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

From: Ilyas Yildirim <iy222.cam.ac.uk>
Date: Tue, 20 Oct 2015 07:01:39 +0100 (BST)

Hi Ross,

> 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?

In Amber 7 Appendix, the fitting of the torsions are described, and you
are correct will all the descriptions. The dihedral energies are made sure
to oscillate between 0 and 2 with the (1+cos) term, and the Vn/2 is there
to describe the energy barrier in the landscape.

> 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?
>
> 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.

If you do fitting for the two cases i) on the the original
dihedral description (1+cos), and ii) only cos, the Vn coefficients you
calculate should be almost the same. I say almost because I have seen
differences starting at the third and fourth digits when comparing the
results of the two methods. This difference should not affect the results
at all as both sets should represent the energy landscape reasonably.

You seem to be worried about the drift in the mean, why? The final results
of the fitting procedure does not use that data. In the fitting procedure,
I believe you have a constant term (which I think is the 'mean' according
to your description) in the fitting, too, am I correct?

My question would be the following though: What will be the effect of
changing (1+cos) to just cos on the system in the MD? Normally this should
not effect the MD results as I always see the torsional terms as
corrections to create energy landscapes to include QM results. Making a
change from (1+cos) to cos will change the potential energy by a
constant number, and will this somehow affect the MD forces? Technically
this should not.

Cheers,

Ilyas Yildirim, Ph.D.
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