Subject: SUMMARY:predictor-corrector/quaternion for SPC

From: "Tahmid I. Mizan" <[email-masked]>
Date: Tue, 23 Aug 1994 11:39:46 -0400

Thanks to everybody who responded to my question regarding the predictor- 
corrector/quaternion method as appled to SPC water. The quaternion method, 
of course, unlike SHAKE, solves the rigid body equations of motion for the 
molecule as a whole. Analytic stability analysis of MD equations is not
possible. Some sort of approximate analysis may be possible by linearizing
the differential equations or by Lyapunov methods. I did not attempt this, 
but rather took a trial-and-error approach. It turns out that for 2 fs or
larger time step, iterating on the evaluation-correction step solves the 
problem. Of course, this means an extra force evaluation per time-step which
is undesirable. However, for 3 fs timestep a P(EC)**2 (two force evaluations
per time step) appears to be stable so that there is some computational
advantage over a 1 fs time-step ( 0.67 force evaluations per fs as opposed
to 1 force evaluation per fs). The 3 fs runs give the correct values of 
all static properties ( I have not calculated autocorrelation functions).
I should mention that for a 4 fs time step, the situation deteriorates and
a P(EC)**3 is required for stability.

T. I. Mizan
University of Michigan

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ORIGINAL QUESTION

I am using the predictor-corrector/quaternion subroutines from Allen & Tildesley
to simulate SPC water. When I use a 1 femtosecond timestep the program runs    
properly and gives the correct results for energy, pressure g(r) etc. However, 
when I use a 2 fs timestep the program 'blows up'. Apparently the OH bond lengths
become larger and larger and it just blows up. So it appears to be some kind
of numerical instability. 

Has anybody else had a similar experience ? Or is it just some error in my  
implementation.

Is there a fix ?

  -- Tahmid Mizan
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