# How to calculate dihedral (not torsion) angles?

Antonio osrisfol at ssmain.uniss.it
Fri Mar 19 06:18:22 EST 1999

```Andrew Martin wrote:
>Suhail Islam (islam at icrf.icnet.uk) wrote:
>: I hope I am not getting too confused here (!), but why
>: can you not simply use the torsion angle calculation.
>: Bonding does not matter, only the order of the 4 points
>: which you consider. This will give you a correct sign.
>: The sign is the sign of the volume formed by the
>: 4 points. Angle between planes do not have a sign (handedness),
>: becuse there are an infinite number of ways to order 4 points
>: on the 2 planes.
>
>I also do not understand the problem here :-)
>
>you only need to look at any piece of code like Gromos Charmm/Xplor
>to see calculation of improper dihedrals (which is what is being
>asked for) is done by exactly the same piece of code as the proper
>dihedral calculation (i.e. where the middle 2 atoms are bonded).
>

I agree with you that calculations of improper dihedrals  is made in the
same way as the proper ones. My problem is *the sequence* of the 4 atoms
involved in the improper dihedral. After you find
the correct sequence, you can directly apply any code for the
dihedral angle calculation. Finding this sequence is not a trivial problem,
in particular when you have to calculate a complicated function of
several improper dihedral angles, so that they should be *all*
treated in the same way. For example, in a six-ring, the angle
between 135 and 561 planes can be obtained as the 3-5-1-6
dihedral, and/or as the 3-1-5-6 one (the 1356 is obviously wrong,
as it would give the angle between 135 and 356 planes).
These two possible choices give opposite dihedral angles, which
may not be important for general considerations, but it's very
important when you have to sum/multiply such angles.

Antonio

osrisfol at ssmain.uniss.it

```