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

From: Gerald Monard <Gerald.Monard.univ-lorraine.fr>
Date: Tue, 20 Oct 2015 22:10:39 +0200

Hi,

On 10/20/2015 12:25 AM, Ross Walker 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?
>

For me, it comes from the original way that the terms are explained to
students (and colleagues) and how MM handles them.
If one takes a bond: there an equilibrium distance, an harmonic
approximation (first order of the development) and the energy is
described as 1/2 k(r-r0)^2 because that's the standard way of explaining
an harmonic spring in mechanics and of relating k to the frequency of
vibration.
Note here that we usually refer to "energy" when it's not an energy but
a deltaE: the reference is the equilibrium (=minimum) geometry.

For the dihedral, it is the same: the "classical" examples are dihedral
rotations of H in ethane and of CH3 in butane. The origin/minimum is the
lowest/trans conformation. Then you need of periodical function (hence
the cos) and because you refer to deltaE, the zero is the global
minimum, hense the 1+ and the Vn/2. For bonded terms, the energies
reflect deviations from equilibrium geometries (yes, I know that we all
know that).

You can ditch out the 1/2 and the 1+, but that's harder to explain to
the average joe (not impossible though).

> 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?
>

Because the reference energy is not the global minimum anymore.
As far as I know, this was taken at the beginning from "simple" torsion.
We can do/optimize far more complex things now.

> 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.
>

The problem that you face is may be that the dihedral surface is far too
complex to match with a simple cos function, especially if your QM PES
is produced by relaxing all internal coordinates when the dihedral
angles are changed. In the original ethane/butane systems, one makes
only the dihedral change with the rest being fixed (bonds and angles).

Gérald.

> 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.
>
>
> All the best
> Ross
>
> /\
> \/
> |\oss Walker
>
> ---------------------------------------------------------
> | Associate Research Professor |
> | San Diego Supercomputer Center |
> | Adjunct Associate Professor |
> | Dept. of Chemistry and Biochemistry |
> | University of California San Diego |
> | NVIDIA Fellow |
> | http://www.rosswalker.co.uk | http://www.wmd-lab.org |
> | Tel: +1 858 822 0854 | EMail:- ross.rosswalker.co.uk |
> ---------------------------------------------------------
>
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Received on Tue Oct 20 2015 - 13:30:04 PDT
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