# Re: [AMBER-Developers] Origin of dihedral term

From: Jason Swails <jason.swails.gmail.com>
Date: Mon, 19 Oct 2015 19:30:51 -0400

On Mon, Oct 19, 2015 at 6:25 PM, Ross Walker <rosscwalker.gmail.com> wrote:

> Hi All,
>
> I am wondering if anyone knows the origin or why the dihedral term we use
> in the AMBER force field has the 1+ term in it.
>
> I.e. we have:
>
> ndih n[i]
> sum sum( 1/2 x Vn(1+cos(n.theta - phi)) )
> i=1 j=1
>
> Specifically we have the 1+cos term in there which is I guess to make the
> cos term oscillate between 0 and 2 rather than -1 and +1 and then we have
> the 1/2 in front of the Vn to get rid of the 2 making it between 0 and Vn.
> However, as far as I can tell this is purely cosmetic. Is that correct?
>

​I always thought of it more as making it *look* a little more like the
other bonded terms (which are harmonic, and have the 1/2 term in front of
the force constant, and as a result have a minimum energy at 0). But
obviously the 1+ has no effect on forces, and the 1/2 can be pulled into
the Vn term (which, in Amber, it already is).

As in I could ditch the 1/2, and ditch the 1+ and just have
> V[i,j].cos(n.theta-phi). The question is if that is true why don't we do
> this - does anyone know?
>

​At this stage, it would be historical.​

The issue arrises not in MD but when we try and refit the torsion terms. If
> we try to fit energies against quantum energies we always have an offset in
> the mean due to the origins not matching - that doesn't matter since it
> would be constant during an MD run. However, if we are fitting Vn terms the
> 1+cos term here causes our mean to drift as we adjust Vn. This is a pain in
> the butt when it comes to getting a good fit. Thus I propose to just fit:
> Vn.cos(n.theta-phi) which, I believe would give perfectly transferable
> parameters to the 1+cos equation.
>

​Lachele actually addressed this precise problem in her presentation at the
Amber developer's meeting last year. The solution is simple: fit the
zero-periodicity term. That *gives* you an arbitrary constant to improve
your fit -- it doesn't contribute to an overfitting problem and solves the
issue you're describing. Then you're free to simply throw that term away
when making the frcmod file since it has no effect on forces. It seems to
me you are rediscovering her problems :). I'm sure she'd be happy to share
her slides if she can find them and you wanted them. </throwing Lachele
under the bus>

Am I missing anything here? - Is there any reason why we couldn't go the
> whole step and just ditch the 1/2 and 1+ terms from the entire force field?
> - Seems to me all that would happen is for a given set of parameters (say
> FF14SB) we just shift the energy origin but everything else would still
> work.
>

​A couple things. If you do a QM scan, you're certainly not going to get
an energy of zero at the midpoint -- the zero point energy will be
arbitrary. The easiest thing to do with your QM scan is simply scale the
whole potential by the minimum energy value, which will give you the same
minimum as the 1+cos() series at 0 (maybe that's why it's done?).

Y
​ou can fit however you'd like, but changing how Amber computes this
internally would break from how every other package calculates proper
torsions. It would make cross-program conversion validation much harder
than it currently is. This is a big deal IMO.

All the best,
Jason

```--
Jason M. Swails
BioMaPS,
Rutgers University
Postdoctoral Researcher
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Received on Mon Oct 19 2015 - 17:00:03 PDT
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