Subject: md, equilibriation times and vibrations

From: <[email-masked]>
Date: Thu, 22 Sep 94 09:10:31 EDT

I've encountered a problem with MD that experienced modellers may be able to 
put my mind to rest about.  Taking an isolated molecule (a mere 28 atoms) 
which had been loosely geometry optimized, I turned it loose in a molecular 
dynamics simulation using PM3 and monitored a few bond torsions and the 
potential energy. (1 fs time step and .1ps bath relaxation).  The potential 
energy slowly drifted downward and after 20ps seemed to be assymptotically 
approaching a binding energy of -2542 kcal/mole.  During this time the 
torsions which I was observing noticeably damped down substantially. 
 Afterwards I optimized the molecule, getting an energy of about -2546 
kcal/mole and started a new md run with the new structure with a heating 
period of 1 ps to 300C.  The potential energy leaped up about 25 kcal/mole 
which seems about right (28 * 3/2 *(RT=.6kcal/mole)).  The potential energy 
is slowly settling back down and presumably will approach -2542 kcal/mole 
again.  Observing the damping out of the torsions and the small change in the 
mean potential energy (4kcal/mole) between the minimized structure and the 
equilibrium one, has lead to worry about where are the zero point vibrations. 
 When the simulations are started the atoms are given randomn directions 
which basically excites all sorts of modes.  As the molecule deexcites and 
the bath carts off the excess energy all the bond vibrations (bends, 
stretches and torsions) seem to be disappearing so that one is left with a 
molecule travelling through space and spinning but that's all.  I dusted off 
my trusty old QM textbook and looked up 1-d harmonic oscillators.  It pointed 
out that zero point energy (that 1/2h(nu)) is a quantum mechanical effect 
arising from the non-commutation of the positon and momentum operators (i.e. 
the Heisenberg uncertainty principle raises its ugly head).  Now in a 
computer simulation of a molecule there is no such problem about commutation. 
 I can know both the position and momentum of the nuclei to arbitrary 
accuracy.  Does this mean that if I wait long enough the vibrations will all 
freeze out completely and I'll be left with a spinning molecule careening 
through space.  One might also point out that it will be spinning and 
careening far too fast since the bath will make sure the overall kinetic 
energy, alot of which should be tied up in vibrations, is correct.  Obviously 
in a liquid, inter-molecular interactions will cause randomization of some 
sort and pump energy back into vibrational modes.  However, the whole thing 
leaves me a little concerned about these kind of calculations.  Can someone 
out there reassure me?

Ross Underhill
[email-masked]