AMBER Archive (2005)

Subject: Re: AMBER: Non-Bonded Cutoff vs PME

From: Thomas E. Cheatham, III (cheatham_at_chpc.utah.edu)
Date: Tue Apr 19 2005 - 18:47:10 CDT

> > Can anyone please comment on the following statement (which i rewrite from
> > SPASMS manual page xxxiii), and also which is a generally accepted truth (i
> > hope)-
> >
> > "the non-bonded cutoff needs to be chosen carefully when employing PBCs. It
> > is essential that the cutoff be small enough that a given particle can not
> > interact with its another particle and second particle's virtual image
> > simultaneously...."
>
> Most people would consider this comment to be outdated now--it was written a
> long time ago, before PME and similar options were widely used. Even at the
> time it was written, the phrase "it is _essential_ that..." was most likely
> based on intuition, and not on any concrete evidence.

I would add to this that likely this comment was taken out of context...

In the context of minimum image boundary conditions (as implemented in
SPASMS) and specific implementations of cutoffs, it *is* essential that
the cutoff be smaller that half the box size since there is/was no code to
handle the interaction of an atom and its image. In AMBER, for example,
you cannot have a "cutoff" (or direct space interaction) that is larger
than 1/2 the box size when in PBC since we have no support for handing the
direct interaction with images outside a periodic box centered on that
given atom.

In CHARMM, however, (and likely other crystal codes) you can run a cutoff
over multiple box images (within the IMAGE facility) as this is supported
by making virtual copies of the unit cell such that you have all the atoms
within a cutoff.

So, is it truth? Within minimum boundary conditions and direct space
interactions it is... The issue you are getting at is how does Ewald/vdw
relate in the context of cutoff and interaction with images. The cutoff
is applied for both the vdw and electrostatics and represents all of the
direct space interactions (those within the cutoff directly interacting
with the specific atom). In SPASMS, no interactions outside the cutoff
were considered and various means could be applied to smooth or shift the
energy (or in the case of CHARMM the force) at the cutoff to minimize the
abrupt truncation. To get longer range interactions, you can use a larger
cutoff, however in AMBER/SPASMS you are limited to minimum image.

Ewald calculations are a means to get the full periodic interaction (for
more detail, see Allen & Tildesley or Leach or google "ewald
electrostatics"). This method implicitly include the image interactions,
however this is done in reciprocal space (and is not subject to the
concept of minimum image) and its accuracy relates to the sum over
k-vectors (or in SPME, the grid, interpolation order, ...). In principle,
you can do SPME over the vdw as well ! to also include (all) the image
interactions as at one point was implemented in AMBER. Ewald works
basically by screening the short-range (direct) interactions and then
correcting for what is absent in reciprocal space. The magnitude of the
screening is controlled by the kappa or beta constant. In AMBER, we
choose the Ewald coefficient (beta) such that the error in the
electrostatics at the cutoff is less than DSUM_TOL.

Is this the right way to do things? I believe so, however others have
proposed in the past that we can get away with atom-based force-shifted
cutoffs in the 12A range, simpler cutoffs [see for example the recent
debatable Biochemistry article by Beck and co-workers 44, 609 (2005)],
reaction fields, isotropic periodic boundary conditions, twin-range
cutoffs, ... and the list goes on. A consequence of applying Ewald (or
PME) or even large cutoffs that include image interactions is that you
directly are including the interaction of yourself with all of (or some
of) your periodic images. This could lead to artifacts. For nice
discussion of potential periodicity artifacts, see the various papers by
Hunenberger. For discussion of cutoffs, see Steinbach & Brooks (~1995 and
earlier). For discussion of cutoff artifacts, see Smith & Pettitt 1991,
Bader & Chandler 1992, Feller et al 1996, Schreiber & Steinhauser 1992,
Cheatham et al 1995.

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