Time step in MD

[jkl #*at*# ccl.net]

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 #*at*# ccl.net