# Re: [AMBER] Energy shifted energy term

From: Jason Swails <jason.swails.gmail.com>
Date: Fri, 10 May 2019 15:04:04 -0400

On Thu, May 9, 2019 at 4:49 PM Debarati DasGupta <
debarati_dasgupta.hotmail.com> wrote:

>
> Hi Daniel,
>
> There is a energy shifted term in "SPAM" on page 690 of Amber18 manual--->
> "Perform profiling of bound water molecules via SPAM analysis[615].
> Briefly, this method identifies and estimates the free energy profiles of
> bound waters via calculation of the distribution of interaction energies
> between the water and itâ€™s environment from explicit solvent MD
> trajectories. The interaction energies are calculated using a force and
> energy-shifted electrostatic term with a hard cutoff"
>
> I would be happy to know what is this force and energy shifted
> electrostatic term?
> I would love to get an idea or at least a reference from where this
> shifted energy term comes from? The SPAM paper says nothing at all!
> Also, in LIE page 666 there is a line "The electrostatic interactions are
> calculated according to a simple shifting function shown below...." Where
> does that equation come from?
> Any reference on that would definitely help.
>

Here is a Wiki page that describes various cutoff methods, including
switching, energy shifting, and force shifting:
https://www.charmmtutorial.org/index.php/The_Energy_Function#Calculation_of_non-bonded_energies:_cut-offs.2C_shifting.2C_switching_etc.

Here are simple descriptions:

Hard cutoff:

The nonbonded potential energy term is non-zero, and unchanged, when the
distance is less than the cutoff, but 0 after the cutoff. The potential
energy function and forces are both discontinuous at the cutoff boundary.
This is really a special case of a switching function where the switching
distance is equal to the cutoff and the switching function is a
discontinuous step function. Can be OK for Lennard-Jones, but this is
horrible for any application of electrostatic interactions.

Switching methods:

A "switching" function is added to a nonbonded term that is subject to a
cut-off so that the net contribution to the potential energy term is 0 at
the cutoff and moves smoothly from the "unadjusted" value to 0 between a
"switching" distance and the cutoff. At the switching distance, the
potential energy functional form changes from the unadjusted form to the
switching function, with the parameters of the switching function set so
that both the energy function and its gradient (the negative of the force)
are continuous everywhere. This introduces a little bit of an impulse at
the point where the switching function takes effect which could give rise
to artifacts if the switching distance is too low.

Energy shift:

The potential energy function is translated down so that the value of the
potential energy function is exactly 0 at the cutoff, but the magnitude of
the force is unchanged. The potential energy function is continuous
everywhere, but the forces are discontinuous at the cutoff.

Force shift:

The potential energy function is adjusted to decay such that both the
forces and the potential energy function is continuous everywhere and both
decay to exactly 0 at the cutoff. There is no impulse like there is with a
switching function, but the shape of the function (and therefore the
magnitudes of the forces) change everywhere, even at short distances (all
other methods keep the same forces at close distances, so this method
changes the force field more than the others, arguably).

-----------

Each of these methods have different trade-offs. The best approach is to
use a method that doesn't have a meaningful cutoff, like Ewald or PME. But
those are not pairwise decomposable like the methods described above are.

The reason that LIE and SPAM use shifting methods is because they don't
rely on forces (so discontinuities in the force are not a big deal), and
they rely on energy differences, which are far less sensitive to the
effects of the shifting function than single-point energies. The reason
those methods don't use PME is because PME wasn't available in cpptraj when
I wrote them :).

HTH,
Jason

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Received on Fri May 10 2019 - 12:30:03 PDT
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