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

[David van der Spoel]

On 2012-10-27 03:02, Andrew DeYoung 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?
>

All dihedrals are included in OPLS/AA, so you get 9 different ones, all 
in phase as well. On top of that is the Coulomb and Van der Waals 
interaction between the H, which will increase the barrier height 
(because the atoms are closest there). In other words the barrier is way 
too high.

> Thank you!
>
> Andrew
>


-- 
David van der Spoel, Ph.D., Professor of Biology
Dept. of Cell & Molec. Biol., Uppsala University.
Box 596, 75124 Uppsala, Sweden. Phone:	+46184714205.
spoel at xray.bmc.uu.se    http://folding.bmc.uu.se