# [gmx-users] Accuracy of force calculation and doubts on PME parameter choice

Nickle Fan nicklefan at gmail.com
Tue Jul 8 05:25:37 CEST 2008

```Dear all:

In most studies, we focus on the accuracy of potential energy. How about the
force? Consider two systems:

1. Two LJ particles (sigma=0.33nm, epsilon=0.625kJ/mol): If the force is
cutoff at 2.5*sigma, so the maximum error in force is at the cutoff length
and equal to ~0.08 kJ/mol nm.

2. Two point charges in a 3*3*3.3nm box (charge separation: 0.5 nm, q1=e,
q2=-e): I tried the following calculations:
a. Ewald summation, rcutoff=1.0nm, ewald_tol=1e-5, FFT_spacing=0.1nm: This
produces: f1=-f2=542.2 kJ/mol nm;
b. PME, rcutoff=1.0 nm, ewald_tol=1e-5; 4th order, FFT_spacing=0.1nm, this
produces: f1=-f2=543.9 kJ/mol nm;
c. PME, rcutoff=1.0 nm, ewald_tol=1e-5; 4th order, FFT_spacing=0.11nm, this
produces: f1=543.97 kJ/mol nm, f2=-544.96 kJ/mol nm;
d. PME, rcutoff=1.0 nm, ewald_tol=1e-5; 4th order, FFT_spacing=0.12nm, this
produces: f1=543.43 kJ/mol nm, f2=-545.49 kJ/mol nm;

Clearly, for LJ particles, the maximum accuracy is ~0.08kJ/mol nm - which
sounds small. But for electrostatics, the error is quite large: if we take
the Ewald results to be the exact solution, then for choice d (which seems
to be a popular choice among gmx-users), the error amounts to be ~ 2.0
kJ/mol nm. Is this error acceptable?

Thanks for your time.

Nick
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