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

Sat Oct 27 03:02:21 CEST 2012

```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

```