosing the integration step too large would result in
errors in integration (like numerically integrating the sin function
with a step of 180 degrees) and would produce wrong trajectories.
For me, time step in MD is mathematics, not physics, like choosing
the grid size in numeric Hartree-Fock atomic calculations:
the smaller the better, and the smaller is much below Heisenberg principle.

However, with Monte Carlo, I do not know how small the amplitude of the
random generator could be in Angstroms before we violate something.
Maybe here the Heisenberg principle is applicable, but I sincerely doubt.
We are also probing the energy surface with a mathematical tool.

Jan Labanowski
Ohio Supercomputer Center
jkl@ccl.net