AMBER Archive (2006)

Subject: Re: AMBER: switching function for electrostatic interactions

From: Thomas Cheatham (
Date: Mon Jun 12 2006 - 11:12:28 CDT

> I am a little confused about which type of cut-off is used by sander or pmemd
> when computing electrostatic interactions with PME.
> I first thought that it was a sharp cut-off as is the case for van der Waals
> interactions, but in the manual, I read that a cubic spline switching
> function is used. I have tried to find an answer in the mailing list and in
> the FAQ but did not find it (or did not understand), so I apologize if this
> question has already been answered some time ago.

...further clarification to what Ross Walker just sent to the list...

With PME (or Ewald in general), the direct space (or standard Coulombic
interactions within the cutoff sphere) interactions are tempered or
smoothed to a small value by multiplication with the complementary error
function (erfc()). Effectively, at the cutoff, the value of any direct
space electrostatic interaction should be small (or less than DSUM_TOL).
In some sense, this is a cutoff of the direct space interactions or
better, a screening of the electrostatic interactions within the cutoff
sphere such that they go to zero outside the sphere; however, effectively
there is no cutoff to the electrostatics since what is missing in the
direct space is calculated in the reciprocal space. [Note that it is
incorrect to think of the direct as short range and the reciprocal as long
range since the direct space interactions are effectively screened by the
erfc() and corrected for in the reciprocal space, i.e. the reciprocal
space includes long-range and some short range electrostatic

The spline you are referring to is not related to the cutoff, but the
order of the fitting function for adapting the point charges on to a grid.
By interpolating the charges to a grid, the reciprocal space can be
calculated using a fast Fourier transform. Generally, to get accuracy in
the ~10**-6 range, an ~1 angstrom grid spacing and a cubic spline
interpolation with a cutoff in the 8 angstrom range are applied. See that
PME paper referenced by Ross Walker and also the Essman et al. JCP
103, 8577-8693 (1995) "A smooth particle mesh Ewald method".

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