# [gmx-users] Conceptual question about the representation of dihedral angles in Gromacs

Arman Mahboubi Soufiani armansoufiani at gmail.com
Sat Oct 27 16:05:36 CEST 2012

```Dear Andrew,

I am a beginner! However, I would like to record my interpretation of the
concept you're confused about and evaluate it by what experts will comment
later.
I am pretty sure your first calculation of 2,7 kcal/mol is correct,
however, since ethane is symmetrical molecule you don't need to perform the
second calculation so as to take into account all the dihedral
interactions. I am not sure how far are you familiar with quantum mechanics
and the orbital theory of two and above electron atoms! Actually, as you
cannot distinguish between electrons there, in the case of ethane you
cannot distinguish between the hydrogen atoms and thus, every time, any Hx
meets any of Hy s makes no difference in calculation of your barrier height
and are all the same.

I hope I could transfer my knowledge to you.
Lets see what others will come up with.

Cheers

On Sat, Oct 27, 2012 at 4:32 AM, Andrew DeYoung <adeyoung at andrew.cmu.edu>wrote:

> Hi,
>
> If you have time, may I ask a conceptual question about how dihedral angles
> are specified in force fields?
>
> Consider ethane, a two-carbon hydrocarbon (H_3C-CH_3).  It has two carbon
> atoms and six hydrogen atoms.  Call the carbons C1 and C2.  Hydrogens H1,
> H2, and H3 are bonded to C1.  Hydrogens H4, H5, and H6 are bonded to C2.  I
> would like to account for all possible H*-C1-C2-H* dihedral angles.
>
> >From organic chemistry, I know that the rotational barrier of ethane is
> approximately 2.9 or 3 kcal/mol (see, for example,
> http://research.cm.utexas.edu/nbauld/teach/ethane.html).
>
> In the OPLS-AA force field, I have found parameters for the dihedral
> HC-CT-CT-HC:
>
>   HC     CT     CT     HC      3      0.62760   1.88280   0.00000  -2.51040
> 0.00000   0.00000 ; hydrocarbon *new* 11/99
>
> If I plot the potential energy V for these RB parameters on a plotter, it
> appears that the barrier height is about 0.9 kcal/mol (I converted from
> kJ/mol by dividing by 4.184).
>
> My question is, do the above parameters correspond to only a _single_
> H-C-C-H dihedral (for example, H1-C1-C2-H4)?
>
> If so, then I will need to specify H1-C1-C2-H5 and H1-C1-C2-H6 in addition
> to H1-C1-C2-H4, I think.  By doing so, I will be essentially adding 3
> different plots: one for H1-C1-C2-H4, one for H1-C1-C2-H5 (phase-shifted by
> 120 degrees relative to H1-C1-C2-H4), and one for H1-C1-C2-H6
> (phase-shifted
> by 240 degrees relative to H1-C1-C2-H4).  In this way, the total barrier
> height will be 0.9 + 0.9 + 0.9 = 2.7 kcal/mol, approximately consistent
> with
> "common knowledge" from organic chemistry.  Is this correct?  In other
> words, the dihedral parameters represent a _single_ dihedral (for example,
> H1-C1-C2-H4), and _NOT_ a group of dihedrals (for example, H1-C1-C2-Hx
> where
> x = 4, 5, 6).  Only by considering all possible dihedrals do we get the
> correct potential overall energy landscape.
>
> One conceptual problem I have with this, though, is that I get the 2.7
> kcal/mol barrier height only by considering H1-C1-C2-Hx, where x = 4, 5,
> and
> 6.  But I also will include H2-C1-C2-Hx and H3-C1-C2-Hx in my topology
> (where x = 4, 5, and 6 in each case).  Does this mean that when I consider
> all possible dihedrals Hy-C1-C2-Hx (x = 4, 5, 6; y = 1, 2, 3), the overall
> barrier height will be 3 * 2.7 = 8.1 kcal/mol instead of 2.7 kcal/mol?
>
> Thank you!
>
> Andrew
>
> --
> gmx-users mailing list    gmx-users at gromacs.org
> http://lists.gromacs.org/mailman/listinfo/gmx-users
> * Please search the archive at
> http://www.gromacs.org/Support/Mailing_Lists/Search before posting!
> * Please don't post (un)subscribe requests to the list. Use the
> www interface or send it to gmx-users-request at gromacs.org.
> * Can't post? Read http://www.gromacs.org/Support/Mailing_Lists
>

```