[gmx-users] PME accuracy

Berk Hess gmx3 at hotmail.com
Fri May 9 10:20:01 CEST 2003

>Bert de Groot wrote:
> >Somewhat worried by this statement (and the rest of the email), I 
>performed >two reruns (with pme_order 4 and 6) to calculate the 
>electrostatic part
> >of the force on an ion in 200 MD snapshots (system: protein/lipids/water, 
> >approximately cubic box with ~80.000 particles). The differences for each 
>component >(and hence the sum) were very small: maximally 2 kJ/mol.nm 
>(whereas the forces >themselves have typical values of +/- 1000 kJ/mol.nm. 
> >
> >So I don't know if the problems described by Vincent are particular to
> >his system (unshielded charges as far as I could see), but at least I was 
> >not able to reproduce the problem for a typical simulation system. >(at 
>least not to the extent described). >
>The inaccuracy in the forces appear mainly at large distances, where the 
>forces are small (less than 70 kJ/mol.nm). I think that to see the problem 
>in your system, you would need to calculate the rms error in the 
>electrostatic forces specifically for the particles that are, say, more 
>than 1.4nm apart.

But if the relative totat error in the force in Bert's case is 0.2%, this is 
completely acceptable.
The error in the potential will probably be much smaller.
The 2 kJ/mol nm Bert gets are exactly on the same order of the error in the 
two ion system.
It is important to know if the errors for a many charge system cancel out 
and as Bert has
shown they seem to do.
For a system with only two ions, you would like a higher accuracy, but for 
such small systems
you can use Ewald sums.

We should however still check if the cosine like error with constant 
amplitude is what you
would expect in PME. What puzzles me especially is that the amplitude of the 
error is
not proportional to the force.


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